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

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Manager
Joined: 31 Jul 2017
Posts: 52

Kudos [?]: 1 [0], given: 63

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

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11 Sep 2017, 01:19
00:00

Difficulty:

65% (hard)

Question Stats:

28% (01:22) correct 72% (01:28) wrong based on 18 sessions

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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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

Last edited by chetan2u on 11 Sep 2017, 07:50, edited 1 time in total.
spoiler

Kudos [?]: 1 [0], given: 63

Math Expert
Joined: 02 Aug 2009
Posts: 5208

Kudos [?]: 5832 [0], given: 117

Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers? [#permalink]

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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

[Reveal] Spoiler:
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

Kudos [?]: 5832 [0], given: 117

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4318

Kudos [?]: 3037 [0], given: 0

GPA: 3.82
Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers? [#permalink]

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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

[Reveal] Spoiler:
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.
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Re: Is X^(a+b) > X^(a-b) if both a and b are positive integers?   [#permalink] 12 Sep 2017, 00:05
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