# Numbers Questions

Q:

Which one of the following cannot be the square of a natural number?

 A) 32761 B) 42437 C) 81225 D) 20164

Explanation:

The square of a natural number never ends in 7.
42437 is not the square of a natural number

31 24151
Q:

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x+y is equal to  ?

 A) 5 B) 4 C) 3 D) 2

Explanation:

Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.

28 23901
Q:

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

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

Explanation:

The pattern is

$∴$The next number= = 4964

52 22954
Q:

A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?

Number = ( 779 x a) + 47, where "a" is the quotient

= (19 x 41 x a) + (19 x 2) + 9

= 19 x (41a + 2) + 9

= 19 x (New quotient) + 9

Required remainder = 9

22905
Q:

How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?

 A) 7 B) 9 C) 11 D) 5

Explanation:

LCM of 2, 3, 7 is 42.

=> (700 – 300)/42 = 9  22/42 => 9 Numbers.

30 21471
Q:

The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :

 A) 3/5 B) 3/10 C) 4/5 D) 5/4

Explanation:

Let the required fraction be x. Then, (1 / x )- x = 9/20
1 - x^(2) / x = 9 / 20  =>  20 - 20 * x^(2) = 9 * x.
20 * x^(2) + 9 *x - 20 = 0.
=> (4 * x + 5) (5 * x - 4) = 0.
=> x = 4 / 5.

34 19764
Q:

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

 A) 2 B) 3 C) 4 D) 5

Explanation:

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

15 19073
Q:

The sum of the two numbers is 12 and their product is 35.What is the sum of the reciprocals of these numbers?

 A) 12/35 B) 1/35 C) 35/8 D) 7/32

Explanation:

Let a and b are the numbers.Then a+b is 12 and ab is 35.

a+b/ab = 12/35

1/b + 1/a = 12/35