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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Thu Oct 15, 2020 10:49 am

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Source: 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

The OA is C

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Source: Beat The GMAT — Problem Solving | Thu Oct 15, 2020 10:49 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sat Oct 17, 2020 12:16 pm

BTGmoderatorLU wrote: ↑
Thu Oct 15, 2020 10:49 am
Source: 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

The OA is 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

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