If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the re

Question

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)

Kudos for a correct  solution .

sunnysid · Answer

(1/a)+(1/b)+(1/c) = 1/abc

(bc+ac+ab)/abc = 1/abc ---> bc+ac+ab=1 ---> ac+ab = 1-bc ---> a(b+c)= 1-bc ---> a= (1 - bc)/(b+c)

Ans- B

GMATinsight · Answer

(1/a)+(1/b)+(1/c) = 1/(a*b*c)

i.e. (bc+ac+ab)/abc = 1/abc

i.e. bc+ac+ab=1

i.e. ac+ab = 1-bc

i.e. a(b+c)= 1-bc

i.e. a= (1 - bc)/(b+c)

Answer: option B

kunal555 · Answer

\frac{1}{a}  +  \frac{1}{b}  +  \frac{1}{c}  =  \frac{1}{abc}

or  \frac{bc + ac + ab}{abc}  =  \frac{1}{abc}

or  ac + ab  =  1 - bc

or  a(c+b)  =  1 - bc

or  a  =  \frac{(1-bc)}{(b+c)}

Answer:- B

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

First, translate the given information into an equation. Go phrase by phrase. The sum of the reciprocals of a, b, and c is 1/a + 1/b + 1/c. Notice that you first take reciprocals, then you add the reciprocals together.

Now, set that equal to “the reciprocal of the product of a, b, and c,” which is 1/(abc). Notice that we first take the product of a, b, and c (which is abc), and then take the reciprocal of that product.

The equation is this:
1/a + 1/b + 1/c = 1/(abc)

Now rearrange to isolate a on one side. Make a common denominator on the left side (abc), so that you can add the fractions:
1/a + 1/b + 1/c = bc/(abc) + ac/(abc) + ab/(abc) = (bc + ac + ab)/(abc)

Since the right side of the original equation is 1/(abc), which happens to have the same denominator, you can set the numerators equal:

bc + ac + ab = 1

Now solve for a:

ac + ab = 1 – bc
a(c + b) = 1 – bc
a = (1 – bc)/(c + b)

Theoretically, you can solve this problem by plugging numbers for the variables, but finding three consistent values of a, b, and c (to satisfy the complicated condition) is rather difficult. A pure algebraic approach is faster and more secure in this case.

The correct answer is B.

ScottTargetTestPrep · Answer

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

If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the re

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If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the re

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