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505-555 Level|   Exponents|      
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Bunuel
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What is the value of 3^(-(x + y))/3^(-(x - y))? 17 Jun 2018, 06:37
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B
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15% (low)

Question Stats:

76% (00:57) correct 24% (01:08) wrong based on 569 sessions

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What is the value of \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)?


(1) x = 2

(2) y = 3
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B
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What is the value of 3^(-(x + y))/3^(-(x - y))? 17 Jun 2018, 06:47
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\(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)= \(3^{-(x + y)+(x - y)}\)=\(3^{-x+y+x-y}\)=\(3^{-2y}\). So the value will depend on the value of \(y\) only.

(1) x = 2. Not Sufficient

(2) y = 3. Sufficient

Answer B.
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What is the value of 3^(-(x + y))/3^(-(x - y))? 17 Jun 2018, 11:09
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Solution



To find:
• The value of the expression \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)

Approach and Working:
We can simplify the given expression as
    • \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)
    = \(3^{(-x - y) – (-x + y)}\)
    = \(3^{(-x - y + x - y)}\)
    = \(3^{(- 2y)}\)

Therefore, if we know the value of y, we can find out the value of the expression

Analysing Statement 1
    • As per the information given in statement 1, x = 2
      o From this statement, we don’t find any information about y

Hence, statement 2 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, y = 3
      o Substituting the value of y, we can find the value of the given expression

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

Answer: B
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What is the value of 3^(-(x + y))/3^(-(x - y))? 30 Apr 2020, 21:23
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Bunuel
What is the value of \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)?


(1) x = 2

(2) y = 3

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
The question asks the value of \(\frac{{3^{-(x+y)}}}{{3^{-(x-y)}}} = 3^{-(x+y)-(-(x-y))} = 3^{-x-y+x-y} = 3^{-2y}\).

Thus condition 2) is sufficient since it tells the value of y.

Condition 1)

Since we don’t know the value of x from condition 1), it does not yield a unique solution and condition 1) is not sufficient.

Therefore, B is the answer.
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What is the value of 3^(-(x + y))/3^(-(x - y))? 25 May 2022, 16:48
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Bunuel
What is the value of \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)?

(1) \(x = 2\)
(2) \(y = 3\)

Target question: What is the value of \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)?
This is a good candidate for rephrasing the target question.

Take: \(\frac{3^{-(x + y)}}{3^{-(x - y)}}\)

Simplify both exponents: \(\frac{3^{(-x - y)}}{3^{(-x + y)}}\)

Apply the quotient law: \(3^{(-x - y) - (-x + y)}\)

Simplify: \(3^{-2y}\)

To find the value of \(3^{-2y}\), we only need to know the value of \(y\). So we can rephrase our target question...

REPHRASED target question: What is the value of \(y\)?

Aside: the video below has tips on rephrasing the target question

Statement 1: \(x = 2\)
No good. We need to find the value of \(y\).
NOT SUFFICIENT

Statement 2: \(y = 3\)
SUFFICIENT

Answer: B

VIDEO ON REPHRASING THE TARGET QUESTION:
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