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If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 06:50
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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
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Brent Hanneson – GMATPrepNow.com



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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 09:01
GMATPrepNow wrote: 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 GMATPrepNowquestion 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



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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 09:16
rohit8865 wrote: GMATPrepNow wrote: 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 question must be 3^k=27 & 2^j=16 The given information is correct as worded: \(3^k\) = 16, and \(2^j\) = 27 The solution to each individual equation is not an integer. Cheers, Brent
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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 09:33
GMATPrepNow wrote: rohit8865 wrote: GMATPrepNow wrote: 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 question must be 3^k=27 & 2^j=16 The given information is correct as worded: \(3^k\) = 16, and \(2^j\) = 27 The solution to each individual equation is not an integer. Cheers, Brent then we can multiply both equation to get 3^k*2^j= 16*27 getting k=3 j=4 thus KJ=12



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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 10:22
rohit8865 wrote: then we can multiply both equation to get 3^k*2^j= 16*27 getting k=3 j=4 thus KJ=12 The question looks a bit odd , but I am with the above solution, answer must be (D)...
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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 13:04
GMATPrepNow wrote: 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 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) = 3We now have two equations: 3 = 2^(4/k)2^(j/3) = 3Since 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: DCheers, Brent
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Re: If 3^k = 16, and 2^j = 27, then kj =
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02 Feb 2017, 13:05
GMATPrepNow wrote: 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 Another approach involves approximation. Given: 2^ j = 27 Notice that 2^ 4 = 16 and 2^ 5 = 32 Since 27 is closer to 32 than it is to 16, we can conclude that j is closer to 5 than it is to 4. Let's say j ≈ 4.7Given: 3^ k = 16 Notice that 3^ 2 = 9 and 3^ 3 = 27 Since 16 is approximately halfway between 9 and 27, we can conclude that k is approximately halfway between 2 and 3. Let's say k ≈ 2.5So, jk ≈ ( 4.7)( 2.5) ≈ 11.75 When we check the answer choices, we see that answer choice D is the closest to 11.75 Cheers, Brent
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Re: If 3^k = 16, and 2^j = 27, then kj =
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15 Feb 2017, 09:22
GMATPrepNow wrote: 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 Another approach. 3^k = 16. Take log to the base 3. k= log 316 = 4 log 32 As log a(b^k) = k log ab 2^j = 27. Take log to the base 2. j = log 227 = 3log 33 k*j = 12 * log 32 * log 23 Thus kj = 12. as log ab * log ba =1



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Re: If 3^k = 16, and 2^j = 27, then kj =
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09 Jul 2017, 07:13
3^k=16 and 2^J=27, we need to find kJ 3^k x 2^J=16 x 27 3^k x 2^J=2^4 x 3^3 i.e. 3^k x 2^J=3^3 x 2^4 Thus, kJ=12 Ans : D
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Re: If 3^k = 16, and 2^j = 27, then kj =
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09 Jul 2017, 08:13
The answer would be D i.e. 12. Multiply the two and get a he respective powers of 2 and 3. Thus k*j=12 Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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Re: If 3^k = 16, and 2^j = 27, then kj =
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14 Jul 2018, 07:38
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Re: If 3^k = 16, and 2^j = 27, then kj = &nbs
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