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M14-36

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M14-36 [#permalink]

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Re M14-36 [#permalink]

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New post 16 Sep 2014, 00:54
Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(a + b - c\) is an integer. Thus, \(2(a + b - c)\) is an even integer.

Statement (2) by itself is insufficient. Consider \(a = b = c = 0\) (the answer is "no") and \(a = 1.25\), \(c = -1.25\), \(b = 0\) (the answer is "yes").


Answer: A
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Re M14-36 [#permalink]

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New post 30 Jan 2015, 08:01
Wont 2(a+b-c) result into an even integer irrespective of the statements below? Thus, making either statement sufficient.
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Re: M14-36 [#permalink]

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apurvadubhashi wrote:
Wont 2(a+b-c) result into an even integer irrespective of the statements below? Thus, making either statement sufficient.


No. For example, if a+b-c=1/2, then 2(a+b-c)=1, or if a+b-c=1/3, then 2(a+b-c)=2/3, not an integer at all.
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M14-36 [#permalink]

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New post 02 Feb 2015, 06:31
Fantastic question!

Just shows how questions that look so easy are actually so deceptive :)

Yeah .... even I marked D - Wrong Ans
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Re: M14-36 [#permalink]

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New post 12 Apr 2015, 11:29
Bunuel wrote:
Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(a + b - c\) is an integer. Thus, \(2(a + b - c)\) is an even integer.

Statement (2) by itself is insufficient. Consider \(a = b = c = 0\) (the answer is "no") and \(a = 1.25\), \(c = -1.25\), \(b = 0\) (the answer is "yes").


Answer: A


I understand why answer is D but can't understand why in explanation used such example: \(a = 1.25\), \(c = -1.25\), \(b = 0\) is (the answer is "yes")
We have question "Is \(2(a+b−c)\) an odd?"
let's put this numbers in the question and we receive: \(2(1.25+0-1.25) = 0 = even\)

I think correct example will be \(a = \frac{1}{4}\) \(b = \frac{1}{4}\) and \(c =0\)
\(b = a - c\) :
\(\frac{1}{4} = \frac{1}{4} - 0\)

and \(2(a+b−c)\):
\(2(\frac{1}{4}+\frac{1}{4}-0) = 1 = odd\)

Am I miss something or this is misprint in explanation?
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Re: M14-36 [#permalink]

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Harley1980 wrote:
Bunuel wrote:
Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(a + b - c\) is an integer. Thus, \(2(a + b - c)\) is an even integer.

Statement (2) by itself is insufficient. Consider \(a = b = c = 0\) (the answer is "no") and \(a = 1.25\), \(c = -1.25\), \(b = 0\) (the answer is "yes").


Answer: A


I understand why answer is D but can't understand why in explanation used such example: \(a = 1.25\), \(c = -1.25\), \(b = 0\) is (the answer is "yes")
We have question "Is \(2(a+b−c)\) an odd?"
let's put this numbers in the question and we receive: \(2(1.25+0-1.25) = 0 = even\)

I think correct example will be \(a = \frac{1}{4}\) \(b = \frac{1}{4}\) and \(c =0\)
\(b = a - c\) :
\(\frac{1}{4} = \frac{1}{4} - 0\)

and \(2(a+b−c)\):
\(2(\frac{1}{4}+\frac{1}{4}-0) = 1 = odd\)

Am I miss something or this is misprint in explanation?


If \(a = 1.25\), \(c = -1.25\), \(b = 0\), then \(2(a + b - c) = 2(1.25+0 -(-1.25)) = 2*2.5=5\), not 0.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M14-36 [#permalink]

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Another way to solve statement 2.

Is 2(a+b−c) an odd integer?

(2) b=a+c


Put b=a+c in original equation.
2(a+a+c-c)--> 2*2a.
If a= 1/4 then 2*2*1/4 is odd. And if a= any odd or even integer 2*2a will be even. Insufficient.

Answer: A
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Re: M14-36   [#permalink] 02 Jan 2018, 03:52
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