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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Difficulty:   5% (low)

Question Stats: 87% (00:43) correct 13% (01:18) wrong based on 51 sessions

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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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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1139
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities)

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$$\frac{2^p}{2^q}$$ = $$2^{p-q}$$

from statement 1:

p = q-2

Then, $$2^{p-q}$$ = $$2^2$$ = 4.

Sufficient.

from statement 2:
pq = 8.
Clearly insufficient.

Manager  S
Joined: 24 Dec 2017
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Concentration: Strategy, Real Estate
Schools: Johnson '21

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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

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.

Thank you
Arjun
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4961
GMAT 1: 770 Q49 V46

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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

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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=>

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.

_________________ Re: 2^p/2^q=?   [#permalink] 19 Sep 2018, 00:58

# 2^p/2^q=?   