A. \(\frac{2}{15}\)

B. \(\frac{48}{5}\)

C. \(15\)

D. \(42\)

E. \(60\)

The OA is C

**Source: Manhattan Prep**

00:00

**A**

**B**

**C**

**D**

**E**

Two positive numbers differ by \(12\) and their reciprocals differ by \(\frac{4}{5}\). What is their product?

A. \(\frac{2}{15}\)

B. \(\frac{48}{5}\)

C. \(15\)

D. \(42\)

E. \(60\)

The OA is C

**Source: Manhattan Prep**

A. \(\frac{2}{15}\)

B. \(\frac{48}{5}\)

C. \(15\)

D. \(42\)

E. \(60\)

The OA is C

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**13519**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1256 members**GMAT Score:**770

swerve wrote:Two positive numbers differ by \(12\) and their reciprocals differ by \(\frac{4}{5}\). What is their product?

A. \(\frac{2}{15}\)

B. \(\frac{48}{5}\)

C. \(15\)

D. \(42\)

E. \(60\)

The OA is C

Source: Manhattan Prep

Let x = the smaller number

So x + 12 = the larger number

NOTE: our goal is to find the value of

We get: 1/x - 1/(x+12) = 4/5

Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5

Multiply both sides by 5 to get: 5 - 5x/(x + 12) = 4x

Multiply both sides by (x + 12) to get: 5(x + 12) - 5x = 4x(x +12)

Expand left side to get: 5x + 60 - 5x = 4x(x +12)

Simplify left side to get: 60 = 4x(x +12)

Divide both sides by 4 to get: 15 =

Answer: C

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

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- Scott@TargetTestPrep
- GMAT Instructor
**Posts:**3997**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**20 members

We can create the equations:swerve wrote:Two positive numbers differ by \(12\) and their reciprocals differ by \(\frac{4}{5}\). What is their product?

A. \(\frac{2}{15}\)

B. \(\frac{48}{5}\)

C. \(15\)

D. \(42\)

E. \(60\)

The OA is C

Source: Manhattan Prep

x - y = 12

and

1/y - 1/x = 4/5 (notice that x > y, so 1/y > 1/x)

Let's multiply the second equation by xy, and we have:

x - y = (4/5)xy

Since x - y = 12, we have:

12 = (4/5)xy

Multiplying both sides by 5/4, we have:

15 = xy

Answer: C

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