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GMATD11
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If a^2b > 1 and b < 2, which of the following could be the value of a? Updated on: 16 Apr 2022, 02:41
Originally posted by GMATD11 on 04 Apr 2011, 04:59.
Last edited by Bunuel on 16 Apr 2022, 02:41, edited 2 times in total.
Renamed the topic and edited the question.
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82% (01:39) correct 18% (02:09) wrong based on 742 sessions

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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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D
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KarishmaB
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If a^2b > 1 and b < 2, which of the following could be the value of a? 04 Apr 2011, 18:42
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GMATD11
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
Show more

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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If a^2b > 1 and b < 2, which of the following could be the value of a? 04 Apr 2011, 05:23
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GMATD11
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
Show more

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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If a^2b > 1 and b < 2, which of the following could be the value of a? 04 Apr 2011, 05:45
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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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If a^2b > 1 and b < 2, which of the following could be the value of a? 04 Apr 2011, 09:18
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a<-0.7 or a>0.7
Answer is D.

Posted from my mobile device
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If a^2b > 1 and b < 2, which of the following could be the value of a? 10 Mar 2016, 11:31
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Take b=1 s=and we can easily say that D is correct.
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If a^2b > 1 and b < 2, which of the following could be the value of a? 19 May 2016, 03:40
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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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If a^2b > 1 and b < 2, which of the following could be the value of a? 21 Jul 2017, 08:25
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VeritasPrepKarishma
GMATD11
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: https://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.
Show more

how you get to know that question is not a^(2b) > 1 but \(a^2*b > 1\)
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If a^2b > 1 and b < 2, which of the following could be the value of a? 22 Jul 2017, 06:18
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jokschmer
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GMATD11
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: https://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 \(a^2*b > 1\)
Show more

The formatting will be unambiguous in actual GMAT questions. If it is an exponent, it will be clearly shown.
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If a^2b > 1 and b < 2, which of the following could be the value of a? 27 Feb 2026, 03:11
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