Two positive numbers differ by 12 and their reciprocals differ by 4/5

Question

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

PareshGmat · Accepted Answer

Answer = C = 15

Let the integers be a & b

a>b

so,  \frac{1}{a} < \frac{1}{b}

a - b = 12

\frac{1}{b} - \frac{1}{a} = \frac{4}{5}

\frac{a-b}{ab} = \frac{4}{5}

ab = \frac{5*12}{4} = 15

82vkgmat · Answer

If 2 numbers are x and y --> y-x = 12, 1/x-1/y = 4/5
So (y-x)/xy= 4/5.
xy = 12*5/4 = 15.

Answer = C.

Ankur9 · Answer

let two positive numbers be x and x+12.
Need to find the product x(x+12)
then 1/x - 1/(x+12) = 4/5
solve to get 12/x(x+12) = 4/5 ----> x(x+12) = 15
Hence C

devmillenium2k · Answer

Let's assume two numbers are x and y -->
As per the question
 y-x = 12, 
1/x-1/y = 4/5 =>(y-x)/xy= 4/5.
Put the value of y-x
xy = 12*5/4 = 15.

Answer C.

Bunuel · Answer

Official Solution:

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

Don’t be afraid to assign variables even when none are given in the problem. "Two positive numbers differ by 12" can be written as:
  x - y = 12 
 
And "their reciprocals differ by  \frac{4}{5} " can be written as:
  \frac{1}{y} - \frac{1}{x} = \frac{4}{5} 
 
(Note: Here, we’ve assigned  x  as the bigger of the two numbers and  y  as the smaller, so we’ve intuited that  \frac{1}{y}  is the larger reciprocal and  \frac{1}{x}  the smaller, and so arranged them in that order to write  \frac{1}{y} - \frac{1}{x} = \frac{4}{5} ).
 
Now we have a system of two variables and two equations. Note that it is NOT necessary to solve for  x  and  y , since we are being asked for the product,  xy .
 
First, let’s simplify the second equation by finding a common denominator for the terms on the left:
  \frac{x}{xy} - \frac{y}{xy} = \frac{4}{5} 
  \frac{x - y}{xy} = \frac{4}{5} 
 
Note that the denominator is  xy , which is exactly the quantity we want to find.
 
Since we know from the first equation that  x - y = 12 , substitute 12:
  \frac{12}{xy} = \frac{4}{5} 
  60 = 4xy 
  15 = xy 
 
Answer: C.

stonecold · Answer

Another great question...
the only thing to lookout here is that if x>y => 1/x<1/y (for both x>0 and y>0)

FB2017 · Answer

Considering x>y and they are the two numbers.

Solve 1/y-1/x=4/5 which will give x-y/xy=4/5 ->eqtn 1.
Now plug in x-y=12 from problem statement.
Solve for xy in eqtn 1.

Option C.

ayushkumar22941 · Answer

let the two number be x and y , from question we get x-y=12
now 1/x -1/y =4/5 
solving this by putting value of x-y=12 we get xy=15

akadiyan · Answer

Very good question indeed, looks simple not only to answer, but also get the question wrong. I overlooked the simple fact mentioned below and chose the wrong answer choice.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Two positive numbers differ by 12 and their reciprocals differ by 4/5

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Two positive numbers differ by 12 and their reciprocals differ by 4/5

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards