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Is rst = 1 ?

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Math Revolution GMAT Instructor
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Re: Is rst = 1 ?  [#permalink]

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New post 10 Dec 2017, 23:56
loki wrote:
Is rst = 1 ?

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


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables, E is most likely to be the answer.
Then we need to consider both conditions 1) & 2) together.

If \(r = s = t = 1\), \(rst = 1\) and it is true.
If \(r = s = t = -1\), \(rst = -1\) and it is false.

Since we have two different cases, the answer is E.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Is rst = 1 ?  [#permalink]

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New post 20 Mar 2018, 12:13
Hi All,

We're asked if (R)(S)(T) = 1. This is a YES/NO question. We know nothing about the three variables (meaning that they could be ANYTHING). We can answer this question by TESTing VALUES.

1) (R)(S) = 1

We know nothing about the value of T….
If T = 1, then (R)(S)(T) =1(1) = 1 and the answer is YES
If T = 0, then (R)(S)(T) =1(0) = 0 and the answer is NO
Fact 1 is INSUFFICIENT

2) (S)(T) = 1

We know nothing about the value of R…
…so we'd have the same situation as in Fact 1 (YES and NO answers)
Fact 2 is INSUFFICIENT

Combined
(R)(S) = 1 and (S)(T) = 1
If R=1, S=1 and T=1, then (R)(S)(T) = 1 and the answer to the question is YES
If R=1/2, S = 2 and T = 1/2, then (R)(S)(T) = 1/2 and the answer to the question is NO.
Combined INSUFFICIENT

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Re: Is rst = 1 ? &nbs [#permalink] 20 Mar 2018, 12:13

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