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# If p is an integer such that (−4)2p+6= 49−p, then p =

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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05 Feb 2015, 08:18
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:14) correct 18% (01:32) wrong based on 181 sessions

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If p is an integer such that $$(-4)^{2p+6}= 4^{9-p}$$, then p =

A. -1
B. 0
C. 1
D. 3
E. 5

Kudos for a correct solution.

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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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05 Feb 2015, 08:56
Bunuel wrote:
If p is an integer such that $$(-4)^{2p+6}= 4^{9-p}$$, then p =

A. -1
B. 0
C. 1
D. 3
E. 5

Kudos for a correct solution.

Plugging in answer C. $$(-4)^8=4^8$$ this is always true.

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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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05 Feb 2015, 10:52
1
Bunuel wrote:
If p is an integer such that $$(-4)^{2p+6}= 4^{9-p}$$, then p =

A. -1
B. 0
C. 1
D. 3
E. 5

Kudos for a correct solution.

This can be solved easily through a very common funda " when bases are equal powers should be equal"

But there is only one catch we have a "-4" instead of 4 ( makes little sense to ask in GMAT)

Look at the powers 2p+6 => this means the power is always EVEN.

So -4^2p+6 is identical to 4^2p+6.

From here on it is simple math.

P=1 , C is the answer.
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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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05 Feb 2015, 19:15

When bases are same, equate the powers. However, in this case, sign of bases are different. It means the exponent should yield an even value

2p+6 = 9-p

p = 1

By placing p=1, we get $$4^8 = (-4)^8$$ which hold true
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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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09 Feb 2015, 04:39
Bunuel wrote:
If p is an integer such that $$(-4)^{2p+6}= 4^{9-p}$$, then p =

A. -1
B. 0
C. 1
D. 3
E. 5

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Explanation: Any non-zero number raised to an even power (2, 4, 6, etc.) will be a positive number. Because we know that p is an integer, it follows that 2p is even, and that 2p+6 is also even. Therefore we know that (−4)^(2p+6) is the same as 4^(2p+6).

If the bases on both sides of an equation are the same, then the exponents must be equal as well, so: 2p+6 = 9-p;

Adding p and subtracting 6 from both sides gives 3p = 3 => p = 1

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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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30 Mar 2015, 08:52
Another way to look at it would be to separate (-4)^2p+6 into [(-1)^2p+6]*[(4)^2p+6].
We can now safely say that 2p+6 is even since there is no negative sign on the right hand side and equate both the powers of 4.
So, 2p+6 = 9-p => p=1.
A way to validate your answer would be to plug in value of p in (-1)^2p+6 = (-1)^8= 1
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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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30 Mar 2015, 12:10
Hi All,

This question is perfect for a bit of "brute force" and TESTing THE ANSWERS. We just have to plug in the 5 choices until we find the one number that makes the two sides of the equation equal...

(-4)^(2P+6) vs. 4^(9-P)

Does (-4)^4 = 4^10?
No. This is NOT the answer

Does (-4)^6 = 4^9
No. This is NOT the answer

Does (-4)^8 = 4^8

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** SVP Joined: 06 Nov 2014 Posts: 1877 Re: If p is an integer such that (−4)2p+6= 49−p, then p = [#permalink] ### Show Tags 31 Mar 2015, 01:27 Bunuel wrote: If p is an integer such that $$(-4)^{2p+6}= 4^{9-p}$$, then p = A. -1 B. 0 C. 1 D. 3 E. 5 Kudos for a correct solution. 2p + 6 is always even. Hence (-4)^(2p + 6) = 4^(2p + 6) Now, (-4)^(2p+6) = 4^(9-p) So, 4^(2p + 6) = 4^(9-p) So, 2p + 6 = 9 - p So, p = 5 Hence option (E). -- Optimus Prep's GMAT On Demand course for only$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
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Re: If p is an integer such that (−4)2p+6= 49−p, then p =  [#permalink]

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22 May 2017, 18:54
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Re: If p is an integer such that (−4)2p+6= 49−p, then p = &nbs [#permalink] 22 May 2017, 18:54
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