GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Sep 2019, 01:36 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # 2^p/2^q=?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7875
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 86% (00:42) correct 14% (01:18) wrong based on 49 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

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

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

_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1035
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

### Show Tags

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

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.
_________________
Press +1 Kudos If my post helps!
Manager  S
Joined: 24 Dec 2017
Posts: 187
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21

### Show Tags

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
CEO  V
Joined: 12 Sep 2015
Posts: 3958

### Show Tags

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

RELATED VIDEO FROM OUR COURSE

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7875
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

=>

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.
_________________ Re: 2^p/2^q=?   [#permalink] 19 Sep 2018, 01:58
Display posts from previous: Sort by

# 2^p/2^q=?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  