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02 Feb 2017, 07:50
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:39) correct
23%
(02:03)
wrong
based on 448
sessions
History
Date
Time
Result
Not Attempted Yet
If \(3^k\) = 16, and \(2^j\) = 27, then kj =
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
02 Feb 2017, 14:04
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GMATPrepNow
If \(3^k\) = 16, and \(2^j\) = 27, then kj =
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
Another approach is to isolate the 3 in both equations. Here’s what I mean:
Given: 3^k = 16
Rewrite 16 as 2^4 to get: 3^k = 2^4
Raise both sides to the power of 1/k to get: (3^k)^(1/k) = (2^4)^(1/k)
Use power of power law to simplify: 3 = 2^(4/k)
Given: 2^j = 27
Rewrite 27 as 3^3 to get: 2^j = 3^3
Raise both sides to the power of 1/3 to get: (2^j)^(1/3) = (3^3) ^(1/3)
Use power of power law to simplify: 2^(j/3) = 3
We now have two equations:
3 = 2^(4/k)
2^(j/3) = 3
Since both equations are set equal to 3, we can write: 2^(4/k) = 2^(j/3)
Since the bases both equal 2, we can conclude that 4/k = j/3
Cross multiply to get: jk = (4)(3)
So, jk = 12
Answer: [spoiler]D[/spoiler]
Cheers,
Brent
General Discussion
02 Feb 2017, 10:01
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GMATPrepNow
If \(3^k\) = 16, and \(2^j\) = 27, then kj =
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
A) 8
B) 9
C) 10
D) 12
D) 15
* Kudos for all correct solutions
GMATPrepNow
question must be 3^k=27 && 2^j=16
Any way
3^k=27=3^3 thus k=3
2^j=16=2^4 thus j=4
so kj= 3*4 =12
Ans D
