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# M28-56

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Math Expert
Joined: 02 Sep 2009
Posts: 52385

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16 Sep 2014, 00:44
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Difficulty:

95% (hard)

Question Stats:

44% (01:52) correct 56% (01:56) wrong based on 119 sessions

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If $$[x]$$ denotes the greatest integer less than or equal to $$x$$ for any number $$x$$, is $$[a] + [b] = 1$$?

(1) $$ab = 2$$.

(2) $$0 \lt a \lt b \lt 2$$.

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Joined: 02 Sep 2009
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16 Sep 2014, 00:44
Official Solution:

Given that some function [] rounds DOWN a number to the nearest integer. For example $$[1.5]=1$$, $$[2]=2$$, $$[-1.5]=-2$$, ...

(1) $$ab = 2$$. First of all this means that $$a$$ and $$b$$ are of the same sign.

If both are negative, then the maximum value of $$[a] + [b]$$ is -2, for any negative $$a$$ and $$b$$. So, this case is out.

If both are positive, then in order $$[a] + [b] = 1$$ to hold true, must be true that $$[a]=0$$ and $$[b]=1$$ (or vise-versa). Which means that $$0 \leq a \lt 1$$ and $$1 \leq b \lt 2$$ (or vise-versa). But in this case ab cannot be equal to 2. So, this case is also out.

We have that the answer to the question is NO. Sufficient.

(2) $$0 \lt a \lt b \lt 2$$. If $$a=\frac{1}{2}$$ and $$b=1$$, then $$[a] + [b] = 0 + 1 = 1$$ but if $$a=\frac{1}{4}$$ and $$b=\frac{1}{2}$$, then $$[a] + [b] = 0 + 0 = 0$$. Not sufficient.

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26 Nov 2014, 08:04
For stmt 1, wouldn't the max value of [a]+[b] be -3? because (-1)(-2)=2, and (-1)+(-2)=-3?

Or am I missing some factors?

Thanks
Math Expert
Joined: 02 Sep 2009
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26 Nov 2014, 08:05
JackSparr0w wrote:
For stmt 1, wouldn't the max value of [a]+[b] be -3? because (-1)(-2)=2, and (-1)+(-2)=-3?

Or am I missing some factors?

Thanks

It says that the maximum possible value of [a] + [b] is -2 (without the restriction ab=2).
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Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
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26 Nov 2014, 08:39
makes sense. Thanks
Senior Manager
Joined: 31 Mar 2016
Posts: 384
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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24 Aug 2016, 03:51
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 02 Nov 2015
Posts: 3

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29 Aug 2016, 07:27
I think this the explanation isn't clear enough, please elaborate.
Manager
Joined: 14 Oct 2012
Posts: 165

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05 Sep 2017, 14:15
Bunuel wrote:
JackSparr0w wrote:
For stmt 1, wouldn't the max value of [a]+[b] be -3? because (-1)(-2)=2, and (-1)+(-2)=-3?

Or am I missing some factors?

Thanks

It says that the maximum possible value of [a] + [b] is -2 (without the restriction ab=2).

Hello Bunuel
What combination would give us value of (-2)?
the max i could think of is [-1.4] + [-1.4] = (-2) + (-2) = (-4)
[?] + [?] = (-1) + (-1) = (-2) ?
Can you please let me know.
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52385

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05 Sep 2017, 20:07
1
manishtank1988 wrote:
Bunuel wrote:
JackSparr0w wrote:
For stmt 1, wouldn't the max value of [a]+[b] be -3? because (-1)(-2)=2, and (-1)+(-2)=-3?

Or am I missing some factors?

Thanks

It says that the maximum possible value of [a] + [b] is -2 (without the restriction ab=2).

Hello Bunuel
What combination would give us value of (-2)?
the max i could think of is [-1.4] + [-1.4] = (-2) + (-2) = (-4)
[?] + [?] = (-1) + (-1) = (-2) ?
Can you please let me know.
Thanks

What I meant was that generally if a and b are negative, then the maximum value of [a] + [b] is -1+(-1)=-2. But you cannot get -2, if ab=2.

For example, [-0.5] + [-0.5] = -1 + (-1) = -2.
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06 Sep 2017, 16:45
It says that the maximum possible value of [a] + is -2 (without the restriction ab=2).[/quote]

Hello Bunuel
What combination would give us value of (-2)?
the max i could think of is [-1.4] + [-1.4] = (-2) + (-2) = (-4)
[?] + [?] = (-1) + (-1) = (-2) ?
Can you please let me know.
Thanks[/quote]

What I meant was that generally if a and b are negative, then the maximum value of [a] + [b] is -1+(-1)=-2. But you cannot get -2, if ab=2.

For example, [-0.5] + [-0.5] = -1 + (-1) = -2.[/quote]

Got it thanks [b]Bunuel
Intern
Joined: 09 Jan 2017
Posts: 3

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28 Dec 2017, 00:25
Hi bunuel,

According to statement 1 we have ab=2 . Cant we right that as 0.2*10 in which case [0.2] + [10]= 10

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52385

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28 Dec 2017, 01:02
ss9031 wrote:
Hi bunuel,

According to statement 1 we have ab=2 . Cant we right that as 0.2*10 in which case [0.2] + [10]= 10

Thanks

What is there to clarify? What is your question?
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Joined: 09 Jan 2017
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28 Dec 2017, 09:38
My question is how statement is sufficient to answer the question when there is another possibility which is

[0.2] + [10] = 10.

If this is the case then we can have multiple answers for this statement and hence statement is not sufficient,

but the correct answer is statement A is sufficient.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52385

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28 Dec 2017, 09:43
ss9031 wrote:
My question is how statement is sufficient to answer the question when there is another possibility which is

[0.2] + [10] = 10.

If this is the case then we can have multiple answers for this statement and hence statement is not sufficient,

but the correct answer is statement A is sufficient.

Thanks

Statement (1) is sufficient because it gives a definite NO answer to the question. The example you consider also give a NO answer to the question whether $$[a] + [b] = 1$$. So, no matter what example you consider for (1), for all you'll get the same NO answer.
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Re: M28-56 &nbs [#permalink] 28 Dec 2017, 09:43
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# M28-56

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