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x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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Updated on: 25 Dec 2018, 17:28
Question Stats:
34% (01:35) correct 66% (01:04) wrong based on 101 sessions
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x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..
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Originally posted by allenh on 06 Sep 2015, 06:07.
Last edited by Bunuel on 25 Dec 2018, 17:28, edited 3 times in total.
Renamed the topic and edited the question.



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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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06 Sep 2015, 07:00
allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. Statement 1: \(a^{(2x)}=b^{(x+6)}\)@a=4 and b=2, \(4^{(2x)}=2^{(x+6)}\), i.e. x can be 1 But the statement will also be balanced if a = 1/b and x = 2 hence NOT SUFFICIENTStatement 2: ab = 1No relation of a and b with x is given so nothing can be concluded about x, hence NOT SUFFICIENTCombining the two statementsab = 1 and \(a^{(2x)}=b^{(x+6)}\) Substituting b = 1/a \(a^{(2x)}=b^{(x+6)}\) => \(a^{(2x)}=(1/a)^{(x+6)}\) i.e. \(a^{(2x)}=b^{(x+6)}\) => \(a^{(2x)}=(a)^{(x+6)}\) i.e. 2x = (x+6) i.e. 3x = 6 i.e. x = 2 SUFFICIENTAnswer: Option C
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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06 Sep 2015, 07:14
allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. Statement 1: It does not provide enough information about a,b and x to get concrete values. Even on simplification, the expression will be in terms of a,b and x. INSUFFICIENT Statement2: ab=1 or a=1/b this statement provides relation between a and b but no information about x. INSUFFICIENT Combining 1 and 2 \((\frac{1}{b})^{(2x)}=b^{(x+6)}\) or \(1= b^{2x}(b^{x+6})\) or \(1= b^{3x+6}\) or \(b^0= b^{3x+6}\) or 0 = 3x+6 or x=2 SUFFICIENT Answer: C This questions is a value based data sufficiency question. You need single value of x. here you cannot take different values of a and b because for each value of a and b you will get different values of x. So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.



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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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06 Sep 2015, 07:34
kunal555 wrote: This questions is a value based data sufficiency question. You need single value of x. here you cannot take different values of a and b because for each value of a and b you will get different values of x. So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.
Not really. When statement 2 mentions that ab=1, then all combinations satisfying ab=1 , MUST give you consistent values. Thus, using a=b=1 is absolutely fine. You can not have C as the correct answer if you got different values of x for different combinations of ab=1. If you did get different values of x, then E would have been the correct answer.



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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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06 Sep 2015, 08:34
Engr2012 wrote: kunal555 wrote: This questions is a value based data sufficiency question. You need single value of x. here you cannot take different values of a and b because for each value of a and b you will get different values of x. So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.
Not really. When statement 2 mentions that ab=1, then all combinations satisfying ab=1 , MUST give you consistent values. Thus, using a=b=1 is absolutely fine. You can not have C as the correct answer if you got different values of x for different combinations of ab=1. If you did get different values of x, then E would have been the correct answer. My bad, did the question in a hurry and missed out on this detail. For all the values of a and b where ab=1, x will be 2, except for a=b=1 or a=b=1 where x will be 6. OA should be E then i guess, not C



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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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06 Sep 2015, 23:48
X=? 1.a^(2x)=b^(x+6) 2.ab=1 In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution. vatiables'number:3 > needs 3 equations > E 1) & 2) if a=b=1, it is possble that 2x is not equal to x+1, therefore the answer is E
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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25 Dec 2018, 08:57
allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. Dear Moderator, Looks like the OA for this one is incorrect. Statement 1: a=1 and b=1 then x can be anything . Hence Insufficient Statement 2 : No info about X , Hence Insufficient 1+2 a=1 and b=1 x= 2 a=1 and b=1 x= 3 Insufficient . ( In fact if a=1 and b=1 then x can be anything ) Also please check this post my MathRevolution: https://gmatclub.com/forum/x1a2xbx ... l#p1570471Hope you will look into this. Thank you.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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25 Dec 2018, 17:29
stne wrote: allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. Dear Moderator, Looks like the OA for this one is incorrect. Statement 1: a=1 and b=1 then x can be anything . Hence Insufficient Statement 2 : No info about X , Hence Insufficient 1+2 a=1 and b=1 x= 2 a=1 and b=1 x= 3 Insufficient . ( In fact if a=1 and b=1 then x can be anything ) Also please check this post my MathRevolution: https://gmatclub.com/forum/x1a2xbx ... l#p1570471Hope you will look into this. Thank you. The correct answer is E. Edited. Thank you.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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26 Dec 2018, 18:38
allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. Statement 1) a can be 1 or 1 or 0. Similarly, b can 1 or 1 or 0. In each case. We can't find the value of x. Statement 2) Nothing has been given about x. Also, a or b can 1 or 1. (1)+(2), Same as statement 1, if a=b=1/1, we can't find the value of x. So, Option E seems correct.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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26 Dec 2018, 18:49
allenh wrote: x = ? (1) \(a^{(2x)}=b^{(x+6)}\) (2) ab = 1 It seems that I should choose C for this one as when you combine these two statements, you will get x=2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E.. If a = b = 1. Then X can take any value. Hence, E.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1
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