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# M70-20

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Math Expert
Joined: 02 Sep 2009
Posts: 49312

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03 Sep 2018, 05:01
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Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:20) wrong based on 3 sessions

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$$a$$ and $$b$$ are integers. $$[x]$$ is the greatest integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

(2) $$a=b^2$$

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Math Expert
Joined: 02 Sep 2009
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03 Sep 2018, 05:01
Official Solution:

We’ll go for LOGICAL because there is a logic to understanding the operator.

Since $$[\frac{a}{b}]$$ is defined as the greatest integer either equal to or less than $$\frac{a}{b}$$, no possible value of $$(a,b)$$ can ever make $$[\frac{a}{b}]$$ necessarily greater than any integer. This means a definitive answer to the question stem, if there is sufficient information, can only be ‘NO!’ – when $$[\frac{a}{b}] < {1}$$. This would be the case if $$b$$ is greater than $$a$$. (1) gives us no such information, and (2) gives us the opposite: the greater integer $$b$$ is, integer $$a$$ becomes even greater. Thus, combining the two we’ll still get $$a > b$$. Therefore, (E) is correct.

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Joined: 28 Aug 2018
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Schools: ESSEC '21

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07 Sep 2018, 01:51
By combining both statements, we get
b=4 and a=16 and thus a/b=4; so we can answer the question, then why option E?
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Joined: 26 Aug 2018
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09 Sep 2018, 12:48
I think this is a high-quality question and I don't agree with the explanation. Ans should be C because combining both 1 and 2 we get B as 4 and A as 16 so we can answer the initial question as "yes".
Re M70-20 &nbs [#permalink] 09 Sep 2018, 12:48
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# M70-20

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