TCS Questions – 10
1.
In a 400 meters race A gives B a start of 7
seconds and beats him by 24 meters. In another race of same distance A beats B
by 10 seconds. The speeds of A and B are in what ratio?
Answer:
10 : 8
In the first race after giving a start of 7
seconds to B, A beats him by 24 meters.
In the second race without any start to B,
A beats him by 10 seconds. Comparing the two we observe that in a time of 3
seconds B runs 24 meters or in one second B runs 8 meters.
Hence for covering 400 meters B would have
taken 400/8 = 50 seconds.
But, A beats B by 10 seconds. Hence the
time taken by A to cover the distance of 400 meters was 50 – 10 = 40
seconds. Thus the speed of A was 400 /
40 = 10 meters/ sec.
The
ratio of speed between A and B is 10 : 8
2.
What is the maximum number of half-pint bottles
of cream that can be filled from a 4 gallon can of cream? ( 2 pints = 1 quarter
and 4 quarters makes one gallon)
Answer:
64
4 Gallons equals 4 * 4 = 16 quarters. 16 quarters equals 16 * 2 = 32 pints. No of half pint bottles equals 32 * 2 = 64.
3.
If the operation ^ is defined by the
equation x ^ y = 2x + y, then what is
the value of ‘a’ in the equation 2 ^ a =
a ^ 3.
Answer:
1
X ^ y = 2x + y applying this we have 2 ^ a = 2*2 + a = 4 +
a (i)
We are informed that 2 ^ a = a ^ 3
Based on the main equation, a ^ 3 will be 2 * a +3 = 2a + 3 (ii)
From
(i) and (ii) we can arrive the value of ‘a’ as 1
4.
If the price of an item is decreased by 10% and
then increased by 10%, the net effect of the change on the price of the item is
how much?
Answer:
Decrease of 1%
The answer can be arrived by using the
successive percentage change formula. The net effect in percentage change of an
item when increased/decreased first by x% and then decreased/increased by y% is given by the formula:
Effective percentage change is x + y + xy/100. Applying the information in the question we have the value – 1% (decrease)
5.
If ‘m’ is an odd integer and ‘n’ an even
integer, which of the following is definitely odd?
a)
(2m+n)(m-n) b) (m+n^2)+ (m-n^2) c) m^2 + mn + n^2 d)
m + n
Answer: both (c) and (d)
Remembering the following may be
of some help:
Odd ± Odd = Even, even ± even = even, odd ± even = odd
Odd * Odd = Odd, even * even = even, even * odd = even
6.
All faces of a cube with an eight inch edge are
painted red. This cube is cut into smaller cubes of two inches. How many of the
smaller cubes will have paint on exactly one face?
Answer: 24 The following will help the
reader in answering questions of this type.
Total number of small cubes n^3
(where ‘n’ is the number into which
the main cube is cut)
In the above question an eight inch edge cube is cut
into 4 smaller two inch edge cubes.
Hence the number of cubes is 4 ^ 3 = 64.
Smaller cubes that are coloured on three sides will
always be 8
( the top four corner pieces and the bottom four
corner pieces)
Number f cubes coloured on two
sides is given by 12 (n-2)
Number of cubes coloured on one
surface is given by 6 * (n-2)^2
Number of cubes having no
colouring at all is given by (n-2)^3
On the above basis the answer for the question is 12 * (4 – 2) = 24.
7.
Two cyclists are training on an oval track. One
of the cyclist the professional takes 4 minutes for completing a full lap. The
other cyclist , the learner takes 6 minutes to complete a lap. After how much
time the two cyclists will again meet each other at the starting point?
Answer:
12 minutes.
The professional will reach the starting point
after every 4 minutes.
The learner will reach the starting point
after every 6 minutes. Thus,
The Professional will be at the starting point after - 4,
8, 12, 16, 20 …. Minutes.
The learner will be at the starting point
after -- 6, 12, 18, 24, ………… Minutes.
From the above it could be seen that after
12 minutes both the cyclists are at the staring point.
8.
M, N, O, and P are different individuals. M is
the daughter of N. N is the son of O. O is the father of P. Among the following
statements which one is true?
a)
M is the daughter of P
b)
If B is the daughter of N, then M & B are
sisters.
c)
If C is the grand-daughter of O, then C and M
are sisters.
d)
P and N are brothers.
Answer: B ( Please draw
a family tree and arrive at the answer)
9.
The sequence {An} is defined by A1 =
2 and An+1 = An + 2n then what is the value of A100 ?
Answer:
9902
We know
A1 = 2 and An+1 = 2n
Hence,
A2 = A1 + 1 =
2 + 2(1) = 4
A3 = A2 + 1 = 4 + 2(2)
= 8
A4 = A3 + 1
= 8 + 2(3) = 14
Thus the terms goes like 2, 4,
8, 14, 22, …….
The differences between the terms goes like 2,4,6,8, ………….. The series is like a quadratic equation.
Suppose:
An = an2 + bn + c then we have A1 = a + b
+ c = 2
A2
= 4a + 2b + c = 4
A3
= 9a + 3b + c = 8
Solving these three we get values for a = 1,
b = -1, c = 2
An = an2 + bn +
c substituting the values of a, b and c
in the equation
We have An = n2 – n +
2 Now substituting 100 in the place of ‘n’ we get the value
A100
= 10000 – 100 + 2 = 9902
10.
Find the number of rectangles ( a square is also
considered as a rectangle) in the following figure.
Answer: 1638
There are 13 vertical lines and 7
horizontal lines. For forming a rectangle, two horizontal lines and two
vertical lines are required.
The two horizontal lines can be selected in
7C2 ways…..21 ways
The two vertical lines can be selected in
13C2 ways …… 78 ways.
Thus the total number of rectangles in the
above figure is 7C2 * 13C2 = 21 * 78 = 1638
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