# Aptitude - Problems on Numbers

Exercise : Problems on Numbers - General Questions
11.
The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
380
395
400
425
Explanation:

Let the numbers be x and y.

 Then, xy = 9375 and x = 15. y

 xy = 9375 (x/y) 15 y2 = 625. y = 25. x = 15y = (15 x 25) = 375. Sum of the numbers = x + y = 375 + 25 = 400.

12.
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
20
23
169
None of these
Explanation:

Let the numbers be x and y.

Then, xy = 120 and x2 + y2 = 289. (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529 x + y = 529 = 23.

13.
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
145
253
370
352
Explanation:

Let the middle digit be x.

Then, 2x = 10 or x = 5. So, the number is either 253 or 352.

Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.

Hence, required number = 253.

14.
The sum of two number is 25 and their difference is 13. Find their product.
104
114
315
325
Explanation:

Let the numbers be x and y.

Then, x + y = 25 and x - y = 13.

4xy = (x + y)2 - (x- y)2

= (25)2 - (13)2

= (625 - 169)

= 456 xy = 114.

15.
What is the sum of two consecutive even numbers, the difference of whose squares is 84?
34
38
42
46 4x + 4 = 84 4x = 80 x = 20. The required sum = x + (x + 2) = 2x + 2 = 42.