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555-605 Level|   Algebra|                        
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Could someone comment on the validity of this solution?

Is rst = 1 ?

(1) rs = 1
(2) st = 1

It's clear to me why either statement alone is insufficient.

However, when combining them t pick between C or E, I substituted the value or r from statement 1 (r = 1/s) into statement 2... essentially, I got both s and t in terms of r.that is, s = 1/r and t = r.

This makes the product rst = r (1/r) (r) = r. This led me to picking E as the answer. Is this valid? All solutions of this question point towards creating tables with counter examples.
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Hi petsitter,

To answer your immediate question: Yes - your Algebraic approach is valid on this question.

You're going to find that most GMAT questions can be approached in more than one way - and sometimes the 'math approach' to a Quant question can be inefficient (meaning that there could be an easier, faster way to get to the correct answer). It's important to remember that the Quant section of the GMAT is NOT a 'math test'; it's a critical thinking test that requires lots of little calculations as you work through it. Thus, to maximize your performance on this section, you should work to develop all of your Quant skills.

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Is r * s * t = 1? Note that r, s, and t can take the value of 1, but also other values. I.e. : 1/2, 2, 1.

1) We cannot say what t is, so insuff.
2) We cannot say what r is, so insuff.

Combined we have:
s=1/r
s=1/t

Assume r=2, then we have:
r=2, s = 1/2, t= 2 to yield 2.

Alternately r,s,t could all be 1, to yield 1.

We do not have enough information. Combined both statements are insufficient.
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Bunuel
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Answer: "E" : Both statements not sufficient


Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.

But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'

Is rst = 1 ?

(1) rs = 1
(2) st = 1

Try r=s=t=1, both statements hold true and rst=1.
Try r=s=t=-1, both statements hold true and rst=-1.

Two different answers. Not sufficient.

Answer: E.


Hi Bunuel,

When the question mentions three different variables like r, s and t, are we allowed to assume that the three variables can have the same value?

Thanks in advance.

Nikhil Singh
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Hi nikhilsingh777,

When a Quant questions tells you nothing about an individual variable, then you have to consider that the variables could be a variety of possibilities (re: that variable could be positive, negative, 0, a fraction, a repeat number, etc.).

In this prompt, Fact 1 tells us that (R)(S) = 1.... but tells us NOTHING about the value of T. Thus, we could have...

R = 1, S = 1, T = anything
R = 1/2, S = 2, T = anything
R = -1/3, S = -3, T = anything
Etc.

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