a2zinterviews

11.	The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
	A.  3
	B.  4
	C.  9
	D.  None of these

Solution

Let the ten's digit be x and unit's digit be y. Then, (10x+y) - (10y+x) = 36. ‹=› 9(x - y) = 36 ‹=› x - y = 4.

12.	The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals?
	A.  1/40
	B.  8/75
	C.  75/4
	D.  75/8

Solution

Let the numbers be x and y. Then, x + y = 40 and xy = 375. Therefore, 1/x + 1/y ‹=› x + y / xy. ‹=› 40/375. = 8 / 75.

13.	If the sum of a number and its square is 182, what is the number?
	A.  15
	B.  26
	C.  28
	D.  None of these

Solution

Let the numbers be x . Then, x + x2 = 182 ‹=›x2 + x - 182 = 0 ‹=›(x + 14) (x - 13) = 0 ‹=› x = 13.

14.	The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?
	A.  4
	B.  6
	C.  8
	D.  16

Solution

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 ‹=› 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) ‹=›2x = 8.

15.	Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
	A.  1
	B.  3
	C.  5
	D.  9

Solution

Let the numbers be x . Then, 7x - 15 = 2x + 10 ‹=›5x = 25 ‹=› x = 5. Hence the required number is 5.