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

 It is currently 20 Jun 2018, 16:00

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is X^(a+b) > X^(a-b) if both a and b are positive integers?

Author Message
Senior Manager
Joined: 31 Jul 2017
Posts: 368
Location: Malaysia
WE: Consulting (Energy and Utilities)
Is X^(a+b) > X^(a-b) if both a and b are positive integers? [#permalink]

### Show Tags

Updated on: 11 Sep 2017, 07:50
00:00

Difficulty:

65% (hard)

Question Stats:

30% (01:09) correct 70% (01:22) wrong based on 20 sessions

### HideShow timer Statistics

Hi All,

Need help on the below question. Would be great if someone can tell me where I am wrong in this. Not Sure of the Difficulty level..

Is X^(a+b) > X^(a-b) if both a and b are positive integers?
(1) X^(a+1) > X^(a-1)
(2) a = b + 2

From the question can we deduce that we need to find X^(2b)>1 - Am I right on this??

Stamnt 1:

X^2 > 1
X^(2b) > 1^(b)

So, X^(2b) > 1 - Sufficient

Stamnt 2:

Insufficient.

Please tell me where I am going wrong on this

Bunuel - Your help would be great on this.

Thanks

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Originally posted by rahul16singh28 on 11 Sep 2017, 01:19.
Last edited by chetan2u on 11 Sep 2017, 07:50, edited 1 time in total.
spoiler
Math Expert
Joined: 02 Aug 2009
Posts: 5899
Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers? [#permalink]

### Show Tags

11 Sep 2017, 08:29
rahul16singh28 wrote:
Hi All,

Need help on the below question. Would be great if someone can tell me where I am wrong in this. Not Sure of the Difficulty level..

Is X^(a+b) > X^(a-b) if both a and b are positive integers?
(1) X^(a+1) > X^(a-1)
(2) a = b + 2

From the question can we deduce that we need to find X^(2b)>1 - Am I right on this??

Stamnt 1:

X^2 > 1
X^(2b) > 1^(b)

So, X^(2b) > 1 - Sufficient

Stamnt 2:

Insufficient.

Please tell me where I am going wrong on this

Bunuel - Your help would be great on this.

Thanks

Hi...
$$x^{a+b}>x^{a-b}$$

Let's see the statements..
$$X^{a+1}>x^{a-1}$$....
Let a=1, x=2..... x^2>x^1...
$$x^{a+b}>x^{a-b}......$$...ans YES
Let a=3,x=-2, ......(-2)^4>(-2)^2...
Let b=2..$$x^{a+b}>x^{a-b}........(-2)^{3+2}>(-2)^{3-2}......(-2)^5>(-2)^1......$$ NO
Insufficient

2)a=b+2

Clearly insuff

Combined

Still the value can vary depending on value of x
Insuff

E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers? [#permalink]

### Show Tags

12 Sep 2017, 00:05
rahul16singh28 wrote:
Hi All,

Need help on the below question. Would be great if someone can tell me where I am wrong in this. Not Sure of the Difficulty level..

Is X^(a+b) > X^(a-b) if both a and b are positive integers?
(1) X^(a+1) > X^(a-1)
(2) a = b + 2

From the question can we deduce that we need to find X^(2b)>1 - Am I right on this??

Stamnt 1:

X^2 > 1
X^(2b) > 1^(b)

So, X^(2b) > 1 - Sufficient

Stamnt 2:

Insufficient.

Please tell me where I am going wrong on this

Bunuel - Your help would be great on this.

Thanks

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. Thus the answer E is most likely.

$$x = 1$$
$$x^{a+b} = x^{a-b}$$: The answer to the question is false.

$$x = 2, a =1, b =1$$.
$$x^{a+b} > x^{a-b}$$: The answer to the question is true.

Therefore, the answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

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 \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers?   [#permalink] 12 Sep 2017, 00:05
Display posts from previous: Sort by