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If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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22 Jul 2016, 00:07
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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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22 Jul 2016, 01:57
Bunuel wrote: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
A. 1 B. 2 C. 3 D. 4 E. 5 Check directly by substituting the value. Sub a = 2 from option B and only this satisfies the condition 16 + 64 = 256 176 => 80 = 80. IMO option B is correct option. OA please...will correct if I missed anything...



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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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22 Jul 2016, 02:36
Well, I worked it out by doing as follows... 4^a+4^a×4=4^a×4^2176 4^a×(1+416)=176 4^a×(11)=11×16 Thus, 4^a=16 So, a=2



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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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22 Jul 2016, 02:51
4^a+4*4^a=16*4^a11*4^2 5*4^a=16*4^a11*4^2 11*4^2=11*4^a 2=a
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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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29 Mar 2018, 12:50
Hi All, While there are several ways to approach this type of question, this prompt can be solved rather quickly by TESTing THE ANSWERS. Before beginning the 'math', consider this: We know that 4^a, 4^(a+1) and 4^(a+2) are consecutive "powers of 4", so we could just "map out the possibilities and find the one that fits: 4^0 = 1 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 Now, which 3 consecutive "powers of 4" fit the given equation (hint: the "176" is a specific value)? It's got to be 2, 3 and 4, so A = 2 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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27 Jun 2018, 05:14
Bunuel wrote: If \(4^a + 4^{(a+1)} = 4^{(a+2)}  176\), what is the value of a?
A. 1 B. 2 C. 3 D. 4 E. 5 Hi Bunuel , will you please show a solution without Testing Values? None of the solutions above are in correct format. Thanks in advance.



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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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27 Jun 2018, 05:38
Solution Given:• \(4^a + 4^{(a+1)}=4^{(a+2)}−176\) To find:Approach and Working:We can rewrite the equation as follows: • \(4^a + 4^{(a+1)}=4^{(a+2)}−176\) Or, \(4^a + 4^{(a+1)}  4^{(a+2)} = 176\) Or, \(4^a (1 + 4 – 4^2) = 176\) Or, \(4^a (1 + 4 – 16) = 176\) Or, \(4^a * (11) = 176\) Or, \(4^a = \frac{176}{11} = 16 = 4^2\) Or, a = 2 Hence, the correct answer is option B. Answer: B
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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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27 Jun 2018, 05:41



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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a?
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02 Jul 2018, 10:05
Bunuel wrote: If \(4^a + 4^{(a+1)} = 4^{(a+2)}  176\), what is the value of a?
A. 1 B. 2 C. 3 D. 4 E. 5 We can reexpress 4^(a + 1) as (4^a)(4^1), and we can reexpress 4^(a + 2) as (4^a)(4^2). Simplifying the given equation, we have: 4^a + (4^a)(4^1) = (4^a)(4^2)  176 4^a + (4^a)(4^1)  (4^a)(4^2) = 176 4^a(1 + 4^1  4^2) = 176 4^a(11) = 176 4^a = 16 4^a = 4^2 a = 2 Answer: B
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Re: If 4^a + 4^(a+1) = 4^(a+2)  176, what is the value of a? &nbs
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