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If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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11 Jun 2015, 04:08
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If \(3^k + 3^k = (3^9)^{3^9}3^k\), then what is the value of k? (A) 11/3 (B) 11/2 (C) 242 (D) 3^10 (E) 3^11 – 1 Kudos for a correct solution.
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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11 Jun 2015, 04:20
Bunuel wrote: If \(3^k + 3^k = (3^9)^{3^9}3^k\), then what is the value of k?
(A) 11/3 (B) 11/2 (C) 242 (D) 3^10 (E) 3^11 – 1
Kudos for a correct solution. Answer: Option
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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13 Jun 2015, 16:58
Hi All, The answer choices to this question are written in a way that helps us to avoid some of the math involved. We're told that 3^K + 3^K = (3^9)^[3^9]  3^K. We're asked for the value of K. To start, we should move all like terms to one side... 3^K + 3^K + 3^K = (3^9)^[3^9] The 'left side' can be rewritten.... 3(3^K) = (3^9)^[3^9] 3^(K+1) = (3^9)^[3^9] Both sides have the same "base 3", so since the "right side exponent" is clearly a BIG INTEGER, we know that... K+1 = a BIG INTEGER K = a BIG INTEGER  1 There's only one answer that fits... Final Answer: GMAT assassins aren't born, they're made, Rich
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If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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14 Jun 2015, 04:59
3^k+3^k=(3^9)^3^9  3^k > moving the  3^k to the other side: 3(3^k) = (3^9)^3^9 > using the properties of powers, we are now adding the exponents: 3^k+1 = 3^ (3^2)^(3^9) (here we broke 9 into 3^2) k+1 = 3^2*3^9 k+1 = 3^11 k = 3^11  1. ANS E
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If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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15 Jun 2015, 03:49
Bunuel wrote: If \(3^k + 3^k = (3^9)^{3^9}3^k\), then what is the value of k?
(A) 11/3 (B) 11/2 (C) 242 (D) 3^10 (E) 3^11 – 1
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:The common term in this problem is the recurring base of 3. We will group like terms (i.e. all the terms with k on the left side, all the other powers of 3 on the right side), then simplify each power of 3 using exponent rules. \(3^k + 3^k = (3^9)^{3^9}  3^k\) \(3^k + 3^k + 3^k = (3^9)^{3^9}\) \(3(3^k) = (3^9)^{3^9}\) \(3^{(k + 1)} = 3^{(9*3^9)}\) \(k + 1 = 9 * 3^9\) \(k + 1 = 3^2 * 3^9\) \(k = 3^{11}  1\) The correct answer is E.
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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02 Jul 2015, 07:55
Can anyone tell me what Im doing mathematically illegal.
I start by seeing all the bases are the same so I go straight to the exponents.
k+k=9x\(3^9\)k
3k=\(3^2*3^9\)
3k=\((3^11)\)
k=\((3^11)/3\)
k=\(3^10\)
I believe I'm doing something wrong in step 2 but not sure if it is or not can anyone confirm?



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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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02 Jul 2015, 09:21
3^k + 3^k = (3^9)^(3^9)  (3^k) 3(3^k) = (3^9)^(3^9) 3^(k+1) = 3^([3^2]*[3^9]) k+1 = 3^2 * 3^9 k+1 = 3^(2+9) = 3^11 so, k = (3^11  1).
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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02 Jul 2015, 12:04
Hi xLUCAJx, The first error is right at the beginning  you cannot combine exponents in the way that you did: 3^K + 3^K is NOT 3^2K 3^K + 3^K = 2(3^K) When you add 3^K to both sides, the 'left side' becomes... 3^K + 3^K + 3^K This can be rewritten as... 3(3^K) = (3^1)(3^K) = 3^(K+1) Using these steps as your 'starting point', what would you do next? GMAT assassins aren't born, they're made, Rich
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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17 Feb 2016, 22:49
(3^9)^3^9= 3^(3^2*3^9)=3^11 now taking all k terms on one side 3^k+3^k+3^k = 3^(k+1) comparing power as bases are same we get k+1=3^11, k=3^111 E answer'



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If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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18 Feb 2016, 04:32
Anyone knows what is the maximum number of "aggregated exponents" GMAT is likely to test? I could only solve this question because it regarded only "2 aggregated powers":\((3^9)^{3^9}\). Does "3 aggregated powers" such as \({3^9}^{3^9}\) are possible to appear on GMAT questions? How to solve them?



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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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02 Mar 2017, 18:09
Bunuel wrote: If \(3^k + 3^k = (3^9)^{3^9}3^k\), then what is the value of k?
(A) 11/3 (B) 11/2 (C) 242 (D) 3^10 (E) 3^11 – 1 Let’s simplify the given equation: 3^k + 3^k = (3^9)^(3^9)  3^k 3^k + 3^k + 3^k = 3^(9 * 3^9) Pull out the common factor 3^k from each term on the left side of the equation: 3^k * (1 + 1 + 1) = 3^(3^2 * 3^9) 3^k * (3) = 3^(3^11) Note that the left side is now 3^k * 3^1, so we combine (add) the exponents: 3^(k + 1) = 3^(3^11) k + 1 = 3^11 k = 3^11  1 Answer: E
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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07 Apr 2019, 07:10
Can anyone please explain how 3^3k is transformed to 3^k+1



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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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07 Apr 2019, 07:17
danz1ka19 wrote: Can anyone please explain how 3^3k is transformed to 3^k+1 I think you mean how is \(3*3^k=3^{k+1}\) Operations involving the same bases:Keep the base, add or subtract the exponent (add for multiplication, subtract for division) \(a^n*a^m=a^{n+m}\) \(\frac{a^n}{a^m}=a^{nm}\) So, \(3*3^k=3^1*3^k=3^{k+1}\) 8. Exponents and Roots of Numbers Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative Megathread
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Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k?
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07 Apr 2019, 07:17






