The sum of the reciprocals of two numbers is 46/21 and the

Question

The sum of the reciprocals of two numbers is 46/21 and the difference of their reciprocals is 10/21. What are the 2 numbers?

(A) 3, 3/29

(B) 3/4 , 7/6

(C) 4/3, 6/7

(D) 8/21, 5/21

(E) 1/21, 1/21

Please provide workings

ncp · Answer

B.

1/x+1/y=46/21

1/x-1/y=10/21

Adding, 2/x=56/21=2"28/21

1/x=28/21 => x=3/4

B is the only choice that contains 3/4.

wshaffer · Answer

I did it a little differently. You know that the reciprocal of a number n is one divided by n. You also know that the LCD is 21. I looked for numbers whose numerators had LCD 21 (because they'd be divided by 1) and B is the only pair that fits (3/4 and 7/6). On test day I'd probably reason it out that way, but if you want to work it out:

1/(3/4) + 1/(7/6) = 4/3 + 6/7 = 28/21+18/21 = 46/21
1/(3/2) - 1/(7/6) = 4/3 - 6/7 = 28/21-18/21 = 10/21

enola · Answer

Thanks for sharing the trick. it really cuts back a lot on time

anindyat · Answer

If we multiply the numerators of the options ...only B yields 21 = 3 * 7
21 is the denominator of both the sum and difference

yogeshsheth · Answer

1/x+1/y=46/21 and 1/x-1/y =10/21
Solving these two we get x/y=9/14
The only option that satisfies this ratio is B.
Thus B is the answer

The sum of the reciprocals of two numbers is 46/21 and the

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