# problems on numbers

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:
 A. 380 B. 395 C. 400 D. 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:
 A. 20 B. 23 C. 169 D. 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:
 A. 145 B. 253 C. 370 D. 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.
 A. 104 B. 114 C. 315 D. 325

Explanation:

Let the numbers be x and y.

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

4xy = (x + y)2 – (xy)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?
 A. 34 B. 38 C. 42 D. 46

Explanation:

Let the numbers be x and x + 2.

Then, (x + 2)2x2 = 84

4x + 4 = 84

4x = 80

x = 20.

The required sum = x + (x + 2) = 2x + 2 = 42.