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

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]
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