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If a^2b > 1 and b < 2, which of the following could be the value of a?
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Updated on: 20 Nov 2014, 06:10
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If a^2b > 1 and b < 2, which of the following could be the value of a? A. 1/2 B. 1/4 C. 1/2 D. 2 E. 2/3
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Originally posted by GMATD11 on 04 Apr 2011, 03:59.
Last edited by Bunuel on 20 Nov 2014, 06:10, edited 1 time in total.
Renamed the topic and edited the question.



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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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04 Apr 2011, 04:23
GMATD11 wrote: If \(a^2*b>1 & b<2\), which of the following could be the value of a?
a) 1/2 b) 1/4 c) 1/2 d) 2 e) 2/3 I will try the substitution method in this one: A. \(a=\frac{1}{2}\) \(a^2*b=\frac{1}{4}*b\) \(\frac{1}{4}*b>1\) \(b>4\) Not Possible. b must be less than 2. B. \(a=\frac{1}{4}\) \(a^2*b=\frac{1}{16}*b\) \(\frac{1}{16}*b>1\) \(b>16\) Not Possible. b must be less than 2. C. \(a=\frac{1}{2}\) \(a^2*b=\frac{1}{4}*b\) \(\frac{1}{4}*b>1\) \(b>4\) Not Possible. b must be less than 2. D. \(a=2\) \(a^2*b=4*b\) \(4*b>1\) \(b>\frac{1}{4}\) Possible. There are infinite numbers between \(\frac{1}{4}\) and 2.E. \(a=\frac{2}{3}\) \(a^2*b=\frac{4}{9}*b\) \(\frac{4}{9}*b>1\) \(b>\frac{9}{4}\) \(b>2.25\) Not Possible. b must be less than 2.
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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04 Apr 2011, 04:45
I too tried plugging numbers, however I luckily chose 2 first as rest others seemed to be fractions and again chose b as 1, so that the square comes out as +ve one of an integer, which apparently should be > 1, and it clicked
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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04 Apr 2011, 08:18
a<0.7 or a>0.7 Answer is D.
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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04 Apr 2011, 17:42
GMATD11 wrote: If a^2b>1 and b<2, which of the following could be the value of a?
a) 1/2 b) 1/4 c) 1/2 d) 2 e) 2/3 You can also solve it using algebra: \(a^2*b > 1\) which implies \(b > \frac{1}{a^2}\) (Since a^2 will be positive) \(b < 2\) So \(\frac{1}{a^2} < b < 2\) Ignore b now. \(a^2  \frac{1}{2} > 0\) So \(a > 1/\sqrt{2}\) or \(a < 1/\sqrt{2}\) (You should be very comfortable arriving at this step from the step above. If you are not, check out the following post: inequalitiestrick91482.html?hilit=inequalities%20trickNotice that \(1/\sqrt{2} = \sqrt{2}/2 = .707\) The only value either less than 0.707 or greater than 0.707 is 2.
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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20 Dec 2014, 03:44
Given  a^(2b)>1, and b>2
But in order for a^(2b)>1, B cannot be less than equal to 0 So, the value of b is 0<b<2, meaning b=1 Which leads us to the following equation a^2>1 => a>1 or a<1 Only one option satisfies it, and that is D



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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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10 Mar 2016, 10:31



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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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19 May 2016, 02:40
given a^2 * b > 1 and b < 2
b must be positive given that a^2 is positive and whole product is greater that 1
so we can say 0< b < 2 hence b must be 1
so a^2 > 1, only one option fits i.e. a= 2



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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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21 Jul 2017, 07:25
VeritasPrepKarishma wrote: GMATD11 wrote: If a^2b>1 and b<2, which of the following could be the value of a?
a) 1/2 b) 1/4 c) 1/2 d) 2 e) 2/3 You can also solve it using algebra: \(a^2*b > 1\) which implies \(b > \frac{1}{a^2}\) (Since a^2 will be positive) \(b < 2\) So \(\frac{1}{a^2} < b < 2\) Ignore b now. \(a^2  \frac{1}{2} > 0\) So \(a > 1/\sqrt{2}\) or \(a < 1/\sqrt{2}\) (You should be very comfortable arriving at this step from the step above. If you are not, check out the following post: http://gmatclub.com/forum/inequalities ... es%20trickNotice that \(1/\sqrt{2} = \sqrt{2}/2 = .707\) The only value either less than 0.707 or greater than 0.707 is 2. how you get to know that question is not a^(2b) > 1 but \(a^2*b > 1\)



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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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22 Jul 2017, 05:18
jokschmer wrote: VeritasPrepKarishma wrote: GMATD11 wrote: If a^2b>1 and b<2, which of the following could be the value of a?
a) 1/2 b) 1/4 c) 1/2 d) 2 e) 2/3 You can also solve it using algebra: \(a^2*b > 1\) which implies \(b > \frac{1}{a^2}\) (Since a^2 will be positive) \(b < 2\) So \(\frac{1}{a^2} < b < 2\) Ignore b now. \(a^2  \frac{1}{2} > 0\) So \(a > 1/\sqrt{2}\) or \(a < 1/\sqrt{2}\) (You should be very comfortable arriving at this step from the step above. If you are not, check out the following post: http://gmatclub.com/forum/inequalities ... es%20trickNotice that \(1/\sqrt{2} = \sqrt{2}/2 = .707\) The only value either less than 0.707 or greater than 0.707 is 2. how you get to know that question is not a^(2b) > 1 but \(a^2*b > 1\) The formatting will be unambiguous in actual GMAT questions. If it is an exponent, it will be clearly shown.
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a?
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