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Difficulty:
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Question Stats:
96% (01:03) correct
4%
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wrong
based on 2797
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If m is an integer such that \((-2)^{2m} = 2^{9 - m}\), then m=
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
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(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
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SOLUTION
If m is an integer such that \((-2)^{2m} = 2^{9 - m}\), then m=
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
First of all, since m is an integer, then 2m=even, and therefore \((-2)^{2m}=2^{2m}\).
So, we'd have:
\(2^{2m} = 2^{9 - m}\);
\(2m=9-m\);
\(m=3\).
Answer: C.
_________________
If m is an integer such that \((-2)^{2m} = 2^{9 - m}\), then m=
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
First of all, since m is an integer, then 2m=even, and therefore \((-2)^{2m}=2^{2m}\).
So, we'd have:
\(2^{2m} = 2^{9 - m}\);
\(2m=9-m\);
\(m=3\).
Answer: C.
_________________
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• Tests: GMAT Club Tests | Forum Quiz
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General Discussion
ershovici
Joined: 29 Jan 2014
Last visit: 09 Feb 2015
Posts: 11
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Babson '17 (A$)
GMAT 1: 720 Q48 V40
GPA: 3.8
So, I choose C. Here is my reasoning:
-2^2m = 2^9-2
from this - (-2)^2m is the same as 2^2m, since the power is even number, so we have
2m = 9-m
3m = 9
m = 3
-2^2m = 2^9-2
from this - (-2)^2m is the same as 2^2m, since the power is even number, so we have
2m = 9-m
3m = 9
m = 3
EMPOWERgmatRichC
Expert
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
Hi All,
While this question might look a little "scary", the answer choices are small numbers and we're just asked to find the one that completes the given equation, so we can use "brute force" on this question.
We're looking for the value of M that makes (-2)^(2M) = 2^(9-M)
We can work through the answers in order (although you might realize that the first couple are much TOO small, given the exponents in this prompt).
IF....
M = 1
(-2)^2 = 4
2^8 = 256
These are NOT equal
M = 2
(-2)^4 = 16
2^7 = 128
These are NOT equal
M = 3
(-2)^6 = 64
2^6 = 64
These ARE equal, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
While this question might look a little "scary", the answer choices are small numbers and we're just asked to find the one that completes the given equation, so we can use "brute force" on this question.
We're looking for the value of M that makes (-2)^(2M) = 2^(9-M)
We can work through the answers in order (although you might realize that the first couple are much TOO small, given the exponents in this prompt).
IF....
M = 1
(-2)^2 = 4
2^8 = 256
These are NOT equal
M = 2
(-2)^4 = 16
2^7 = 128
These are NOT equal
M = 3
(-2)^6 = 64
2^6 = 64
These ARE equal, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Posts: 8
What if the question was (-2)^3m = 2^9-m?
Is this possible?
Is this possible?
Nasahtahir
No real m satisfies that equation.
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ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 14 Sep 2026
Posts: 22,738
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,738
Bunuel
Recall that when a negative number is raised to an even power, the result is positive. Since 2m is even, (-2)^(2m) = 2^(2m), and we have:
2^(2m) = 2^(9 - m)
2m = 9 - m
3m = 9
m = 3
Answer: C
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Posts: 6
since 2m is even, then 9-m must be even
we can exclude all even numbers : 2,4,6, we left with 1 and 3
2*1 = 2
9-1 = 8
so one is not the solution
2*3 = 6
9-3 = 6
so m = 3 .
we can exclude all even numbers : 2,4,6, we left with 1 and 3
2*1 = 2
9-1 = 8
so one is not the solution
2*3 = 6
9-3 = 6
so m = 3 .
Posts: 1
(-2)^2m=2^(9-m)
=> (-1*2)^2m= 2^(9-m)
=> (-1)^2m +2^2m=2^(9-m)
=>2^2m=2^(9-m)
=> 2m= 9-m
=> m=3
* whatever m is odd or even the power of -1 will always even number as multiplied by 2 and resulting in +1
=> (-1*2)^2m= 2^(9-m)
=> (-1)^2m +2^2m=2^(9-m)
=>2^2m=2^(9-m)
=> 2m= 9-m
=> m=3
* whatever m is odd or even the power of -1 will always even number as multiplied by 2 and resulting in +1
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