Number Problems - Quantitative Aptitude, Arithmetic Ability Questions and Answers

Q:

How many prime numbers exist in $6^{5}\times 35^{9}\times 11^{3}$ ?

A) 29	B) 31
C) 33	D) 27

Answer & Explanation Answer: B) 31

Explanation:

Given $6^{5}\times 35^{9}\times11 ^{3}$

$\Rightarrow \left ( 2\times 3\right )^{5} \times \left ( 5\times 7\right )^{9} \times11^{3}$ $\small \Rightarrow2 ^{5}\times 3^{5}\times 5^{9}\times 7^{9}\times11 ^{3}$

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

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Q:

Find the remainder when 1234 x 1235 x 1237 is divided by 8.

A) 4	B) 2
C) 0	D) 6

Answer & Explanation Answer: D) 6

Explanation:

When we divide 1234 by 8, remainder is 2

When we divide 1235 by 8, remainder is 3

When we divide 1237 by 8, remainder is 5

$\Rightarrow 2\times 3\times 5=30$

As 30 will not be the remainder because it is greater than 8,

when 30 divided by 8, remainder = 6.

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Q:

The largest 4 digit number exactly divisible by 88 is ?

A) 9944	B) 9768
C) 8888	D) 9988

Answer & Explanation Answer: A) 9944

Explanation:

The largest 4 digit number is = 9999
After dividing 9999 with 88, we get 55 as remainder
so largest 4 digit number divisible by 88 = 9999-55 = 9944.

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Q:

A number divided by 296 leaves the remainder 75. If the same number is divided by 37, what will be the remainder ?

A) 0	B) 1
C) 11	D) 8

Answer & Explanation Answer: B) 1

Explanation:

Let x be the number.

Given: x = 296n + 75 [where n is quotient]

$\small \Rightarrow$ (378n) +( 372 + 1)
$\small \Rightarrow$ 37(8n + 2) + 1
Hence, when x divided by 37, 1 is the remainder.

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Q:

What will come in place of the question mark (?) in the following questions ?

22% of ? + 166.64 = 340

A) 788	B) 786
C) 784	D) 792

Answer & Explanation Answer: A) 788

Explanation:

(kx22)/100 = 340 - 166.64 = 173.36
k = (173.36 x 100)/22
k = 788

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