If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

[AAPL]

Magoosh

If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

A. 5/24
B. 5/16
C. 16/5
D. 25/4
E. 45/4

OA C

[Scott@TargetTestPrep]

Magoosh

If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

A. 5/24
B. 5/16
C. 16/5
D. 25/4
E. 45/4

OA C

Solution:

We can let the two numbers be a and b, and we need to find ab. We can create the equations:

a + b = 6

and

1/a + 1/b = 15/8

Simplifying the second equation, we have:

b/ab + a/ab = 15/8

(b + a)/ab = 15/8

Since b + a = a + b = 6, we have:

6/ab = 15/8

15ab = 48

ab = 48/15 = 16/5

Answer: C