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Manager  Joined: 10 Nov 2010
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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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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, 04:59.
Last edited by Bunuel on 20 Nov 2014, 07:10, 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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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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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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a<-0.7 or a>0.7

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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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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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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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GRE 1: Q169 V154 Re: If a^2b > 1 and b < 2, which of the following could be the value of a?  [#permalink]

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Take b=1 s=and we can easily say that D is correct.
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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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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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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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Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: If a^2b > 1 and b < 2, which of the following could be the value of a?  [#permalink]

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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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_________________ Re: If a^2b > 1 and b < 2, which of the following could be the value of a?   [#permalink] 14 Sep 2018, 11:12
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