a2zinterviews

26.	There are two numbers such that the sum of twice the first and thrice the second is 39. while the sum of thrice the first and twice and the second is 36. The larger of the two is
	A.  4
	B.  8
	C.  9
	D.  11

Solution

Let the numbers be x and y. Then, 2x + 3y = 39 ----------(I) and 3x + 2y = 36 ---------(II) On solving (I) and (II), we get : x = 6 and y = 9. Therefore Larger number = 9.

27.	Two numbers differ by 5. If their product is 336, then the sum of the two numbers is
	A.  21
	B.  28
	C.  37
	D.  44

Solution

Let the numbers be x and y. Then, x - y = 5 and xy = 336. ‹=›(x + y)2 = (x - y)2 + 4xy ‹=›25 + 4 x 336 = 1369 ‹=›x + y = √1369 = 37.

28.	Twenty times a positive integer is less than its square by 96. What is the integer?
	A.  20
	B.  24
	C.  30
	D.  34

Solution

Let the numbers be x. Then, x2 - 20x = 96 = 0 ‹=›(x + 4)(x - 24) = 0. ‹=›x = 24. ‹=›x= 4.

29.	If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is
	A.  40
	B.  44
	C.  80
	D.  88

Solution

Let the numbers be x and y. Then, (x + y) = 22 and x2 + y2 = 404. ‹=› Now, 2xy = (x + y)2 - (x2 + y2) ‹=›(22)2 - 404 ‹=›484 - 404 = 80 ‹=›xy = 40.

30.	A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by
	A.  3
	B.  5
	C.  9
	D.  11

Solution

Let the ten's numbers be x, and unit's digit be y. Then, number = 10y + x. Number obtained by interchanging the digits = 10 y + x. Therefore (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.