Source: Official Guide for the GMAT 12th Ed. Section 6.3 Data Sufficiency; #95

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# Is rst = 1?

Is rst = 1? (1) rs = 1 (2) st = 1 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

### 2 Explanations

1

Hello,

Why can't we subtract rs=1 from st=1? This would give us rs-st=0. From here we could get s(r-t)=0 and therefore s=0 and t=r. Either way we know that rst does not equal 1. I'm confused as to why the answer is not C. Would appreciate any help. Thanks.

Jan 2, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Subtracting one equation from the other is actually OK to do. And you're correct that after subtracting, we can factor out an s, leaving us with the following expression.

s(r-t) = 0

While this algebra gives us two possible answers (s=0 or r-t =0), before concluding that these are two valid solutions, it's necessary to check these responses against the initial conditions of the question. Since we have combined the statements, we must consider both:

1. rs = 1
2. st = 1

In both cases, s?0. If s=0, then the product of s with any number would also have to equal 0. However, statements 1 and 2 indicate that the product of s and another number is not 0. Based on this analysis, we can determine that the possible solution s=0 is not a valid solution for the problem. We are therefore left with the other solution, r-t = 0, from which we can conclude that r=t. Since r and t can equal any number, as long as they equal the same number, we cannot say for sure if rst=1.

I hope this helps :) Mike McGarry, Magoosh Tutor