NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 19:17 It is currently 26 Apr 2024, 19:17
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
maheshsrini
Manager
Manager
Joined: 10 Jan 2010
Posts: 76
Own Kudos [?]: 516 [24]
Given Kudos: 33
GPA: 4
WE:Programming (Computer Software)
Send PM
If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink] New post   02 Oct 2011, 15:45
3
Kudos
21
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

66% (02:32) correct 34% (02:18) wrong based on 454 sessions
Hide Show 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.
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619249 [6]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   27 Oct 2013, 10:28
5
Kudos
1
Bookmarks
Expert Reply
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.

Answer: B.
General Discussion
User avatar
144144
Manager
Manager
Joined: 08 Nov 2010
Posts: 204
Own Kudos [?]: 496 [0]
Given Kudos: 161
 Q50  V41
GPA: 3.9
WE 1: Business Development
Send PM
GMAT ToolKit User
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   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.
User avatar
fluke
Retired Moderator
Joined: 20 Dec 2010
Posts: 1114
Own Kudos [?]: 4702 [1]
Given Kudos: 376
Send PM
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   04 Oct 2011, 03:56
1
Kudos
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"
User avatar
AccipiterQ
Manager
Manager
Joined: 26 Sep 2013
Posts: 151
Own Kudos [?]: 598 [0]
Given Kudos: 40
Concentration: Finance, Economics
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Send PM
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   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...
User avatar
ronr34
Senior Manager
Senior Manager
Joined: 08 Apr 2012
Posts: 259
Own Kudos [?]: 239 [0]
Given Kudos: 58
Send PM
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619249 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   10 Nov 2013, 14:42
Expert Reply
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 ?
User avatar
ronr34
Senior Manager
Senior Manager
Joined: 08 Apr 2012
Posts: 259
Own Kudos [?]: 239 [0]
Given Kudos: 58
Send PM
Re: MGMAT DS Statistics- Is Q + 5 an integer [#permalink] New post   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 :(
User avatar
D
gvij2017
Director
Director
Joined: 09 Aug 2017
Posts: 689
Own Kudos [?]: 415 [0]
Given Kudos: 778
Send PM
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink] New post   29 Sep 2018, 22:20
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?
User avatar
B
Sonia2023
Manager
Manager
Joined: 20 Feb 2022
Posts: 63
Own Kudos [?]: 15 [0]
Given Kudos: 88
Location: India
Concentration: Finance, Other
Send PM
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink] New post   29 Sep 2023, 06:43
chetan2u Bunuel - When we say "P is divisible by 2", can we safely assume that P is an integer and not a decimal number because even 2.2 is divisible by 2.

Thank you.
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31969 [1]
Given Kudos: 291
Send PM
Reviews Badge
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink] New post   29 Sep 2023, 07:00
1
Kudos
Expert Reply
Sonia0106 wrote:
chetan2u Bunuel - When we say "P is divisible by 2", can we safely assume that P is an integer and not a decimal number because even 2.2 is divisible by 2.

Thank you.



Yes, P divisible by 2 means P is even integer.
User avatar
B
DanTheGMATMan
Tutor
Joined: 02 Oct 2015
Posts: 59
Own Kudos [?]: 22 [0]
Given Kudos: 4
Send PM
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink] New post   29 Sep 2023, 07:42
Expert Reply
For option 2-

If \(\frac{(3P + 2Q + 10)}{2}\) is even, then 3P + Q + 5 must be even (once the 2 in the denominator has canceled out with the 2 in each part of the trinomial in the numerator. Moreover, they have to add up to an integer so if P is an integer so so must Q be.
GMAT Club Bot
gmatclubot
Re: If P is divisible by 2, is Q + 5 an integer? (1) The median [#permalink]
29 Sep 2023, 07:42
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions