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# M70-20

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Math Expert
Joined: 02 Sep 2009
Posts: 50711

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Updated on: 16 Oct 2018, 01:16
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Difficulty:

55% (hard)

Question Stats:

38% (00:12) correct 62% (00:24) wrong based on 13 sessions

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

(1) $$ab = 64$$

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

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Originally posted by Bunuel on 03 Sep 2018, 04:01.
Last edited by Bunuel on 16 Oct 2018, 01:16, edited 3 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50711

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03 Sep 2018, 04:01
Official Solution:

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

Since $$[\frac{a}{b}]$$ is defined as an 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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Re M70-20 &nbs [#permalink] 03 Sep 2018, 04:01
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# M70-20

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