GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 01:18 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If P is divisible by 2, is Q + 5 an integer? (1) The median

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 10 Jan 2010
Posts: 89
GPA: 4
WE: Programming (Computer Software)
If P is divisible by 2, is Q + 5 an integer? (1) The median  [#permalink]

Show Tags

1
7 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:32) correct 35% (02:15) wrong based on 208 sessions

HideShow timer Statistics

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.

_________________
-If you like my post, consider giving KUDOS
Senior Manager  Joined: 08 Nov 2010
Posts: 273
WE 1: Business Development
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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.
_________________
Retired Moderator Joined: 20 Dec 2010
Posts: 1588
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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"
_________________
Manager  Joined: 26 Sep 2013
Posts: 184
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58262
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

3
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.

_________________
Senior Manager  Joined: 08 Apr 2012
Posts: 327
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58262
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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 ?
_________________
Senior Manager  Joined: 08 Apr 2012
Posts: 327
Re: MGMAT DS Statistics- Is Q + 5 an integer  [#permalink]

Show Tags

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 Senior Manager  G
Joined: 09 Aug 2017
Posts: 479
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median  [#permalink]

Show Tags

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

If P= 4.4 then still P is divisible by 2.
Now, where am I wrong?
Non-Human User Joined: 09 Sep 2013
Posts: 13082
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If P is divisible by 2, is Q + 5 an integer? (1) The median   [#permalink] 12 Oct 2019, 14:09
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  