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If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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01 Oct 2012, 05:20
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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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 ? [#permalink]
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01 Oct 2012, 05:54
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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 ? [#permalink]
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01 Oct 2012, 20:18
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1) Square both the side & get the same equation as in stem >Sufficient 2) Insufficient Answer A
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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31 Oct 2012, 23:40
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 ? [#permalink]
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01 Nov 2012, 07:25
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 ? [#permalink]
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10 Nov 2012, 22:22
bb, I tried navigating below link, but it says "You are not authorised to read this forum". Can you check please? theofficialguideforgmatreview13theditionquant134495.html
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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13 Nov 2012, 18:05
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 ? [#permalink]
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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17 Nov 2014, 15:24
As was noted earlier in this post, this question uses the formula (x+y)^2=x^2+2xy+y^2. In this question xy=1 because x^0=1. This allows for the 2's to cancel out. Posted from GMAT ToolKit



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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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05 May 2015, 15:02
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. When you square both sides, I don't understand where the +2 comes from? Can you please explain?



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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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05 May 2015, 15:53
dutchmen991 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. When you square both sides, I don't understand where the +2 comes from? Can you please explain? Hello dutchmen991this is formula that used to square expression: \((a+b)^2 = (a+b)(a+b) = a^2+2ab+b^2\) In our case we have \(3^x + 3^{x}=3^x + \frac{1}{3^{x}}\) When we square this expression we will have: \((3^x + \frac{1}{3^{x}})*(3^x + \frac{1}{3^{x}})=9^x+3x∗\frac{1}{3^x}+\frac{1}{3^x}*3^x+\frac{1}{9^x}=9^x+2*3^x*\frac{1}{3^x}+9^{x}\)
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If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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05 May 2015, 16:04
Harley1980 wrote: dutchmen991 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. When you square both sides, I don't understand where the +2 comes from? Can you please explain? Hello dutchmen991this is formula that used to square expression: \((a+b)^2 = (a+b)(a+b) = a^2+2ab+b^2\) In our case we have \(3^x + 3^{x}=3^x + \frac{1}{3^{x}}\) When we square this expression we will have: \((3^x + \frac{1}{3^{x}})*(3^x + \frac{1}{3^{x}})=9^x+3x∗\frac{1}{3^x}+\frac{1}{3^x}*3^x+\frac{1}{9^x}=9^x+2*3^x*\frac{1}{3^x}+9^{x}\) Thanks for the reply. I didn't realize this was difference of squares because I didn't know how to deal with the negative exponent. Is this the same concept being tested in the following two problems? is5klessthan144719.htmlif2x2x23213whatisthevalueofx130109.html



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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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05 May 2015, 16:21
dutchmen991 wrote: Thanks for the reply. I didn't realize this was difference of squares because I didn't know how to deal with the negative exponent. Is this the same concept being tested in the following two problems? is5klessthan144719.htmlif2x2x23213whatisthevalueofx130109.htmlYeah, all this tasks tests understanding of work with exponents/powers. You can search them by tag: search.php?search_id=tag&tag_id=60
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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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22 May 2016, 15:24
Thought process here:
question is asking : is 9^x + 9^x = b?
so we need to figure out how to make this happen from the data
1) 3^x + 3^x = √b+2) square both sides (3^x + 3^x)(3^x + 3^x) = b+2 9^x + 9^x + 2 = b + 2 subtract 2 = 9^x + 9^x = b. SUFFICIENT
2)x > 0 This could give you multiple answers, so cannot work



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Re: If x is an integer, is 9^x + 9^{x} = b ? [#permalink]
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22 May 2016, 15:24
Thought process here:
question is asking : is 9^x + 9^x = b?
so we need to figure out how to make this happen from the data
1) 3^x + 3^x = √b+2) square both sides (3^x + 3^x)(3^x + 3^x) = b+2 9^x + 9^x + 2 = b + 2 subtract 2 = 9^x + 9^x = b. SUFFICIENT
2)x > 0 This could give you multiple answers, so cannot work




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