# Numbers Questions

Q:

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

 A) n is odd B) n + 1 cannot be a prime number C) (n + 2) divided by 7 has remainder 2 D) n + 3 is divisible by 5

Answer & Explanation Answer: D) n + 3 is divisible by 5

Explanation:

You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 7 , 12, 17, 22 etc.

From this series we can see that n does not have to be odd.

Also n + 1 can be a prime because, for example, 12 + 1 = 13

And (n + 2) / 7 has a remainder 2 in some cases but not all.

Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases. However, adding 3 to any of the values of n will always give a multiple of 5.

0 3214
Q:

 A) 961 x 861 B) 961 x 961 C) 961 x 2 D) 29791

Explanation:

We know that ${a}^{m}×{a}^{n}={a}^{m+n}$

$\therefore {\left(31\right)}^{31-27}$ = ${31}^{4}$ = 961 x 961.

Filed Under: Numbers - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank PO

6 3150
Q:

x = y - (50/y), where x and y are both > 0

If the value of y is doubled in the equation above, the value of x will

 A) decrease B) stay the same C) increase four fold D) increase to more than double

Explanation:

The best approach is to pick a number that satisfies the rules that x and y are greater than 0. So for example you could choose 25 for y.

The value of x before doubling is then 25 - 50/25 = 23

The value after doubling y will be 50 - 50/50 = 49, which is more than double.

0 3133
Q:

If

 A) 144 B) 72 C) 36 D) 24

Explanation:

a4 = a2 x a2 = 12 x 12 = 144

1 3099
Q:

Find the next number in the series 125, 80, 45, 20, ....

 A) 5 B) 15 C) -5 D) 10

Explanation:

The pattern is -45, -35, -25, -15

The next number = 20-15= 5

14 3083
Q:

A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot).

 A) 17 B) 18 C) `19 D) 20

Explanation:

The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P).

Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17

2 2919
Q:

Find the unit digit of 4198 + 612345 + 34866 + 2411 + 1.

 A) 3 B) 2 C) 1 D) 0

Explanation:

Given that, ${4}^{198}+{6}^{12345}+{348}^{66}+{24}^{11}+1$

Now Power Cycle of

4 is 4, 6

6 is 6

8 is 8, 4, 2, 6

1 is 1

${4}^{198}$- 198 is even number , So the unit digit value is 6

${6}^{12345}$ - It is always 6

${348}^{66}$-  66/4 the remainder is 2 , So the second value is 4

${24}^{11}$- 11 is odd number, So the unit digit value is 4

1 - It is always 1

Total = 21

Therefore, The unit digit is 1

Filed Under: Numbers - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank PO

6 2729
Q:

Find the next number in the series 14, 916, 2536,......

 A) 4981 B) 6481 C) 4964 D) 6449

$\therefore$The next number= = 4964