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2^p/2^q=?

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Math Revolution GMAT Instructor
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2^p/2^q=?  [#permalink]

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New post 17 Sep 2018, 01:23
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[Math Revolution GMAT math practice question]

\(\frac{2^p}{2^q}=?\)

\(1) p = q + 2\)
\(2) pq=8\)

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2^p/2^q=?  [#permalink]

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New post 17 Sep 2018, 01:28
\(\frac{2^p}{2^q}\) = \(2^{p-q}\)

from statement 1:

p = q-2

Then, \(2^{p-q}\) = \(2^2\) = 4.

Sufficient.

from statement 2:
pq = 8.
Clearly insufficient.

A is the answer.
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2^p/2^q=?  [#permalink]

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New post 17 Sep 2018, 02:21
There are 2 methods to answer this question.

Method 1: 2^p/2^q = 2^p-q.
This approach is based on the property X^m/X^n = X^m-n

St 1: P=Q+2
P-Q=2
Hence Sufficient.

St 2: PQ=8
Clearly insufficient

Hence A is the answer

Method 2: Plug in however this method will consume more time but one can definitely arrive at the answer within 2 mins.

St 1: P=Q+2
Let P=3, then Q=1
Plug this back into the question
2^p/2^q = 2^3/2^1 = 8/2 = 4

Try with another 2 more numbers and you will notice the answer is always 4. Therefore you can confirm the statement is sufficient.

St 2: PQ=8
P x Q = 8 (P=1 & Q=8) or (P=8,Q=1)
In fact we can have multiple combinations here and the final answer will vary.

Hence A is the answer


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Re: 2^p/2^q=?  [#permalink]

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New post 17 Sep 2018, 06:51
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(\frac{2^p}{2^q}=?\)

\(1) p = q + 2\)
\(2) pq=8\)


Target question: What is the value of (2^p)/(2^q) ?
This is a good candidate for rephrasing the target question.
Aside: The video below has tips on rephrasing the target question

Take: (2^p)/(2^q)
Apply the Quotient law to get: 2^(p - q)
This means (2^p)/(2^q) = 2^(p - q)
So, in order to evaluate (2^p)/(2^q), all we need to do is determine the value of p - q
So,......
REPHRASED target question: What is the value of p-q ?

Statement 1: p = q + 2
Subtract q from both sides to get: p - q = 2
So, the answer to the target question is p - q = 2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: pq = 8
There are several values of x and y that satisfy statement 2. Here are two:
Case a: p = 8 and q = 1. In this case, the answer to the REPHRASED target question is p - q = 7
Case b: p = 4 and q = 2. In this case, the answer to the REPHRASED target question is p - q = 2
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Re: 2^p/2^q=?  [#permalink]

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New post 19 Sep 2018, 01:58
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Modifying the question:
What is the value of \(\frac{2^p}{2^q}= 2^{p-q}\)?
So, we need to be able to find the value of \(p-q.\)

Thus, condition 1), which is equivalent to \(p – q = 2\), is sufficient.

Condition 2):
If \(p =4\) and \(q = 2\), then \(\frac{2^p}{2^q}= 2^{p-q} = 2^2 = 4.\)
If \(p =8\) and \(q = 1\), then \(2^p/2^q= 2^{p-q} = 2^7 = 128.\)
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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Re: 2^p/2^q=? &nbs [#permalink] 19 Sep 2018, 01:58
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