Question

If x # y is defined for all integers by the equation above, and if x # y is 7, what is a possible value of x?

The answers given are 14, 7, 1, 49, and 3.

Answer 1

• A. 14

Explanation:

Given

• x#y = 1/(1/x + 1/y)

This is symmetrical for x and y, so

• y#x = 1/(1/y + 1/x) is same as above

If x#y = 7, then:

• 7 = 1/(1/x + 1/y)
• 1/(1/7) = 1/(1/x + 1/y)
• 1/7 = 1/x + 1/y

Possible value of x is 14, then y = 14 as well:

• 1/7 = 1/14 + 1/14
• 1/7 = 2/14
• 1/7 = 1/7

Correct choice is A