Aptitude - Problems on Numbers
Overview Exercise "Nothing is impossible to a willing heart."
- (Proverb)
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:
Answer: A
Explanation:
Let the numbers be x and y .
Then, x y = 9375 and
x = 15.
y
y 2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
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:
Answer: C
Explanation:
Let the numbers be x and y .
Then, x y = 120 and x 2 + y 2 = 289.
x + y )2 = x 2 + y 2 + 2x y = 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:
Answer: A
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.
Answer: C
Explanation:
Let the numbers be x and y .
Then, x + y = 25 and x - y = 13.
4x y = (x + y )2 - (x - y )2
= (25)2 - (13)2
= (625 - 169)
= 456
x y = 114.
15.
What is the sum of two consecutive even numbers, the difference of whose squares is 84?
Answer: E
Explanation:
Let the numbers be x and x + 2.
Then, (x + 2)2 - x 2 = 84
x + 4 = 84
x = 80
x = 20.
x + (x + 2) = 2x + 2 = 42.
y2 = 625.
Sum of the numbers = x + y = 375 + 25 = 400.