TCS PAPER PATTERN
Pattern 1:
Q) (1/2) of a
number is 3 more than the (1/6) of the same number?
a) 6 b)7 c)8 d)9
Sol: Let the
number be x,
((1/2)*x)=3+(1/6)*x,
Then solve x
Q) (1/3) of a
number is 3 more than the (1/6) of the same number?
a) 6 b)16 c)18
d)21
Q) (1/3) of a
number is 6 more than the (1/6) of the same number?
a) 6 b)18 c)36
d)24
Q) (2/3) of a
number is 4 more than the (1/6) of the same number?
a) 6 b)8 c)36
d)24
Q) (1/3) of a
number is 5 more than the (1/6) of the same number?
a) 6 b)36 c)30
d)72
Pattern 2:
Q)There are two
water tanks A and B, A is much smaller than B. While water fills at the rate of
1 liter every hour in A, it gets filled
up like, 10, 20,
40,80, 160…..in tank B. (At the end of first hour, B has 10 liters, second hour
it has 20 liters and so on). If tank B is
1/32 filled of
the 21 hours, what is total duration of hours required to fill it completely?
a) 26 B)25 c)5
d)27
Sol: Given that B
fills up at the rate 10,20,40 etc...
This is a
geometric progression where a = 10 r = 2
so after 21 hrs
lts in B = a*r21
= 10 * 221
This is equal to
1/32 volume of B
SO TOTAL VOLUME
OF B = 32 * 10 * 221
which is =10 *
226
So hrs required
to fill up B is 26
Or
for every hour water in tank in B is doubled,
Let the duration
to fill the tank B is x hours.
x/32 part of
water in tank of B is filled in 21 hours,
Next hour it is
doubled so,
2*(x/32) part i.e
(x/16) part is filled in 22 hours,
Similarly (x/8)th
part in 23 hours,(x/4)th part is filled in 24 hours,
(x/2)th part is
filled in 25 hours, (x)th part is filled in 26 hours
So answer is 26
hours.
Q)There are two
pipes A and B. If A filled 10 liters in an hour, B can fill 20 liters in same
time. Likewise B can fill 10, 20, 40, 80,
160…... If B
filled in 1/16 of a tank in 3 hours, how much time will it take to fill the
tank completely?
a) 9 B)8 c)7 d)6
Q)There are two
water tanks A and B, A is much smaller than B. While water fills at the rate of
1 liter every hour in A, it gets filled
up like, 10, 20,
40,80, 160…..in tank B. 1/8 th of the tank B is filled in 22 hours. What is the
time to fill the tank fully?
a) 26 B)25 c)5
d)27
Q)A tank is
filled with water. In first hour 10 liters, second hours 20 liters, and third
hour 40 liters and so on…If time taken to fill ¼
of the tank if 5
hours. What is the time taken to fill up the tank?
a) 5 B)8 c)7
d)12.5
Q)If a tank A can
be filled within 10 hours and tank B can be filled ¼ in 19 hours then, what is
the time taken to fill up the tank
completely?
a) 21 B)38 c)57
d)76
Pattern 3:
Q)6 persons
standing in queue with different age group, after two years their average age
will be 43 and seventh person joined with
them. Hence the
current average age has become 45. Find the age of seventh person?
a) 43 b)69 c)52
d)31
Sol: a+b+c+d+e+f+
Z = 45*7 =315
a+b+c+d+e+f+ 12 =
43*6 = 258
therefore :
a+b+c+d+e+f = 246
so age of seventh
person "Z" is = 315 - 246 = 69
Q)In a market 4
men are standing. The average age of the four before 4years is 45, after some
days one man is added and his age
is 49. What is
the average age of all?
a) 43 b)45 c)47
d)49
Sol: Avg 4 yrs
ago = 45
so avg now = 49
a person of age
49 is added
so avg remains 49
Q)In a shopping
mall with a staff of 5 members the average age is 45 years. After 5 years a
person joined them and the average
age is again 45
years. What.s the age of 6th person?
a) 25 b)20 c)45
d)30
Sol: After 5
years average age becums 50
Total age = 250
new member joins
suppose age x
so (250 + x) / 6
= 45
x = 20
Q)In a market 4
men are standing .The average age of the four before 2 years is 55, after some
days one man is added and his age
is 45. What is
the average age of all?
a) 55 b)54.5
c)54.6 d)54.7
Sol: After 2
years average age becomes 57
Total age=228
New member joins,
his age is 45
So, (228 + 45)/6
= 54.6 ans
Pattern 4:
Q)In the reading
room of a library, there are 23 reading spots. Each reading spot consists of a
round table with 9 chairs placed
around it. There
are some readers such that in each occupied reading spot there are different
numbers of readers. If in all there are
36 readers, how
many reading spots do not have even a single reader?
a)8 b)none c)16
d)15
Sol: There are
some readers such that in each
occupied reading
spot there are different numbers of
readers.
1+2+3+4+5+6+7+8=
36 readers
so ,8 spots have
different readers.
remainings are 23-8= 15.
15 spots are
empty.
Or
he just said that
in each different spot there are different
number of
readers. So there will be many possibilities...
It is same as
number of ways in which you can make a sum of
9 using only
digits from 1 to 9 each at most once...
Consider
1+2+3+6+7+8+9 =
36
In this case
answer is: 23-7 = 16
but different
answers are possible depending on case u choose
Q)In the reading
room of a library, there are 10 tables, 4 chairs per table. In each table there
are different numbers of people
seated. How many
tables will be left out without at least 1 person?
a) 8 b)6 c)2 d)7
Q)In the reading
room of a library, there are 10 tables, 4 chairs per table. In each table there
are different numbers of people
seated. How many
ways they will sit in the library so that no chair would be blank?
a) 8 b)6 c)2 d)7
Sol: 10 tables,
each with 4 chairs
Each table has a
different number of persons sitting....This is not possible as there are only 4
chairs..
The different
combinations can be 0, 1, 2, 3 and 4...the sixth table would have one of the
above combinations..Thus the rule is
violated..
Plus, if
different numbers of people occupy a table, there would be blank spaces...so
how can we calculate the possibilities of the
library being
fulling occupied..
This is an
ambiguous question!
Pattern 5:
Q)A man jogs at 6
mph over a certain journey and walks over the same route at 4 mph. What is his
average speed for the journey?
a) 2.4 mph b) 4.8
mph c) 4 mph d) 5 mph
Sol: Average
speed=2*x*y/(x+y)=2*6*4/(6+4)=4.8 kmph
Q)A man travels
from A to B at 4 mph over a certain journey and returns over the same route to
A, at 5 mph. What is his average
speed for the
journey?
a) 4.44 mph b)
4.8 mph c) 4.887 mph d)5 mph
Q)A person is
rock climbing at an altitude of 800 m. He go up by 7 mph. and come down by 9
mph. what was his average speed?
a) 7.875 mph b)
7.125 mph c) 7mph d) 7.5 mph
Q)Find average
speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of
200m?
a) 28.8 mph b)
27.8 mph c) 27.5mph d) 30 mph
Q)Person travels
to a hill, if he goes from A to B with speed of 4kmph and returns back to B
with speed of 5kmph. What is his
average speed of
journey?
a) 4.5kmph b)
4.44kmph c) 9kmph d) 4.245kmph
Q)A man travels
from A to B at 70 mph over a certain journey and returns over the same route to
A, at 80 mph. What is his average
speed for the
journey?
a) 74.66 b)75
c)74.33 d)74.99
Q)Find average
speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of
200m.
a) 28.8 b)28 c)27
d)28.6
Pattern 6
Q)Susan made a
block with small cubes of 8 cubic cm volume to make a block ,3 small cubes
long, 9 small cubes wide and 5 small
cubes deep. She
realizes that she has used more small cubes than she really needed. She
realized that she could have glued a fewer
number of cubes
together to lock like a block with same dimensions, if it were made hollow.
What is the minimum number of cubes
that she needs to
make the block?
a) 114 b) 135 c)
21 d) 71
Sol: dimensions
of small cube = 2*2*2
Length of cube =
3 small cubes long = 6 cm
Breadth = 9 small
cubes wide = 18 cm
Height = 5 small
cubes deep = 10 cm
Volume = 6*18*10
= 1080cm^3
Volume of hollow
cube = (6-4)(18-4)(10-4)
= 168 cm^3
total number of
blocks needed = 1080-168 /8 = 912/8 = 114
Q)A boy wants to
make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he
realized he can make same
cuboids by making
it hollow. Then it takes some cubes less. What is the number of the cubes to be
removed?
a) 2000 b) 5000
c) 3000 d) 7000
Sol: Total volume
of cube = 5 * 6 * 7 = 210 m cube
volume of smaller
cube 0.03
Total cubes reqd
= 7000
for hollow cube
no. of small cubes reqd = 5/0.03 *4 + 6/.03 * 4 + 7/0.03 *4
which is approx
2000 so 5000 cubes have to be removed
Note:4 sides of
5,6 and 7 in the cube...so multiplied by 4
Q)Smita was
making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of
cubes needed to make a hollow cube
looking of the
same shape?
a) 98 b) 104 c)
100 d) 61
Sol: Jst count
the no. of cubes for each face
take the 1st one
25 small cubes reqd
now for 2 faces
adjacent to it 20 are reqd
2 faces adjacent
to all these 12 are reqd
and for the last
one 9 are reqd
so 98
Q)Leena cut small
cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm,
width 50 cm and depth 50 cm.
How many more
cubes does she need to make a perfect cube?
a)500 b)250 c)750
d)650
Sol: Volume left
for perfect cube = 100*100*100 - 100*50*50
No. of cubes reqd
= (100*100*100 - 100*50*50)/10*10*10 = 750
Q)Leena cut small
cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width
3 cm and depth 3 cm. How many
more cubes does
she need to make a perfect cube?
a) 910 b) 250 c)
750 d) 650
Q)A lady builds
9cm length, 10cm width,3cm height box using 1 cubic cm cubes. What is the
minimum number of cubes required to
build the box?
a) 730 b) 270 c)
720 d) 310
Sol: no. of cubes
required = 9*10*3 /1 = 270
Pattern 8:
Q) (40*40*40 –
31*31*31)/(40*40+40*31+31*31)=?
a)8 b)9 c)71 d)51
Q) (98*98*98 –
73*73*73)/( 98*98*98 – 73*73*73)=?
a).171 b).4
c).420 d).415
Q) (209*144)^2 +
(209*209)+(209*144)+(144*144) = ?
a)905863729
b)905368729 c)905729368 d)65
Pattern 9:
Q)
((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16
d)15
Q)x/2y = 2a,then
2x/x-2ay=?
a)4 b)8 c)16 d)2
Q)3X/5Y =
5Y/3X…..Find the value of X/Y
a)3/5 b)5/3 c)2/5
d)5/2
Q)What is the
value of (3X+8Y)/(X-2Y), if X/2Y=2
a)8 b)none c)10
d)13
Q)
(4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)48/5 b)46/5
c)47/5 d)49/5
Q)
((4x+2y)/(4x-2y)= ? as (x/2y) = 2
a)8/7 b)9/7
c)11/7 d)6/7
Pattern 10:
Q)A girl has to
make pizza with different toppings. There are 8 different toppings. In how many
ways can she make pizzas with 2
different
toppings?
a)16 b)56 c)112
d)28
Sol: The number
of ways of choosing r distinct objects from n distinct objects is given by the
formula
C(n, r) =
n!/r!*(n-r)!
where n! =
n(n-1)(n-2).......3*2*1
If order was
important, the number of arrangements is
P(n,r) n!/(n-r)!
Now suppose you
wanted to display one topping in the middle and the other around the edge, you
would be considering arrangements
and the answer
would be
P(8, 2) = 8!/6!
= 8*7
= 56
However, suppose
that you wish to sprinkle toppings randomly over the pizza base. Since it does
not matter what the arrangements
are, the number
of ways is
C(8, 2) = 8! /
2!*6!
= 8*7 / 2*1
= 56/2
= 28
This is correct.
Q)A pizza shop
made pizzas with many flavors. There are 10 different flavors, in that 7
flavors are taken to make pizza. In how
many ways they
can arrange?
a)240 b)120 c)65
d)210
Sol:
10c7=10c3=120
Q)A pizza shop
made pizzas with many flavors. There are 9 different flavors, in that 2 flavors
are taken to make pizza. In how many
ways they can
arrange?
a)16 b)26 c)36
d)46
Sol: 9c7=9c2=36
Pattern 11:
Q)3, 22, 7, 45,
15,? , 31
a)91 b)151 c)90
d)5
Sol: we can
divide this into two series
Series 1:
3, 7, 15, 31
Here, every next
number = 2*n + 1, where n is the preceding number
Series 2:
22, 45, x
This is the same
as Series 1
So, x = 45*2+1 =
91
Q)2. 8 6 17 14 35
31 75 _ 143?
Sol: From the
given question it is clear that
the difference
between the consecutive two digits is 2,3,4,....
8-6=2
17-14=3
35-31=4
75-x=5;
from the above
equation we get that x value is 70
final solution is
70
the series become
8 6 17 14 35 31 75 70 143 137..........
Q)Inspired by
Fibonacci series Sangeet decided to create his own series which is 1, 2, 3, 7,
7, 22, 15, 67, 31, _, 63?
a)202 b)31 c)76
d)49
Sol: Ans=202
bcos in the given
series there are two other series..in the form of
1 ,2 ,3 ,7 ,7 ,22
,15 ,67 ,31 ,_ ,63;
choose the
alternate digits:1,3,7,15,31,63
these are follow
the pattern like n*2+1
1
3=n*2+1(wher n=1)
7=n*2+1(wher n is
the previous number)
15=7*2+1(where
n=7)
31=15*2+1(wher
n=15)
63=31*2+1(where
n=31)
but we dont need
this series.just for understanding i gave the above matter
anothe series in
the given series in:2 ,7 ,22 ,67 ,_
we hav to find
the number in the blank
this series is in
the form of n*3+1
so the series
consists of the following numbers 2
7=2*3+1(where
n=2)
22=7*3+1(wher
n=7)
67=22*3+1(wher n=22)
for the next
number we need to multiply the previous number with 3 and add a 1 to the result
finally next
digit=67*3+1=202
the final series
1,2,3,7,7,22,15,67,31,202,63
Q)3, 12, 7, 26,
15, ?
a)54 b)27 c)108
d)31
Sol: Series 1: 3,
7, 15 …
Series 2:12,
(12*2+2)26, (26*2+2)54 ans
Q)1! + 2! + ……. +
50!=?
a)3.1035*10^64
b)2.1021*10^65 c)3.1035*10^63 d)3.1035*10^62
Sol: The answer
is 3.10351E+64
There is no
formula as such
We can find this
by solving it in Microsoft Excel!
Q)1, 2, 3, 6, 7,
14, _, 32?
Sol: its
obviously 16.
divide in two two
pairs such that it is
1-2
3-6
7-14
_-32
see the pattern
is going n- n*2
therfore _-16*2
gives 16_16*2
hence answer is
16.
Q)5, 9, 12, 18,
26, 36, 47, 72, _?
a)75 b)135 c)100
d)55
Sol: Series1:
9,18,36,72….2*n
Series2:
5,12,26,47,75….difference is 7 multiples, so ans :75
Q)3, 15, x, 51,
53,159,161
a)17 b)34 c)54
d)112
Sol: Difference
between the two consecutive numbers is 2; exclude 3 here
consider 17 here
then
17-15=2 and next
number will be 17*3=51
same process
continued.
53-51=2 and next
number is 53*3=159
Ans is 17
Pattern 12:
Q)Simple question
but big one on average age.sth like a, b, c weighted separately 1st a, b, c
,then a& b, then b &c ,then c & a at
last abc, the
last weight was 167,then what will be the average weight of the 7 reading?
a)95 b)95.428
c)95.45 d)94
Sol: a+b+c =167
given
first a is weighd
then b then c then a+b , b+ c , c+ a and lastly a+b+c
so total = a + b
+ c+ (a+ b) + (b+c) + (c+a) + (a+b+c)
= 4(a+b+c)
so avg of 7
weighs = 4/7 * 167 = 95.428
Pattern 13:
Q)A toy train
produces 10 different sounds when it moves around a circular toy track of
radius 5 m at 10 m per min. However, the
toy train is
defective and it now produces only 2 different tunes at random. What are the
odds that the train produces for consecutive
music tones of
the same type?
a) 1 in 16 B)1 in
4 c)1 in 8 d)1 in 32
Sol: it can
produce sound A , prob = 1/2 * 1/2 * 1/2 * 1/2 = 1/8
or sound B , prob
= 1/8
so prob of
consecutive sound = 1/8 + 1/8 = 1/4
or
Total number of
cases 2 can be chosen out of 10 = 10c2 = 45 ways.
first note in 10
ways , second note in 1 way only.
so prob = 10/45 =
2 out of 9
or
First Time choose
sound =1/2
second
third
fourth
fifth =1/2
total=(1/2)^5=1/32
Q)A car
manufacturer produces only red and blue models which come out of the final
testing area at random. What are the odds
that five
consecutive cars of same color will come through the test area at any one time?
a)1 in 16 b)1 in
125 c)1 in 32 d)1 in 25
Sol: Probability
that a car is red or blue = 1/2
So, probability
that each of the five cars are of a color =
Probability that
a car is blue + Probability that a car is red
= (1/2)5 + (1/2)5
= 2*(1/2)5
=1/16
Pattern 15:
Q)A triangle is
made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What
will be the area of the square made
from the same
rope?
a)280.5625
b)240.5625 c)280.125 d)240
Sol: Length of
the rope = 67
Length of side of
square = 67/4
Area of square =
(67/4)2
Q)A triangle is
made from a rope. The sides of the triangle are 21 cm, 24 cm and 28 cm. What
will be the area of the square made
from the same
rope?
a)280.5625
b)333.0625 c)333.0125 d)400
Sol: Length of
the rope = 73
Length of side of
square = 73/4
Area of square =
(73/4)2
Pattern 16:
Q)What is the
distance between the z-intercept from the x-intercept in the equation
ax+by+cz+d=0
Sol: ax + by + cz
+ d = 0
At the
z-intercept, 'x' and 'y' are both zero.
cz + d = 0 -->
z = -d/c --> The z-intercept is the point (0, 0, -d/c).
At the
x-intercept, 'y' and 'z' are zero.
ax + d = 0 -->
x = -d/a --> The x-intercept is the point (-d/a, 0, 0).
The distance
between the points (0, 0, -d/c) and (-d/a, 0, 0) is
sqrt[ (-d/a)2 +
(-d/c)2 ] = sqrt (d2/a2 + d2/c2) = d sqrt(1/a2 + 1/c2)
Pattern 17:
Q)A scientist was
researching on animal behavior in his lab. He was very interested in analyzing
the behavior of bear. For some
reason he
travelled 1mile in north direction & reached at North Pole. There he saw a bear.
He then followed the bear around 1 hr
with a speed of
2km/hr in east direction. After that he travelled in south direction &
reached at his lab in2 hrs. Then what is the color
of the bear?
a)white b)black
c)gray d)brown
Sol: Since it is
the north pole, the colour of the bear is white!
As brown and
black bears are not found on the poles!
Pattern-18:
Q)Out of 7
children the youngest is boy then find the probability that all the remaining
children are boys
a)1/64 b)1/32
c)1/128 d)1/256
Sol: the first
result doesn't affect subsequent ones.
for each birth,
P[boy] will be 1/2
using the
multiplicative principle,.
P[next 5 are
boys] = 1/2 *1/2 *1/2 *1/2 *1/2 = 1/32 <-------
Pattern 19:
Q)Usha bought a
linen cloth and rope to build a tent. If the rope is 153 m long and it is to be
cut into pieces of 1m length, then how
many cuts are to
be made to cut the ropes into 153 pieces?
a)153 b)152 c)154
d)155
Sol: Number of
cuts = n - 1
so it will be 152
cuts
Q)A person has to
make 146 pieces of a long bar. He takes 4 seconds to cut a piece. What is the
total time taken by him in seconds
to make 146
pieces?
a)584 b)580 c)730
d)725
Sol: Number of
cuts=146-1
145*4=580
Q)A person has to
make 141 pieces of a long bar. He takes 2 seconds to cut a piece. What is the
total time taken by him in seconds
to make 141
pieces?
a)560 b)280 c)112
d)324
Sol: Number of
cuts=141-1
140*2=280
Pattern 20:
Q)Spores of a
fungus, called late blight, grow and spread infection rapidly. These pathogens
were responsible for the Irish potato
famine of the
mid-19th century. These seem to have attacked the tomato crops in England this
year. The tomato crops have reduced
and the price of
the crop has risen up. The price has already gone up to $45 a box from $27 a
box a month ago. How much more
would a vegetable
vendor need to pay to buy 27 boxes this month over what he would have paid last
month?
a) $27 b)$ 18
c)$45 d)$ 486
Sol: Change in
price = 45 - 27 = 18
So for 27 boxes =
27 * 18 = 486
Pattern 21:
Q)A Person buys a
horse for 15 ponds, after one year he sells it for 20 pounds. After one year,
again he buys the same horse at 30
pounds and sells
it for 40 pounds. What is the profit for that person?
Sol: 20 - 15 = 5
40 - 30 = 10
total Profit=15
Pattern 22:
Q)John buys a
cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper
exchanged the cheque with his neighbor
and gave change
to John. After 2 days, it is known that cheque is bounced. Shop keeper paid the
amount to his neighbor. The cost
price of cycle is
19 dollars. What is the profit/loss for shop keeper?
a)loss 23 b)gain
23 c)gain 54 d)Loss 54
Sol: Shopkeeper
paid 4 $ to john while giving change
He also paid
neighbor 35 $
Total payment 39
$
Cost 19 $
Loss 20 $
Pattern 23:
Q)A lady has fine
gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are
out and it is totally dark. In spite of
the darkness, she
can make out the difference between a hat and a glove. She takes out an item
out of the closet only if she is sure
that if it is a
glove. How many gloves must she take out to make sure she has a pair of each
color?
a)50 b)8 c)60
d)42
Sol: since it is
dark....
take worst case
satisfy largest
number first.....
since she wants
it in pair
32 red
24 yellow
1+1 yellow+blue
2 blue
=60
Q)A lady has fine
gloves and hats in her closet- 14 blue, 20 red, and 18 yellow. The lights are
out and it is totally dark. In spite of
the darkness, she
can make out the difference between a hat and a glove. She takes out an item
out of the closet only if she is sure
that if it is a
glove. How many gloves must she take out to make sure she has a pair of each
color?
Sol: Since its
dark….
Take worst case..
Satisfy largest
number first….
20 red
18 yellow
2 blue
=40
Q)A lady has fine
gloves and hats in her closet- 13 blue, 27 red, and 40 yellow. The lights are
out and it is totally dark. In spite of
the darkness, she
can make out the difference between a hat and a glove. She takes out an item
out of the closet only if she is sure
that if it is a
glove. How many gloves must she take out to make sure she has a pair of each
color?
Sol: Since its
dark…
Take worst case…
Satisfy largest
number first…
40 yellow
26 red
1 +1 red + blue
2 blue
=70
Q)A lady has fine
gloves and hats in her closet- 25blue, 7 red, and 9 yellow. The lights are out
and it is totally dark. In spite of the
darkness, she can
make out the difference between a hat and a glove. She takes out an item out of
the closet only if she is sure that
if it is a glove.
How many gloves must she take out to make sure she has a pair of each color?
Q)A lady has fine
gloves and hats in her closet- 26 blue, 30 red, and 56 yellow. The lights are
out and it is totally dark. In spite of
the darkness, she
can make out the difference between a hat and a glove. She takes out an item
out of the closet only if she is sure
that if it is a
glove. How many gloves must she take out to make sure she has a pair of each
color?
Pattern 24:
Q)Sangakara and
Ponting selects batting by using a dice, but dice is biased. So to resolve,
Ponting takes out a coin. What is the
probability that
coin shows correct option?
a)1/2 b)1/6
c)1/12 d)6/10
Sol: 1/2
Q)There is a die
with 10 faces. It is not known that fair or not. 2 captains want to toss die
for batting selection. What is the possible
solution among
the following?
a) If no. is odd
it is head, if no. is even it is tail
b) If no. is odd
it is tail, if no. is even it is head
c) Toss a die
until all the 10 digits appear on top face. And if first no. in the sequence is
odd then consider it as tail. If it is even
consider it as
head.
Sol: ans is c)
in question
itself it will clearly mentioned whether that is it was a not known fair or
not. so first we have to check whether it is fair
or not. so we
toss a die until all the 10 faces appear on top, then only we can decide which
one is odd and which one is even
Pattern 25:
Q)In a family
there are some boys and girls. All boys told that they are having equal no of
brothers and sisters and girls told that
they are having
twice the no. of brothers than sisters. How many boys and girls present in a
family?
a)4 boys and 3
girls b)3 boys and 4 girls c)2 boys and 5 girls d)5 boys and 2 girls
Sol: for each boy
in option 1 there are 3 brothers and 3 sisters
for each girl in
option 1 there are 2 sisters and 4 brothers
so answer is
option 1
Pattern 26;
Q)10men and 10
women are there, they dance with each other, is there possibility that 2 men
are dancing with same women and
vice versa?
a)22 b)20 c)10
d)none
Sol: Since 10 is
an even number, and people dance in couples, there wouldn't be a lone dancer.
So never!
Q)There are 100
men and 100 women on the dance floor. They want to dance with each other. Then
which of the following
statements is
always true:
a) There are 2
men who danced with equal no. of women.s
b) There are 2
women who danced with equal no. of men
a) both a and b
b)only a c)only b d)none
Sol: none
Pattern 27:
Q)Middle- earth
is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits
and elves are peaceful creatures that
prefer slow,
silent lives and appreciate nature and art. The dwarves and the men engage in
physical games. The game is as follows.
A tournament is
one where out of the two teams that play a match, the one that loses get
eliminated. The matches are played in
different rounds,
where in every round; half of the teams get eliminated from the tournament. If
there are 8 rounds played in knock
out tournament,
how many matches were played?
a)257 b)256 c)72
d)255
Sol: The number
of teams for 8 rounds is:
256->128->64->32->16->8->4->2->1
Thus initially
der wer 256 teams.
But wat is askd
is the numbr of matches that were played to reach the winner.
The number of
matches for 8 rounds is:
128->64->32->16->16->8->4->2->1
128+64+32+16+8+4+2+1=255
Q)A game is
played between 2 players and one player is declared as winner. All the winners
from first round are played in second
round. All the
winners from second round are played in third round and so on. If 8 rounds are
played to declare only one player as
winner, how many
players are played in first round?
a)256 b)512 c)64
d)128
Sol: 256
Pattern 28:
Q)Metal strip of
width „x. cm. 2 metal strips are placed one over the other, then the combine
length of 2 strips is „y.. If „z. strips are
placed in that
manner. What is the final width of that arrangement?
Sol: only the
height of the metal strip changes,the length as well the width of the metal
strip remains same....so the answer can be
concluded as 'x'
Q)A, B, C, D, E
are there among A, B, C are boys and D, E are girls D is to the left of A and
no girl sits at the middle and at the
extemes. Then
what is the order of their sittings.
Sol: There are
two possibilities
Case 1: _ D A E _
Case 2: _E _ D A
The blanks can be
filled by the two boys that are left
Given proper
options, we can choose the appropriate one
Pattern 29:
Q)There is 7
friends (A1, A2, A3....A7).If A1 have to have shake with all without
repeat(distinct=>Permutaion). How many
handshakes
possible?
a)6 b)21 c)28 d)7
Sol: A1 can shake
hands with 6 people, A2-A7
A2 can shake
hands with 5 people, A3-A7 and so on
If there are n
people, there are (n-1)! ways for them to shake hands.
In this case,
6!=720 ways.
Q)49 members
attended the party. In that 22 are males, 17 are females. The shake hands
between males, females, male and
female. Total 12
people given shake hands. How many such kinds of such shake hands are possible?
a)122 b)66 c)48
d)128
Sol: 12C2 = 66
Pattern 30:
Q)B is taller
than j and 3 pillars. P is shorter than B and 2 pillars is j shorter/taller
than P?
a)yes b)no c)may
be d)can.t find
Sol: According to
the first condition,
B > j + 3
pillars
According to the
second condition,
B + 2 pillars
> P
Rewriting the
first equation,
B + 2 pillars
> j + 5 pillars
Comparing it with
the second equation,
we can't say any
thing about P and j!
Q)There are 1000
pillars for a temple. 3 friends Linda, Chelsey, Juli visited that temple. (Some
unrelated stuff) Linda is taller than
Chelsea and
taller than 2 of 1000 pillars. Julia is shorter than Linda. Find the correct
sentence?
a) Linda is
shorter among them
b) Chelsea is
taller than Julia
c) Chelsea is
shorter than Julia
d) Cannot
determine who is taller among Chelsea and Julia
Sol: J<C< L
or C<J<L
Therefore ans is
d
Pattern-31
Q)Entry ticket to
an exhibition ranges from 1p to 31p. You need to provide exact change at the
counter. You have 31p coin. In how
many parts will u
divide 31p so that u will provide the exact change required and carry as less
coins as possible?
a)4 b)5 c)6 d)7
Sol: 2n =>
n=0,1,2,3,4 < 25(32)
Since given 31p,
2n results in
1,2,4,8,16
Through any
combination of 1,2,4,8,16 we can acquire any denomination needed at
counter.....
So, total 5
combinations
Pattern 32
Q)Peter and Paul
are two friends. The sum of their ages is 35 years. Peter is twice as old as
Paul was when Peter was as old as Paul
is now. What is
the present age of Peter?
a)8 b)20 c)16
d)15
Sol: go fr
options ..
take 20 as
peter's present age den pauls age wud be 15(20+15)=35..
also when peter
was 15,i.e at the age of paul.(20-15)=5.then pauls age wud be (15-5)=10 and it
was double that of peters present
age
.'.optin 2
OR
let pauls age be
'a' and peters be 'e'
e+a=35 (given)
e=35-a ------eq1
when peter was as
old as paul that is when peter's age was 'a' i.e e-(e-a) [for example if e was
9 and a was 5, e-a is 4,9-4=5 so e-(e-
a)]
pauls age was
a-(e-a) =2a-e
now peters age is
e=2(2a-e)
e=4a-2e
3e=4a
3(35-a)=4a
105-3a=4a
a=15
hence e=20
Pattern 33
Q)20 men
handshake with each other without repetition. What is the total number of
handshakes made?
a)190 b)210 c)150
d)250
Sol: 20th man =
19 handshakes
19th man = 18
....1st man = 0
so we get a
series from 1 to 19 handshakes where n = 19 a = 1 d =1
So total
handshakes = sum of the series = n/2(2a+(n-1)d) = 190
Q)10 people are
there, they are shaking hands together, how many hand shakes possible, if they
are in no pair of cyclic sequence.
a)45 b)9 c)12
d)10
Sol: 10th man = 9
handshakes
9th man = 8
….1st man =0
So we get a
series from 1 to 9 handshakes where n=9 a=1 d=1
So, total
handshakes = sum of the series = n/2(2a+(n-1)d) = 45
Pattern 34
Q)If there are 2
wheelers and 4 wheelers parked in a school located at the heart of the city,
find the number of 4 wheelers parked
there if there
were 20 two wheelers parked there
a)48 b)50 c)52
d)64
Sol: Question
incomplete
Q)If there are 2
wheelers and 4 wheelers parked in a school located at the heart of the city,
find the number of 4 wheelers parked
there if there
were 58 wheels are parked there
a)10 b)33 c)22
d)none
Sol: no of 4
wheelers are 10.i.e. 10*4=40 wheels.
no. of wheels
left = 58-40=18
hence no. of 2
wheelers=18/2=9
22 and 33 cant be
ans bcz it will make no. of wheels greater than 58
Pattern 35
Q)A man whose age
is 45 yrs has 3 sons named John, Jill, jack. He went to a park weekly twice. He
loves his sons very much. On a
certain day he
found the shop keepers selling different things. An apple cost 1penny,
2chocalate costs 1penny & 3 bananas cost 1
penny. He has
bought equal number of apple, chocolate & banana for each son. If the total
amount he invest is 7 penny then how
many he has
bought from each piece for his son?
a)1app,1cho,1
banana b)1 app,2cho,3 banana c)1app,2cho,1banana
Q)One person had
three children. He had 7 pennies. Find the distribution of the fruits among the
three children. A melon costs 1
penny, 2 oranges
cost 1 penny and 3 grapes cost 1 penny
a)2 melons, 1
orange, 1 grape b) 2 melons, 2 orange, 1 grape c) 1 melons, 2 orange, 1 grape.
PATTERN 36
Q)The age of the
two friends were in the ration of 6:5.If the sum of their ages is 55.Then after
how many years their ratio will
become 8:7?
a)11 b)7 c)10
d)12
Sol: 6x+5x = 55
x = 5
so ages 30 and 25
So after 10 yrs
40 and 35
so ratio is 8:7
Q)The age of the
two friends were in the ration of 6:5.If the sum of their ages is 66.Then after
how many years their ratio will
become 7:6?
a)11 b)6 c)10
d)12
Sol: 6x+5x=66
X=6
So ages 36 and 30
So after 6 years
42 and 36
So ratio is 7:6
Q)The age of the
two friends were in the ration of 2:3.If the sum of their ages is 55.Then after
how many years their ratio will
become 4:5?
a)11 b)33 c)22
d)44
Sol: 2x+3x=55
X=11
So ages 22 and 33
So after 22 years
44 and 55
So ratio is 4:5
PATTERN 37
Q)A volume of
10936 l water is in a container of sphere. How many semi sphere of volume 4l
each will be required to transfer all the
water into the
small semi spheres?
a)2812 b)8231
c)2734 d)4222
Sol: ans =
10936/4 = 2734
PATTERN 38
Q)A person is
manufacturing a house. He bought 20 ropes of wire which has a density of 300
Kg/m3.The height of the building to be
constructed is 40
m. If the capacity of the current passed in the wire is 20 A and the voltage
capacity is 80 Volts.Then what will be
the opposing
force to the current if the wire is used ?
a)2 b)4 c)8
d)1600
Sol: by ohms law
v = ir
so r = v/i
so r = 80/20 = 4
PATTERN 39
Q)A horse chases
a pony 2 hours after the pony runs. Horse takes 3 hours to reach the pony. If
the average speed of the horse is
81Kmph.Then what
is the average speed of the pony?
a)46.4 b)51
c)53.4 d)48.6
Sol: pony = 2
hours + 3 hours= 5 hours.
horse= 3 hours= 3
hours.
3*81=243
243/5=48.6=>average
speed of pony.
Q)A horse chases
a pony 3 hours after the pony runs. Horse takes 4 hours to reach the pony. If
the average speed of the horse is
35 kmph, what s
the average speed of the pony?
Sol: pony = 3
hours + 4 hours= 7 hours.
horse= 4 hours= 4
hours.
3*35=105
105/7=15=>average
speed of pony.
PATTERN 40
Q)The difference
between two no is 9 and the product of the two is 14.What is the square of
their sum?
a)120 b)130 c)137
d)145
Sol: x-y=9
xy=14
(x+y)2-(x-y)2 =
4xy
(x+y)2= 4xy +
(x-y)2
(x+y)2= 4*14 + 81
=137
Q)The sum of two
no is 5 and the product of the two is 14.What is the sum of their squares?
Q) The sum of the
squares of two no is 12 and their sum is 15.Find the product of the two no?
PATTERN 41
Q)On planet
korba, a solar blast has melted the ice caps on its equator. 9 years after the
ice melts, tiny planetoids called echina
start growing on
the rocks. Echina grows in the form of circle, and the relationship between the
diameter of this circle and the age of
echina is given
by the formula d = 4*v (t-9) for t = 9 where d represents the diameter in mm
and t the number of years since the
solar blast.Jagan
recorded the radius of some echina at a particular spot as 7mm. How many years
back did the solar blast occur?
a) 17 b)21.25
c)12.25 d)14.05
Q)On planet
korba, a solar blast has melted the ice caps on its equator. 9 years after the
ice melts, tiny planetoids called echina
start growing on
the rocks. Echina grows in the form of circle, and the relationship between the
diameter of this circle and the age
of echina is
given by the formula d = 4* sqrt(t-9) for t = 9
Where d
represents the diameter in mm and t the number of years since the solar blast.
Jagan recorded
the radius of some echina at a particular spot as 12mm. How many years back did
the solar blast occur
Sol: so
d=24 = 12*2
now
24=4*sqrt(t-9)
6^2=t-9
36+9=t
t=42
PATTERN 42
Q)A man goes 50Km
north , then turned left walked 40Km, then turned right ? In which direction he
is?
a)North b)South
c)East d)West
PATTERN 43
Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 4.s will be present in the
numbers?
a)18 b)19 c)20
d)21
Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 6.s will be present in the
numbers?
a)18 b)19 c)20
d)21
Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 1.s will be present in the
numbers?
a)18 b)19 c)20
d)21
Q)In T.Nagar the building were numbered from 1
to 100.Then how many 0.s will be present in the numbers?
a)18 b)19 c)20
d)11
PATTERN 44
Q)A number when
divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder
of 21. What is the remainder
left, when twice
the number is divided by 3D?
13 b) cannot be
determined c) 3 d) 42
Sol: suppose the
no. is a
a = Dx +8 ...1
a = 3Dy + 21 ...2
So from 1 & 2
we get
D(x-3y) = 13
13 is prime so
x-3y has to be 1
let x = 4 and y =
1
We get a = 60
2a = 120
So 120 when
divided by 3D = 39
we get remainder
as 3
So answer is 3
PATTERN 45
Q)Ferrari S.P.A
is an Italian sports car manufacturer based in Maranello, Italy. Founded by
Enzo Ferrari in 1928 as Scuderia Ferrari,
the company
sponsored drivers and manufactured race cars before moving into production of
street-legal vehicles in 1947 as Ferrari
S.P.A. Throughout
its history, the company has been noted for its continued participation in
racing, especially in Formula One where
it has employed
great success .Rohit once bought a Ferrari. It could go 4 times as fast as
Mohan's old Mercedes. If the speed of
Mohan's Mercedes
is 35 km/hr and the distance traveled by the Ferrari is 490 km, find the total
time taken for Rohit to drive that
distance.
20.72 b) 5.18 c)
238.25 d) 6.18
Q)Ferrari S.P.A
is an Italian sports car manufacturer based in Maranello, Italy. Founded by
Enzo Ferrari in 1928 as Scuderia Ferrari,
the company
sponsored drivers and manufactured race cars before moving into production of
street-legal vehicles in 1947 as Ferrari
S.P.A. Throughout
its history, the company has been noted for its continued participation in
racing, especially in Formula One where
it has employed
great success .Rohit once bought a Ferrari. It could go 4 times as fast as
Mohan's old Mercedes. If the speed of
Mohan's Mercedes
is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total
time taken for Rohit to drive that
distance.
20.72 b) 5.18 c)
238.25 d) 6.18
PATTERN 46
Q)A sheet of
paper has statements numbered from 1 to 70. For all values of n from 1 to 70.
Statement n says ' At least n of the
statements on
this sheet are false. „Which statements are true and which are false?
a) The even
numbered statements are true and the odd numbered are false.
b) The odd
numbered statements are true and the even numbered are false.
c) The first 35
statements are true and the last 35 are false.
d) The first 35
statements are false and the last 35 are false.
Sol: Suppose the
first 35 statements are true!
Statement 1: At
least 1 statement is false [TRUE]
Statement 2: At
least 2 statements are false [TRUE]
...
Statement 35: At
least 35 statements are false [TRUE]
--------------------------------------------------------------------
Statement 36: At
least 36 statements are false [FALSE]
..
Statement 40: At
least 40 statements are false [FALSE]
--------------------------------------------------------------------
AT LEAST puts the
minimum tag or the floor tag on the statements
So, if the first
35 statements are true and the rest are false, everything fits into place!
PATTERN 47
Q)A man goes
north 37km.turns left goes 2km.turns right goes 17km.turns right goes 2km. find
distance b/w starting ending point.
a) 54 b) 27 c) 81
d) 67
Try representing
the statement as a pictoral representation. The 2 Km turns becomes reversed in
the second 2 Km turn.
The total
distance travelled therefore is 17+37 = 54 Km
http://writer.zoho.com/image.do?imgurl=6a81fa48dd4787c104f2cf6020717e46daf9820e459103a3545be997962f98eeb1712ee0bda409c5f71a3e5272a9d65d
Q)If a person
moves 15km straight and turns 45 km right and moves 15Km staright then how much
distance
he needs to walk
to reach starting point?
PATTERN 48
Q)If there are 30
cans out of them one is poisoned if a person tastes very little he will die
within 14 hours so if there are mice to test
and 24 hours to
test, how many mices are required to find the poisoned can?
a) 3 b) 2 c) 6 d)
1
Sol: Have 6 mice
for testing,
Give each mice
contents from 5 cans each
5 5 5 5 5 5
After 14 hours,
one of the mice will die
So, we will know
which 5 cans must have the poison
Then , take the
contents of these 5 cans and give to the remaining 5 mice each.
We will know in
due time which can is poisoned.
PATTERN 49
Q)If a and b are
mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is
35 liters, find the amount of b?
A) 13.34 b) 15.73
c) 16.73 d) 9.45
Sol: total ratio
= 24:40:25
sso b in 35 lts =
40/89 * 35
which is 15.73
PATTERN 50
Q)If we subtract
a number with y, we get 4 increase of number, once it got divided by y
itself... Find that number??
A) 13 b) 12 c) 14
d) 11
Sol: Let number
be x
then x - y = x/y
+ 4
=> xy - y^2 =
x + 4
now we need
options to solve , one pair can be x = 12 and y = 6
options are
incorrect
PATTERN 51
Q)It is the class
with the seating arrangement in 4 rows and 8 columns. When the teacher says
'start' the girl who is sitting in first
row and first
column will say 1, then the next girl sitting behind her will say 4, the next
girl sitting behind that girl will say 7, in a
particular order
each girl is telling a number, the following girls told 10, 13 next turn is
yours what u will say?
a) 15 b) 17 c) 14
d) 16
Sol: 1 4 7 10 13
16
this is the
series
PATTERN 52
Q)It is dark in
my bedroom and I want to get two socks of the same color from my drawer, which
contains 24 red and 24 blue
socks. How many
socks do I have to take from the drawer to get at least two socks of the same
color?
A) 2 b) 3 c) 48
d) 25
Sol: 3 socks are
only reqd to get socks of the same color
Q)Lady has 2
select gloves & hat from a basket. In the dark, she can distinguish
hat&gloves.14red, 20blue, 18green r there. Find
probability that
any selected glove pair has same color.
Sol: SAME AS
PATTERN 23
Q)A lady had fine
gloves and hats. 25 blue, 7 red and 9grey. She had to select a pair among them.
But there was no light so she
had to select in
darkness the correct pair with a glove and a hat. Therefore how many
combinations of same color she can select?
PATTERN 53
Q)If the Valentine.s
Day in 2005 falls on Monday, then on which day will the Valentine.s Day fall on
2010?
A) Saturday b)
Thursday c) Wednesday d) Sunday
Sol: 14/2/2005 is
a Monday
So, from
1/1/2005, days till 14/2/2005 = 31 + 14 = 45
45 mod 7 = 3
Let us say
Saturday = 1
Sunday = 2
Monday = 3
Tuesday = 4
..
Friday = 7
Now, 14/2/2010 is
365*5(1/1/2005 to 31/12/2009) + 1(as 2008 is a leap year) + 31(jan 2010)+14(feb
2010) = 1871 days from
1/1/2005
1871 mod 7 = 2
So, if 3 =
Monday, 2 = Sunday
So, 14/2/2010 is
a Sunday!
PATTERN 54
Q)A person run
from A to B.He took ¼ of the time less to reach B when compare to run at normal
Speed.Then how many
percentage he has
increased his speed?
a)40 b)44.4
c)33.3 d)22.2
Sol: We proceed
as follows
d=s*t
when t1=(3/4)t
then
d=s1'*t1
s*t=s'1*(3/4)t
then
s1/s=4/3
Therefore
increase in speed=s1/s-1=1/3or100/3 %=33.33%
So answer is
option 3
Q)An athlete
decides to run the same distance in 1/4th less time that she usually took. By
how much percent will she have to
increase her
average speed?
a)40 b)44.4
c)33.3 d)22.2
Sol: let he takes
time t at speed s
now new time is
3/4t , so speed will become 4/3s
so speed is 1.33s
, that is speed increases by 33.3%
hence option 3
PATTERN 55
Q)In a building
there are 5 rooms. Each having a equal area .The length of the room is 4m and
breadth is 5 m. The height of the
rooms is 2m. If
17 bricks are needed to make a square meter then how many bricks are needed to
make the floor of a particular
room?
a) 320 b) 380 c)
340 d) 300
Sol: 340 bricks
for 1 room considering height of brick as 1 as it is not given
As 17 bricks for
1 sq m
So l*b for room =
5*4 = 20 sq m
So bricks =
20*17= 340
PATTERN 56
Q)One man want to
build a wall .The length and breadth of the wall are 20 and 30 respectively. He
need 35 bricks for one square
centimeter then
how many bricks he need?
a)21,500 b)30,000
c)21,000 d)20,000
Sol: total area =
20 * 30 =600
so bricks reqd =
600 * 35 = 21000
PATTERN 57
Q)In a hotel we
can order two types of varities,but we can make 6 more variteis in home.One can
choose the four varities with two
from hotel as
must.Find how many ways one can order.
a)14 b)15 c)56
d)28
Sol: we have to
choose 2 out of 6
so answer = 6C 2
=15
PATTERN 58
Q)If a pipe can
fill the tank within 6hrs.But due to leak it takes 30 min more. Now the tank is
full then how much time will it take to
empty the tank
throught the leak.?
a)78 b)56 c)66
d)59
Sol: let the leak
per hour be 1/x.
((1/6)-(1/x)=1/6.5
so,1/x=1/78
x=78
PATTERN 59
Q)The bacteria
has the probability of split into 3 and probability to die is 1/3rd of the
total bacteria.Let the probability is P.Some of
them survived
with probability 1/5.Then which among the following relation is true?
a)P=1/3+1/5*3
b)P=1/5*(1/8-3)
Sol: First option
is correct as , prob to die is 1/3 and surviving is remaining which is 1/5 *3
as it becomes 3 times
hence option 1
Q)There is a
bacteria which has the probability of die 1/3 of its total number or it may
tripled. Find out the probability
A.
P=1/3+(2/3*p^3) B. P=2/3+(2/3*p^3) C. P=2/3+(1/3*p^3) D P=2/3+(2/3*p^3)
Sol: probability
of die is 1/3
or
its get tripled
the probability
of tripled is 2/3*p*p*p
thats 2/3*p^3
so both the
probability combined as P=1/3+(2/3*p^3)
PATTERN 60
Q)There was a
grand mother in a village who had a grand child. Upon asking her grand Childs
age she told that she is as older as
many days old as
her daughters age in weeks and as many days as her own age in years. The sum of
the three is 130.then how old
is the child.?
Sol: as per ur
logic ,
the baby is 127
days old...
her mother 2
years old...
and tat old lady
is 127 years old..
PATTERN 61
Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 4.s will be present in the
numbers?
a)18 b)19 c)20
d)21
Sol: 10 4s in
units place
10 in 10s place
so answer is 20
Q)In Tnagar many
buildings were under residential category. For buildings they number as 1 to
100. For shops, corporation
numbered between
150 and 200 only prime numbers. how many time 6 will appear in building
numbering?
PATTERN 62
Q)Amrith told to
Anand in front of a Photo that “He is the son of my father.s son”. Find who is
in the picture if amrith have no
brothers and
sisters.
a)Amrith himself
b)Amrith.s Uncle c)Amrith.s Father d)Amrith.s son
Q)One person has
no siblings and says,” the guy in the photo is the only son of my father „s
son”. What is the relation of the guy to
the person?
PATTERN 63
Q)One grand
father has 3 grand children two of the age difference is 3.Eldest child age is
3 times the youngest childs age and the
eldest child age
is two year more than the sum of other two children. Find what is the age of
the elders child?
a)18 b)22 c)30
d)10.
Sol: let say,
a,b, & c are the children, where a is eldest.
a=3C.......(1)
b+c+2=a...........(2)
jst check all the
options which are dividable by 3. (18 & 30)
a=18 => c=6
put this value in
(2) => b=10. which is not satisfied the condition (two of the age difference
is 3).
if we take a=30,
then we get c=10 & b=18. which also not satisfied the condition.
so i think there is a problem with que. or in
my understanding.
please help if
there is any mistake in my calculations.
Q)One grandfather
has three grandchildren, two of their age difference is 3, eldest child age is
3 times youngest child.s age and
eldest child.s
age is two times of sum of other two children. What is the age of eldest child?
Sol: consider
that the grand child are x,y,z
then based on the
conditions we have,
'two of their age
difference is 3'
this leads to 3
possibilities
x-y=3
y-z=3
x-z=3
but only one will
be correct
'eldest child age
is 3 times youngest child's age'
x=3z
'eldest child's
age is two times of sum of other two children'
x=y+z+2
but since x=3z,
x-z=3 is not feasible
and again x-y=3
is also not feasible..
so we got,
y-z=3
x=3z
x=y+z+2
we got three
equations, 3 unknowns..
this lead to one
possibility..
x=15
y=8
z=5
PATTERN 64
Q)In a school,
for a student out of 100 he got 74 of average for 7 subjects and he got 79
marks in the 8th subject. what is the
average of all
the subject?
a)76.251 b)80.25
c)74.265 d)74.625
Sol: total marks
of 8 subjects = 74*7 + 79 = 597
average = 597/8 =
74.625
PATTERN 65
Q)3 persons a,b,c
were there A always says truth,B lies on Monday,tusday,& Wednesday.but C
lies on thrusday,Friday & saturday
.one day A
said”that B & C said to A that” B said “yesterday way one of the days when
I lies”,C said that”yesterday way one of the
days when I lies
too”.then which day was that?
a)Sunday
b)Thursday c)Saturday d)Tuesday
Sol: If today is
Monday, Yesterday was Sunday. Now B should lie on monday so Sunday was NOT one
of the days he lies on...Correct.
And C shouldn't
lie on monday so sunday was one of the days he lies on....Incorrect. So it's
not Monday.
If today is
Tuesday, Yesterday was Monday. Now B should lie on Tuesday so Monday was NOT
one of the days he lies on...Incorrect.
So it's not
Tuesday.
If today is Weds,
Yesterday was Tue. Now B should lie on Weds so Tues was NOT one of the days he
lies on...Incorrect. So it's not
Weds.
If today is
Thurs, yesterday was Weds. Now B should NOT lie on Thurs so Weds was one of the
days he lies on....Correct. And C
should lie on
Thurs so Weds was NOT one of the days he lies on...Correct. So It's THURSDAY.
If today is Fri,
yesterday was Thurs. Now B should NOT lie on Fri so Thursday was one of the
days he lies on...Incorrect. So It's Not
Friday
If today is Sat,
yeterday was Fri. Now B should NOT lie on Sat so Fri was was one of the days he
lies on...Incorrect. So it's Not
Saturday.
If today is Sun,
yesterday was Sat. Now B should NOT lie on Sun so Sat was one of the days he
lies on...Incorrect. So it's NOT Sunday.
Answer: It was on
a Thurday
PATTERN 66
Q)Which is the
smallest no which divides 2880 and gives a perfect square?
a)4 b)9 c)3 d)5
Sol: ans d
PATTERN 67
Q)How many 9
digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by
4 if the repetition is allowed?
a)57 b)56 c)59
d)58
Q)how many 13
digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by
4 if repetition of digits is allowed?
Q)By using
1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation
of no. is allowed??
Q)Form 8 digit
numbers from by using 1, 2,3,4,5 with repetition is allowed and must be
divisible by4?
Q)How many of 14
digit numbers we can make with 1,2,3,4,5 that are divisible by 4. Repetitions
allowed.
PATTERN 68
Q)Consider two
tumblers, the first containing Water and next contains coffee. Suppose you take
one spoon of water out of the first
tumbler and pour
it into the second tumbler. After moving you take one spoon of the mixture from
the second tumbler and pour it
back into the
first tumbler . Which one of the following statement holds now?
a) There is less
coffee in the first tumbler than water in the second tumblers
b) There is more
coffee in the firs tumbler than water in the second tumbler
c) There is as
much coffee in the first tumbler as there is water in the second tumbler
d)None of the
statements holds true
Sol: Consider 100
mls volume of cup
First 100 mls of
ink goes in cola
total mixture in
2nd cup 1100 mls where 100 ink so ink concentration is 1/11
Now in 100 mls of
mixture 1/11 * 100 mls is ink and 10/11 * 100 mls is cola
10/11 * 100 mls
of ink is left in cola cup whereas we see 10/11 * 100 cola goin in ink cup
So same amount in
both cups
Q)Two bowls are
taken, one contains water and another contains tea.one spoon of water is added
to second bowl and mixed well,
and a spoon of
mixture is taken from second bowl and added to the second bowl. Which statement
will hold good for the above?
PATTERN 69
Q)Six friends
decide to share a big cake. Since all of them like the cake, they begin
quarreling who gets to first cut and have a piece
of the cake. One
friend suggests that they have a blindfold friend choose from well shuffled set
of cards numbered one to six. You
check and find
that this method works as it should simulating a fair throw of a die. You check
by performing multiple simultaneous
trials of picking
the cards blindfold and throwing a die. You note that the number shown by the
method of picking up a card and
throwing a real
world die, sums to a number between 2 and 12. Which total would be likely to
appear more often – 8,9 or 10?
a) 8 b)All are
equally likely c)9 d)10
Sol: 8 will have
higher probability as
for 8
(2,6) (6,2) (3,5)
(5,3) and (4,4)
which is greater
than 9 or 10
so answer is 8
PATTERN 70
Q)Given a
collection of points P in the plane , a 1-set is a point in P that can be
separated from the rest by a line, .i.e the point lies
on one side of
the line while the others lie on the other side. The number of 1-sets of P is
denoted by n1(P). The minimum value of
n1(P) over all
configurations P of 5 points in the plane in general position (.i.e no three
points in P lie on a line) is
a) 3 b)5 c)2 d)8
Sol:
C:\Documents and
Settings\vivek\Desktop\TCS Aptitude_files\image(1).do
C:\Documents and
Settings\vivek\Desktop\TCS Aptitude_files\image.do
Arrange points in
a circle..so answer is 5
PATTERN 71
Q)Anoop managed
to draw 7 circles of equal radii with their centres on the diagonal of a square
such that the two extreme circles
touch two sides
of the square and each middle circle touches two circles on either side. Find
the ratio of the radius of the circles to
the side of the
square.
a)1:(2+ 7v2)
b)(2+ 7v2):1
c)1:(4+ 7v3)
d)1:(2+ 6v2)
Sol: The extreme
circles will have radius perpendicular to sides..so the part of diagonal till
the centre of cirlce will be sqrt(2)r
[Make diagram and
it will be clear]..now remaining portion is r , 5 more circles will contribute
10r and last circle will contribute
sqrt(2)r + r.
total 12r +
2sqrt(2)r = sqrt(2) side
so ratio of r:s =
1/2+6sqrt(2)
Q)An orange glass
has orange juice. and white glass has apple juice. Both equal volume 50ml of
the orange juice is
taken and poured
into the apple juice. 50ml from the white glass is poured into the orange
glass. Of the two
quantities,
calculate the amount of apple juice in the orange glass and the amount of
orange juice in the white glass
Sol: To look
simple assume both glasses have 200ml juice.50ml orange from glass1 added to
apple in glass2. So
glass1 have 150ml
orange and glass2 have 250ml (200ml apple+50ml orange). In glass2 clearly, for
every 1 ml of
orange,there is 4
ml of apple. So if you take 50ml,there will be [40ml apple + 10ml orange].It is
added to glass1. Now
glass1 has [160ml
org + 40ml app]. Subtract the same amount from glass2, it will have[160ml app+
40ml org].But
see the question,
apple in orange glass= 40ml and orange in white glass=40ml.So both are equal.
Q)Alok and Bhanu
play the following min-max game. Given the expression N=40+X+Y-Z, where X, Y
and Z are
variables
representing single digits (0 to 9), Alok would like to maximize N while Bhanu
would like to minimize it.
Towards this end,
Alok chooses a single digit number and Bhanu substitutes this for a variable of
her choice (X, Y or
Z). Alok then
chooses the next value and Bhanu, the variable to substitute the value. Finally
Alok proposes the value
for the remaining
variable: Assuming both play to their optimal strategies,the value ofN at the
end of the game would
be:
Sol: Numbers from
0 to 9 [0 1 2 3 4 5 6 7 8 9]
1)Let alok choose
0, without thinking bhanu will place it in X or Y. (Since 0 is part of lower
values, see above)
2)So the
expression becomes 40+X-Z. Now if alok chose 9 bhanu will keep in Z. So it
becomes 31+X.Now alok will
choose 9 in order
to maximise. Now sum becomes 40. (Now Continued from step 2 only i.e after the
expression
became 40+X-Z.
Don't think of step 1. It is explained later below. ) But alok has better way.
He chose 5, then bhanu
places it in Z
(because 5 is a part of higher value). Expression becomes 35+X. Now alok will
choose 9. So final value
=44. Remember
that the max value and min value for the expression (X-Z) will always be 4 if
they play optimal
strategies.Try
keeping different values, you can get upto max of 44 only if they play optimal
strategies.
3)Now see step 1.
Alok can increase the value of Y upto 4.(Bhanu still places it in Y as it is
lower value) So he can get
upto 48.
4)Now first let
alok chose 5,
case i)Bhanu
places it in Z. Expression becomes 35+X+Y. Alok must choose two 9's to maximize.
So it is 35+18=53
case ii)Bhanu
places it in Y or X(doesn't matter). Now the expression becomes 45+X-Z.
Remember max or min value
of (X-Z) can be 4
only. So value of expression = 45+4=49. Clearly (case ii) is lower. So if alok
chose 5 bhanu
should place in X
or Y.
5)But alok is
clever. He chose 6 as first number. Follow step 4 again. You get 2 cases. Now
max value is 50.
6)Alok choses 7
as first number. Now see that the value becomes 51 in both cases of step 4. So
here bhanu can place
it in any
variable, it doesn't matter.
7)But if alok
chose 8 as his first number. (case i) of step 4 becomes 40+18-8 =50.So alok
does not use 8 at all. So 51
remains max value
for alok and min value for bhanu.
Q) Alice and Bob
play the following coins-on-a-stack game. 50 coins are stacked one above the
other. One of them is
a special (gold)
coin and the rest are ordinary coins. The goal is to bring the gold coin to the
top by repeatedly moving
the topmost coin
to another position in the stack. Alice starts and the players take turns. A
turn consists of moving
the coin on the
top to a position i below the top coin. We will call this an i-move (thus a
0-move implies doing
nothing). The
proviso is that an i-move cannot be repeated; for example once a player makes a
2-move, on
subsequent turns
neither player can make a 2-move. If the gold coin happens to be on top when
it's a player's turn
then the player
wins the game. Initially, the gold coins the third coin from the top. Then
a) In order to
win, Alice first move should be a 0-move.
b) In order to
win, Alice first move should be a 1-move.
c) Alice has no
winning strategy.
d) In order to
win, Alice first move can be a 0-move or a 1-move
Sol:
C:\Documents and
Settings\vivek\Desktop\TCS Aptitude_files\image(3).do
C:\Documents and
Settings\vivek\Desktop\TCS Aptitude_files\image(4).do
Look at the
figures and understand moves. All the moves shown here are with respect to
initial position onlySee that 0-move does nothing.
Let O stand for
an ordinary coin and G stand for the gold coin
Initially,
O1-O2-G-O3-O4-..-O20
Suppose Alice
does the 1-move. Then,
O2-O1-G-O3-O4-..-O20
Then Bob can
follow two paths
1. Bob does a
0-move
2. Bob does a
2-move or a higher move
1. If Bob does a
0-move, A cannot do a 1-move or 0-move. So, A would do a 2-move or a higher
move. Then,
O1-G-O3-..-O20
Bob then cannot
do a 0-move. So A wins
2. If Bob does a
2-move or higher, A would do a 0-move and win!
So, for A to win,
1-move is the best strategy!
Q)A circular
dashboard of radius 2.0 foot is at a distance of 20 feet from you. You throw a
dart at it and it hits the
dartboard at some
point Q in the circle. What is the probability that Q is closer to the center
of the circle than the
periphery?
Sol: Here the
distance 20 feet is irrelevant. Don't think of it. Now see the
diagram below:
Consider the
general situation i.e radius = r. Now we divide the dart board into two halves.
Any point in the inner
circle is clearly
closer to the center than perifery since we have divided the circle as r/2 and
r/2. The dart can hit at
any point in the
circle. So total sample space is whole area of the circle =
(pi)(r2)----------eq(1). Now we need to find
area of the inner
circle. Its (pi)*(r/2)2= (pi)*(r2/4)-----------eq(2). Probability is (required
event)/(sample space) =
eq(2)/eq(1) =
1/4=0.25.
thanx for the pattern,
ReplyDeleteplease post few more papers..
Thanks jam......
ReplyDelete