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Math DS:

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eyunni
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Math DS: [#permalink] New post   18 Oct 2007, 11:27
Is \(\frac{4Q}{11}\) a positive integer?

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

Show SpoilerOA
C

Source: GMAT Club Tests - hardest GMAT questions

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yuefei
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[#permalink] New post   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
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eyunni
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[#permalink] New post   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.
Guys, any other answers?
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smily_buddy
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[#permalink] New post   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.
Any other thoughts please.
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eyunni
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[#permalink] New post   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.
Any other thoughts please.


There is the missing link. You are right. That is why we need both conditions. (C) is the OA.
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[#permalink] New post   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
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[#permalink] New post   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
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Re: [#permalink] New post   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 ?
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Re: Math DS (m05q29) [#permalink] New post   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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Re: Math DS (m05q29) [#permalink] New post   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.
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Re: Math DS (m05q29) [#permalink] New post   26 Jun 2010, 10:16
https://mathforum.org/library/drmath/view/55940.html

- Explanation as to why there are no negative prime numbers.
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Re: Math DS (m05q29) [#permalink] New post   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
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Re: Math DS (m05q29) [#permalink] New post   15 Apr 2012, 13:53
Expert Reply
eyunni wrote:
Is \(\frac{4Q}{11}\) a positive integer?

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

Show SpoilerOA
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.

Answer: C.

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