CDAC CAT SectionA Practice Questions

1. If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true?

A. n is even

B. n is prime

C. n is a perfect cube

D. n is odd

Show Answer ?

Answer : n is odd.

Explination:

For example, take 1,2,3,4,5 numbers which are consecutive.
2,4 are even which gives even result when multiplied.1,3,5 are odd which gives odd result when multiplied.
even *odd=even
so

$1 \cdot 2 \cdot 3 \cdot 4 \cdot 5$ $1*2*3*4*5$ =even number
even + 1 =odd number

2. A ladder is touching a wall and the base of the ladder is 15 m away from the wall. When the ladder is pulled away from the wall by 2 m, it becomes parallel to the ground. Find the distance of the initial point of contact of the ladder and the wall from the ground.

A. 10m

B. 8m

C. 12m

D. 17m

Show Answer ?

Answer : 8m.

Explination:

From the question height of the ladder becomes 15+2=17m
Formula :

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$
a=15,c=17

$b^{2} = 289 - 225$ $b^2=289-225$
b=8

3. Find the number of numbers from 1 to 100 that are divisible by 2 or 3 or 5

A. 68

B. 74

C. 71

D. 103

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4. In a party of 40 people, everyone shakes hands with all the other persons exactly once. What is the total number of handshakes happening?

A. 780

B. 820

C. 40!

D. None of these

Show Answer ?

Answer : 780.

Explination:

Suppose there were ‘n’ people.
Then each shook hands with (n-1) people.
Formula:

$n \frac{n - 1}{2}$ $n(n-1)/2$ keep n=40

$2^{73} - 2^{72} - 2^{71}$
$2^73 – 2^72 – 2^71$ is the same as

A. 2^69

B. 2^70

C. 2^71

D. 2^72

Show Answer ?

Answer : 2^71.

Explination:

$2^{71} \cdot (2^{2} - 2^{1} - 2^{0}) = 2^{71} \cdot (1) = 2^{71}$ $2^71*(2^2-2^1-2^0)=2^71*(1)=2^71$

Ans:

$2^{71}$ $2^71$

6. How many 3 digit even numbers can be formed such that if one of the digits is 5, then the next digit is 7?

A. 5

B. 9

C. 365

D. 15

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7. Find the least number which when divided by 5 and 9 will leave remainders of 3 and 7 respectively.

A. 47

B. 88

C. 43

D. 92

Show Answer ?

Answer : 43.

Explination:

Try trail and error method
If you take a number its last digit should give a number that is divisible by 5 when subtracted or added with 3
take 88-3=85
and

$\frac{88}{9}$ $88/9$ gives a remainder of 7
But in question they asked for least number
so, try with 43

$\frac{43}{5}$ $43/5$ gives remainder 3 and

$\frac{43}{9}$ $43/9$ gives remainder 7.

8. In a 300m race, A beats B by 24m or 6 seconds. Find the time taken by A to finish the race.

A. 75 sec

B. 81 sec

C. 69 sec

D. 60 sec

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9. A tank can be filled in x hours, but because of a leak, it takes 40 hours to fill the tank. Find x if the leak can empty the tank in 60 hours.

A. 30

B. 24

C. 36

D. 20

Show Answer ?

Answer : 24.

Explination:

Let the work done by tank A in one hour is

$\frac{1}{x}$ $1/x$ .
and work done by leak in one hour is

$\frac{1}{y}$ $1/y$ .

$\frac{1}{x} - \frac{1}{y} = \frac{1}{40}$ $1/x-1/y=1/40$
given y=60

$\frac{1}{x} - \frac{1}{60} = \frac{1}{40}$ $1/x-1/60=1/40$
x=24

10. X, Y and Z have a total of Rs.224 with them. If their shares are increased by Rs.5, 9 and 2 respectively, then the ratio of their amounts is 3:2:1. Find the original amount with Y.

A. Rs.71

B. Rs.115

C. Rs.38

D. Rs.120

Show Answer ?

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