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# 2^p/2^q=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9032
GMAT 1: 760 Q51 V42
GPA: 3.82

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17 Sep 2018, 00:23
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5% (low)

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

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[Math Revolution GMAT math practice question]

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

$$1) p = q + 2$$
$$2) pq=8$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1126 Location: India Concentration: Operations, General Management GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities) 2^p/2^q=? [#permalink] ### Show Tags 17 Sep 2018, 00:28 $$\frac{2^p}{2^q}$$ = $$2^{p-q}$$ 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. Manager Joined: 24 Dec 2017 Posts: 180 Location: India Concentration: Strategy, Real Estate Schools: Johnson '21 2^p/2^q=? [#permalink] ### Show Tags 17 Sep 2018, 01:21 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 Thank you Arjun GMAT Club Legend Joined: 11 Sep 2015 Posts: 4889 Location: Canada GMAT 1: 770 Q49 V46 Re: 2^p/2^q=? [#permalink] ### Show Tags 17 Sep 2018, 05:51 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 RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9032 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: 2^p/2^q=? [#permalink] ### Show Tags 19 Sep 2018, 00:58 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: 2^p/2^q=?   [#permalink] 19 Sep 2018, 00:58