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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, 05:20
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If x is an integer, is \(9^x + 9^{x} = b\) ? (1) \(3^x + 3^{x} = \sqrt{b + 2}\) (2) x > 0 Practice Questions Question: 53 Page: 279 Difficulty: 600 The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions Project
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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, 05:20
SOLUTIONIf 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.
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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, 05:40
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, 05:54
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, 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 ? (1) 3^x + 3^(x) = (b + 2)
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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 ? (1) 3^x + 3^(x) = (b + 2)
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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 ? (1) 3^x + 3^(x) = (b + 2)
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14 Nov 2012, 02:51
JJ2014 wrote: why is 3^x * 3^x = 9x? shouldnt it be 9^2x? \(3^x * 3^x=3^{x+x}=3^{2x}=9^x\). For more check Number Theory chapter of our Math Book: mathnumbertheory88376.htmlHope it helps.
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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, 22:35
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, 12:56
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, 10:31
saroshgilani wrote: If x = 0, then the questions asks whether b = 2. (1) gives \(2 = \sqrt{b+2}\) > b = 2. Sufficient. Hope it's clear.
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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, 14:46
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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06 Feb 2019, 04:24
when we square 3^x+3^x the result should not be 9^x^2+9^x^2? thank you in advance



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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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Updated on: 08 Apr 2019, 06:46
Bunuel VeritasKarishma or other experts, is this correct? Stem: 9^x+9^ x = b? (3^2)^x+(3^2)^x = b? 3^2(1^x+1^x) 3^2(2) =18 = b?1) 3^x+3^x = √(b+2) 3(1^x+1^x) = (3^x+3^x)^2 = b+2 3(2) = 3^2x + 3^0 + 3^0 + 3^2x = b+2 36 = b+2 3^2x + 3^2x + 2 = b + 2 34 = b 3^2x+3^2x = b Definite yes, Sufficient 2) Irrelevant because base 1 will always be 1 if x is an int.Edit: Thanks Karishma, I must have been half asleep when I did this one... Takeaway: Don't confuse multiplication and addition of exponents when factoring out!
Originally posted by energetics on 05 Apr 2019, 13:48.
Last edited by energetics on 08 Apr 2019, 06:46, edited 3 times in total.



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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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05 Apr 2019, 22:52
energetics wrote: Bunuel VeritasKarishma or other experts, is this correct? Stem: 9^x+9^ x = b? (3^2)^x+(3^2)^x = 3^2(1^x+1^x) = 3^2(2) = 18 = b? 1) 3^x+3^x = √(b+2) 3(1^x+1^x) = 3(2) = 36 = b+2 34 = b Definite no, Sufficient 2) Irrelevant because base 1 will always be 1 if x is an int. No energetics. Note that we cannot add the exponents when the terms are added. We do that only when the terms are multiples. 3^a * 3^b = 3^(a + b)  Correct 3^a + 3^b is not 3^(a + b).
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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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05 Apr 2019, 23:42
Bunuel wrote: If x is an integer, is \(9^x + 9^{x} = b\) ?
(1) \(3^x + 3^{x} = \sqrt{b + 2}\)
(2) x > 0
Question : is \(9^x + 9^{x} = b\) Statement 1: \(3^x + 3^{x} = \sqrt{b + 2}\)i.e. Squaring both sides \(3^{2x} + 3^{2x} +2*(3^x*3^{x} = √(b+2)\) i.e. \(3^{2x} + 3^{2x} +2 = (b+2)\) i.e. \(9^x + 9^{x} = (b)\) i.e. answer to the question is DEFINITELY YES hence SUFFICIENT Statement 2: x > 0No association of x with b is given to check the question statement's authenticity to answer the question hence NOT SUFFICIENT Answer: Option 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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04 Jun 2019, 06:01
I'm confused ... 3^x * 3^x should be equal to 3^2x not 9^x if answer is 9^x it must to be (3^2)^x.... it's totally different can someone explain thank in advance.....




Re: If x is an integer, is 9^x + 9^(x) = b ? (1) 3^x + 3^(x) = (b + 2)
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