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Joined: 02 Sep 2009
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Math Expert
Joined: 02 Sep 2009
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Re M2856
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16 Sep 2014, 01:44
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 viseversa). Which means that \(0 \leq a \lt 1\) and \(1 \leq b \lt 2\) (or viseversa). 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. Answer: A
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Joined: 08 Feb 2014
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Re: M2856
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26 Nov 2014, 09:04
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



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Re: M2856
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26 Nov 2014, 09:05



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Re: M2856
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26 Nov 2014, 09:39
makes sense. Thanks



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Re M2856
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24 Aug 2016, 04:51
I think this is a highquality question and I agree with explanation.



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Re M2856
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29 Aug 2016, 08:27
I think this the explanation isn't clear enough, please elaborate.



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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 BunuelWhat 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



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Re: M2856
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05 Sep 2017, 21:07



Manager
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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



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Re: M2856
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28 Dec 2017, 01:25
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
Please clarify
Thanks



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Re: M2856
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28 Dec 2017, 02:02



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Re: M2856
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28 Dec 2017, 10:38
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.
Please explain how it so
Thanks



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Re: M2856
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28 Dec 2017, 10:43










