If abc 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Aug 12, 2020 6:24 pm

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If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =

A. (1 + bc)/(b + c)
B. (1 – bc)/(b + c)
C. (1 + b + c)/(bc)
D. (1 – b – c)/(bc)
E. (1 – b – c)/(b + c)

OA B

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Wed Aug 12, 2020 6:24 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If abc 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =

by Scott@TargetTestPrep » Sat Aug 15, 2020 3:52 am

BTGmoderatorDC wrote: ↑
Wed Aug 12, 2020 6:24 pm
If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =

A. (1 + bc)/(b + c)
B. (1 – bc)/(b + c)
C. (1 + b + c)/(bc)
D. (1 – b – c)/(bc)
E. (1 – b – c)/(b + c)

OA B

Solution:

We are given that 1/a + 1/b + 1/c = 1/abc and we need to solve a in terms of b and c. Multiplying the equation by abc, we have:

bc + ac + ab = 1

a(c + b) = 1 - bc

a = (1 - bc)/(b + c)

Answer: B

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