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Re: If 0 < a < < 1, then which of the following must be true? (A [#permalink]
1
Did by plugging values as per inequality:

0< a < 1/b < b --> 0< ab < 1 < b
so ab is a fraction and b is whole or whole + fraction --> took values:
a = 1/3 and b = 2
checking via plug in, only E works --> 4> 2> 1/3 > 1/9

(even if we take b as 1.5 it works).
Answer E
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Re: If 0 < a < < 1, then which of the following must be true? (A [#permalink]
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a is a fraction but b is a positive number
according to the context, 0<a<1/b<1
so, the denominator of a > the positive integer b.

the power increment of a will lower the value of fraction.

so, b2 > b > a > a2
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Re: If 0 < a < < 1, then which of the following must be true? (A [#permalink]
Think of it like this...

0 < a < 1/b < 1 ==> 0 < a < 1 and 0 < 1/b < 1
So clearly a^2 is going to get smaller because it's less than one.

What about b? 0 < 1/b < 1 ==> 1 < b (multiply by b, we know the signs to flip because we're given that 0 < 1/b)

So b is greater than 1 and b^2 is greater than b.

Finally, 0 < a^2 < a < 1 < b < b^2
==> a^2 < a < b < b^2.
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Re: If 0 < a < < 1, then which of the following must be true? (A [#permalink]
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