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# If P is divisible by 2, is Q + 5 an integer? (1) The median

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Manager
Joined: 10 Jan 2010
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WE: Programming (Computer Software)
If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink]

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02 Oct 2011, 15:45
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If P is divisible by 2, is Q + 5 an integer?

(1) The median of P and Q is not an integer.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer.
[Reveal] Spoiler: OA

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Senior Manager
Joined: 08 Nov 2010
Posts: 408
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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03 Oct 2011, 10:15
maheshsrini wrote:
If P is divisible by 2, is Q + 5 an integer?

(1) The median of P and Q is not an integer.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer.

Date - P is even. The question is basically - Does Q is an integer?

So - Statement 1 - INSU.
Lets say P=2,Q=3 ----> The answer is YES.
P=2, Q=2.5 ----> The answer is NO.

statement 2 - SUFF.
$$(3p+q+q+10)/3 = Integer$$

3p/3 = p ----> Integer.

2Q+10/3 = Integer. we know that 10/3 is not an integer. therefore 2Q is not an integer as well.
so 2q=not integer.
Q = not integer/2 ----> Q is not an integer.
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Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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04 Oct 2011, 03:56
maheshsrini wrote:
If P is divisible by 2, is Q + 5 an integer?

(1) The median of P and Q is not an integer.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer.

2)
(3P+Q+Q+10)/3=3P/3+2(Q+5)/3
3P/3=P(Even integer)
2(Q+5)/3=Even Integer {:Note: P=Even; Even+Even=Even}
2(Q+5)=3*Even integer
Q+5=3*Even Integer/2=3*Integer{:Note: All Even integers contain at least ONE 2}
"Q+5" must be an integer. {:Note: 3*Integer=Integer; Integer * Integer= Integer}
Sufficient.

Ans: "B"
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Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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26 Oct 2013, 12:30
144144 wrote:
maheshsrini wrote:
If P is divisible by 2, is Q + 5 an integer?

(1) The median of P and Q is not an integer.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer.

Date - P is even. The question is basically - Does Q is an integer?

So - Statement 1 - INSU.
Lets say P=2,Q=3 ----> The answer is YES.
P=2, Q=2.5 ----> The answer is NO.

statement 2 - SUFF.
$$(3p+q+q+10)/3 = Integer$$

3p/3 = p ----> Integer.

2Q+10/3 = Integer. we know that 10/3 is not an integer. therefore 2Q is not an integer as well.
so 2q=not integer.
Q = not integer/2 ----> Q is not an integer.

could there be more discussion on this one? I don't get how you go from knowing 10/3 is not an integer to knowing that 2Q is not an integer either...
Math Expert
Joined: 02 Sep 2009
Posts: 39626
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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27 Oct 2013, 10:28
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AccipiterQ wrote:
144144 wrote:
maheshsrini wrote:
If P is divisible by 2, is Q + 5 an integer?

(1) The median of P and Q is not an integer.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer.

Date - P is even. The question is basically - Does Q is an integer?

So - Statement 1 - INSU.
Lets say P=2,Q=3 ----> The answer is YES.
P=2, Q=2.5 ----> The answer is NO.

statement 2 - SUFF.
$$(3p+q+q+10)/3 = Integer$$

3p/3 = p ----> Integer.

2Q+10/3 = Integer. we know that 10/3 is not an integer. therefore 2Q is not an integer as well.
so 2q=not integer.
Q = not integer/2 ----> Q is not an integer.

could there be more discussion on this one? I don't get how you go from knowing 10/3 is not an integer to knowing that 2Q is not an integer either...

If P is divisible by 2, is Q + 5 an integer?

P is divisible by 2 implies that P is an even integer --> P=2*integer, for some integer k.

(1) The median of P and Q is not an integer. The median of P and Q is $$\frac{P+Q}{2}=\frac{2*integer+Q}{2}=integer+\frac{Q}{2}$$. So, we are given that $$integer+\frac{Q}{2}$$ is not an integer. This means that Q/2 is not an integer, thus Q is not an even integer, which means that Q is either an odd integer or not an integer at all. Not sufficient.

(2) The average (arithmetic mean) of 3P, Q, and Q + 10 is an even integer --> $$\frac{3P+Q+Q + 10}{3}=even$$ --> $$3P+2Q+10=3*even=even$$ --> $$2Q=even-3P-10=even-even-even=even$$ --> $$2Q=even$$ --> $$Q=\frac{even}{2}=integer$$. Sufficient.

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Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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10 Nov 2013, 14:05
Hi
Can you find what's wrong with my reasoning?

(3Q/3) + (2Q+10)/3 = even int
Q + (Q+5)/3 = even int
Q+5 = even int -Q = even int
Q = even int- 5 = odd int.
Math Expert
Joined: 02 Sep 2009
Posts: 39626
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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10 Nov 2013, 14:42
ronr34 wrote:
Hi
Can you find what's wrong with my reasoning?

(3Q/3) + (2Q+10)/3 = even int
Q + (Q+5)/3 = even int
Q+5 = even int -Q = even int
Q = even int- 5 = odd int.

How did you get (Q+5)/3 from (2Q+10)/3 ?
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Joined: 08 Apr 2012
Posts: 453
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink]

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13 Nov 2013, 02:32
Bunuel wrote:
ronr34 wrote:
Hi
Can you find what's wrong with my reasoning?

(3Q/3) + (2Q+10)/3 = even int
Q + (Q+5)/3 = even int
Q+5 = even int -Q = even int
Q = even int- 5 = odd int.

How did you get (Q+5)/3 from (2Q+10)/3 ?

Sorry... my mistake
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Joined: 09 Sep 2013
Posts: 15935
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink]

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22 Nov 2014, 16:58
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Re: If P is divisible by 2, is Q + 5 an integer? (1) The median   [#permalink] 22 Nov 2014, 16:58
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# If P is divisible by 2, is Q + 5 an integer? (1) The median

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