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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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If a^2b > 1 and b < 2, which of the following could be the value of a?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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New post 04 Apr 2011, 17:42
3
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: inequalities-trick-91482.html?hilit=inequalities%20trick

Notice 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?  [#permalink]

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New post 20 Dec 2014, 03:44
1
1
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?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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New post 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%20trick

Notice 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?  [#permalink]

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New post 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%20trick

Notice 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?  [#permalink]

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New post 14 Sep 2018, 10:12
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Re: If a^2b > 1 and b < 2, which of the following could be the value of a? &nbs [#permalink] 14 Sep 2018, 10:12
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