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If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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01 Oct 2012, 04:20
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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01 Oct 2012, 04:20




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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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01 Oct 2012, 04:40
1) \(3^x + 3^^x = \sqrt{b + 2}\) square both sides \(9^x+2*3^x*\frac{1}{3^x}+9^{x} = b+2\) Therefore, \(9^x + 9^{x} = b\). Sufficient.2) Tells us nothing about b, but rather that x is a positive number. Insufficient. Knowing this, the solution is A  statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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01 Oct 2012, 04:54
This was tough. I spent at least 3 minutes (during the exam is not possible) We can rephrase the stimulus but I see a lot of options to do. Is not straight (at least for me). Ok better to look at the statements 2) this say nothing about \(=\)between the left part of equation and the right part INSUFF1) square boot sides so we have \((3^x + 3^x)^2\)\(=\)\(\sqrt{b + 2}^2\) Now we 'd have \(9^x\) that is, is the same of \(3^2x\) > \(9^x + 9^x + 2 ( 3^x + 3^x)\)\(=\) \(b + 2\) > \(9^x + 2 + 9^x = b + 2\) In the end \(9^x + 9^x = b\) SUFF A should be the answer Note: \(2 ( 3^x + 3^x)\) is zero because we have \(3^ x x\) . a number power zero is 1 > \(2*1 = 2\) for me is more than 600 level
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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31 Oct 2012, 22:40
Bunuel wrote: SOLUTION
If x is an integer, is \(9^x + 9^{x} = b\) ?
(1) \(3^x + 3^{x} = \sqrt{b + 2}\) > square both sides > \(9^x+2*3^x*\frac{1}{3^x}+9^{x}=b+2\) > \(9^x + 9^{x} = b\). So answer to the question is YES. Sufficient.
(2) x > 0. No sufficient.
Answer: A.
Kudos points given to everyone with correct solution. Let me know if I missed someone. Question please: Can we do anything with the 9^x + 9^{x} = b or simplify any more than what is given? I tried to do something more but could not find anything proper...



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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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01 Nov 2012, 06:25
ikokurin wrote: Bunuel wrote: SOLUTION
If x is an integer, is \(9^x + 9^{x} = b\) ?
(1) \(3^x + 3^{x} = \sqrt{b + 2}\) > square both sides > \(9^x+2*3^x*\frac{1}{3^x}+9^{x}=b+2\) > \(9^x + 9^{x} = b\). So answer to the question is YES. Sufficient.
(2) x > 0. No sufficient.
Answer: A.
Kudos points given to everyone with correct solution. Let me know if I missed someone. Question please: Can we do anything with the 9^x + 9^{x} = b or simplify any more than what is given? I tried to do something more but could not find anything proper... I'd say \(9^x + 9^{x}\) the simplest way of writing this expression and as you can see from the solution we don't even need to manipulate with it further to answer the question.
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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13 Nov 2012, 17:05
why is 3^x * 3^x = 9x? shouldnt it be 9^2x?
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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14 Nov 2012, 01:51



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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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19 Aug 2014, 21:35
yb wrote: If x is an integer, is 9^x + 9^(x) = b ?
1) 3^x + 3^(x) = sqrt(b+2)
2) x>0 Note that 9^x is the square of 3^x so we know that we should try to square stmnt 1. 1) \(3^x + 3^{x} = \sqrt{(b+2)}\) \(3^{2x} + 3^{2x} + 2*3^x*3^{x} = \sqrt{(b+2)}^2\) \(9^x + 9^{x} = b + 2  2 = b\) We answer with 'Yes' and hence this statement alone is sufficient. 2) x > 0 Obviously not sufficient. Answer (A)
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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05 Dec 2015, 11:56
Bunuel , what is x=0 ?
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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06 Dec 2015, 09:31



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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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16 Jul 2017, 13:46
If x is an integer, is \(9^x + 9^{x} = b\) ? \(3^{2x} + 3^{2x} = b\) (1) \(3^x + 3^{x} = \sqrt{b + 2}\) \(3^x + 3^{x} = \sqrt{b + 2}\) Squaring on both sides: \((3^x + 3^{x})^2 = b + 2\) \(3^{2x} + 2 * 3^{x} * 3^{x} + 3^{2x} = b + 2\) \(3^{2x} + 2 + 3^{2x} = b + 2\) \(3^{2x} + 3^{2x} = b\) This matches to the abovesimplified equation of the question. Hence, (1) ===== is SUFFICIENT(2) x > 0 Clearly Not Sufficient Hence, (2) ===== is NOT SUFFICIENTHence, Answer is ADid you like the answer? 1 Kudos Please
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Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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26 Nov 2018, 23:56
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