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# Math DS (m05q29)

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Director
Joined: 11 Jun 2007
Posts: 637

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18 Oct 2007, 11:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is $$\frac{4Q}{11}$$ a positive integer?

1. $$Q$$ is a prime number
2. $$2Q$$ is divisible by 11

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions
Manager
Joined: 02 Aug 2007
Posts: 145

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18 Oct 2007, 11:39
B.
The question is asking whether Q is a multiple of 11.

1) Q as a prime number does not help us in answer the question.
INSUFF

2) 2Q is a multiple of 11, so 4Q should also be a multiple of 11.
SUFFICIENT
Director
Joined: 11 Jun 2007
Posts: 637

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18 Oct 2007, 13:30
yuefei wrote:
B.
The question is asking whether Q is a multiple of 11.

1) Q as a prime number does not help us in answer the question.
INSUFF

2) 2Q is a multiple of 11, so 4Q should also be a multiple of 11.
SUFFICIENT

I got the same answer but that is not the OA.
Manager
Joined: 30 Jan 2006
Posts: 62

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18 Oct 2007, 16:26
I think the answer is C.

The reason is the question is asking if 4Q/11 is a +ive integer. 2Q/11 is divisble by 11 but it can be -ive also.
Director
Joined: 11 Jun 2007
Posts: 637

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18 Oct 2007, 16:41
smily_buddy wrote:
I think the answer is C.

The reason is the question is asking if 4Q/11 is a +ive integer. 2Q/11 is divisble by 11 but it can be -ive also.

There is the missing link. You are right. That is why we need both conditions. (C) is the OA.
VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

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18 Oct 2007, 17:40
1. prime number, it can give us a non integer
2. can be negative and positive

applied together 1 and 2. we say that prime cannot be negative and 2 gives us multiple so C
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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18 Oct 2007, 18:51
St1:
If Q = 11, then 4Q/11 is a positive integer.
If Q = 2, then 4Q/11 is not a positive integer.
Insufficient.

St2:
2Q/11 = integer.
If Q = 22, then 2Q/11 = integer and 4Q/11 = positive integer
if Q = -33/2, then 2Q/11 = integer but 4Q/11 != positive integer.
Insufficient.

St1 and St2:
Q = 11, then 2Q/11 = integer and 4Q/11 = positive integer.
Sufficient.

Ans C
Intern
Joined: 06 Sep 2009
Posts: 21
Location: Mumbai

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25 Oct 2009, 06:20
Ravshonbek wrote:
1. prime number, it can give us a non integer
2. can be negative and positive

applied together 1 and 2. we say that prime cannot be negative and 2 gives us multiple so C

Little confused guys, prime numbers cannot be negative ? It means -11 is not qualified as a prime number ?
SVP
Joined: 29 Aug 2007
Posts: 2473

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25 Oct 2009, 10:45
eyunni wrote:
Is 4Q/11 a positive integer?

(1) Q is a prime number
(2) 2Q is divisible by 11

1: Q could be 2 or 3 or 5 or 7 or 11 or 13. NSF..
2: Q could be -ve, 0 or +ve. For ex: -11 or -5.50 or 0 or 5.50 or 11 or any multiples of 11. NSF..

1&2: Q must be a prime and 2Q must be divisible by 11.

Q must be a prime eliminates the chances that Q is a -ve, 0 and fraction.
Given that Q is a prime and 2Q must be divisible by 11 eliminate the chances that Q is other than 11.

Therefore Q = 11 and 4Q/11 is a +ve integer i.e. 4.

Thats a good question though....
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Intern
Joined: 14 Sep 2009
Posts: 26
Location: New York, NY

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29 Nov 2009, 08:16
Hey I know I'm joining this thread really really late - but can anyone confirm whether prime numbers can be negative?

I checked the Wikipedia Prime page (I can't post the link!) but I didn't see anything definitive.
Manager
Joined: 17 Jan 2010
Posts: 59
Concentration: Entrepreneurship, Strategy
GMAT 1: 730 Q49 V41
WE: Consulting (Consulting)

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26 Jun 2010, 10:16
http://mathforum.org/library/drmath/view/55940.html

- Explanation as to why there are no negative prime numbers.
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Intern
Joined: 12 Mar 2010
Posts: 10
GMAT 1: 710 Q48 V38

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26 Jun 2010, 18:12
C

1) Q can be 11 => it works or Q can be 3 => is not good, hence insufficient
2) 2Q is divisible by B, but we don't know if the result of this division is a positive integer, hence insufficient

1 & 2 together work
Math Expert
Joined: 02 Sep 2009
Posts: 39661

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15 Apr 2012, 13:53
eyunni wrote:
Is $$\frac{4Q}{11}$$ a positive integer?

1. $$Q$$ is a prime number
2. $$2Q$$ is divisible by 11

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

(1) $$q$$ is a prime number --> if $$q=2$$ then the answer is NO but if $$q=11$$ then the answer is YES. Not sufficient.

(2) $$2q$$ is divisible by 11 --> $$\frac{2q}{11}=integer$$ --> $$2*\frac{2q}{11}=\frac{4q}{11}=2*integer=integer$$, but we don't know whether this integer is positive or not: consider $$q=0$$ and $$q=11$$. Not sufficient.

(1)+(2) Since $$q$$ is a prime number and $$2q$$ is divisible by 11, then $$q$$ must be equal to 11 (no other prime but 11 will yield integer result for $$\frac{2q}{11}$$ ) --> $$\frac{4q}{11}=4$$. Sufficient.

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Re: Math DS (m05q29)   [#permalink] 15 Apr 2012, 13:53
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# Math DS (m05q29)

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