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# Numbers Questions

Home > Quantitative Aptitude > Numbers > General Questions
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Find the smallest number which leaves 22,35, 48 and 61 as remainders when divided by 26, 39, 52 and 65 respectively.

A886

B776

C786

D675

Explanation:

26-22=4
39-35=4
52-48=4
65-61=4
LCM of (26,39,52,65)=780
So smallest number = (780-4) = 776

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Which of the following numbers are completely divisible by 11?
A. 3245682
B. 283712
C. 438416
D. 36894

AOnly A

BOnly B

COnly C

DOnly D

EAll are divisible

Explanation:

Note: If the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.

[(Sum of digits at odd places) - (Sum of digits at even places)]/11
=> [(3+4+6+2) - (2+5+8)]/11 => (15 - 15)/11 = 0/11 = 0
similarly others number are divisible by 11

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The product of two positive numbers is p. If each of the numbers is increased by 2, the new product is how much greater twice the sum of the two original numbers?

A3

B4

C5

D2

Explanation:

Lets assume number are x,y
So, there product = xy
Given number increased by 2
so, now number are x+2,y+2.
Given product is twice the sum of two original No.
=> product = (x+2)(y+2) = 2(x+y)
=> xy+2x+2y+4 =2(x+y)
=> xy+4
so it increase by 4

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A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?

A8

B9

C10

D11

Explanation:

1 yard = 3 feet = 3*12 = 36 inches
4 yard = 4*36 = 144 inches
The maximum number of bows will be 4 yards divided by 15 inches = 144/15 = 9.6

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A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

A18

B24

C42

D81

Explanation:

Check the options, by subtracting 18 from each option for getting reverse number.
42 - 18 = 24 (which is in reverse)

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What is the unit digit in (27)^20

A1

B5

C12

D20

Explanation:

unit digit of 27 is 7 having power 20
which means 4n.
=> 7^20=1

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what is the least number by which 16,800 must be divided to get a number perfect square

A21

B42

C24

D40

Explanation:

16,800/42=400
400=(20)^2

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what is least perfest square. which is divisible by 24, 30,60?

A1600

B3600

C14400

D32400

Explanation:

lcm of 24,30,60 is 120

The least prefect square divided by 24,30 60 is 3600

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Which one of the following numbers is exactly divisible by 11?

A235641

B245642

C315624

D415624

Explanation:

Note: If the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11. [(Sum of digits at odd places) - (Sum of digits at even places)]/11.
4+5+2 = 11 and 1+6+4 = 11 . Then 11-11 =0.

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What should be multiplied to 2880 to make it a perfect square?

A3

B5

C2

DNone of these

Explanation:

Note: To make perfect square, all the powers of prime factors should be even.
2880 = 2^6 * 3^2 * 5
So, In 2880 powers of prime factors 2 and 3 are even.
But power of prime factor 5 is 1, which is odd.
So, to make it a perfect square we need to multiply number by 5.

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