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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   95% (hard)

Question Stats: 17% (01:51) correct 83% (01:51) wrong based on 29 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 V
Joined: 02 Sep 2009
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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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Manager  B
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if u combine two, b^3=64 then b=4. and a=16, thus sufficient. Am I wrong?
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Bunuel wrote:
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.

Hello chetan2u Bunuel

OS above is not clear to me...

Can you explain with some other approach...

I find OA dubious....

Thanks.
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Math Expert V
Joined: 02 Aug 2009
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3
1
Bunuel wrote:
$$a$$ and $$b$$ are integers. $$[x]$$ is an integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

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

Harshgmat
Yes the question is a bit confusing because we have been dealing with such questions with a bit different wordings.

Had it been $$[x]$$ is the GREATEST integer less than or equal to $$x$$, the answer would be YES. Because a/B would be 4 and thus >1.

However here GREATEST is missing, so the value could be anything but not greater than a/B..
So if a/b=4, [a/b] can be 4,3,2,1,0,-1,-2.....
So it could be any integer as shown above and $$\frac{a}{b}\leq{4}$$

The difference is the word GREATEST not being there.

Hope it helps.
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chetan2u wrote:
Bunuel wrote:
$$a$$ and $$b$$ are integers. $$[x]$$ is an integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

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

Harshgmat
Yes the question is a bit confusing because we have been dealing with such questions with a bit different wordings.

Had it been $$[x]$$ is the GREATEST integer less than or equal to $$x$$, the answer would be YES. Because a/B would be 4 and thus >1.

However here GREATEST is missing, so the value could be anything but not greater than a/B..
So if a/b=4, [a/b] can be 4,3,2,1,0,-1,-2.....
So it could be any integer as shown above and $$\frac{a}{b}\leq{4}$$

The difference is the word GREATEST not being there.

Hope it helps.

chetan2u

Thanks. Kudos.

Posted from my mobile device
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Bunuel

This question is marked as sub-600 level question. As per stats the question has 75% Difficulty level based on the 30 responses.

My concern is that the test I took now (I guess M70? ) is basically categorizing all questions as sub 600 where as that is the actual level of difficulty.

My accuracy in the test is 73% but then it will be for sub 600 questions.. That is clearly not the case.

CC bb
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VP  V
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GMAT 1: 600 Q46 V27 ### Show Tags

TheNightKing wrote:
Bunuel

This question is marked as sub-600 level question. As per stats the question has 75% Difficulty level based on the 30 responses.

My concern is that the test I took now (I guess M70? ) is basically categorizing all questions as sub 600 where as that is the actual level of difficulty.

My accuracy in the test is 73% but then it will be for sub 600 questions.. That is clearly not the case.

CC bb

Following up..I would want to know your thoughts.

Thanks!
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It is only 21 sessions. Not sure where 30 came from but it takes time for the system to stabilize And for low volume questions to get their footing... and after some time the tag updates the tag automatically.

Posted from my mobile device
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GMAT 1: 600 Q46 V27 ### Show Tags

bb wrote:
It is only 21 sessions. Not sure where 30 came from but it takes time for the system to stabilize And for low volume questions to get their footing... and after some time the tag updates the tag automatically.

bb

I understand that. My concern is that does that level of difficulty get reflected on the test also?

If the tag gets updated but the test doesn't reflect it then it seems pointless to me.!
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You are missing on great learning if you don't know what this is: Project SC Butler Re: M70-20   [#permalink] 08 Apr 2020, 12:55

# M70-20

Moderators: chetan2u, Bunuel  