Math DS:

Question

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

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

C 
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yuefei · Answer

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

eyunni · Answer

I got the same answer but that is not the OA.
Guys, any other answers?

smily_buddy · Answer

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.

eyunni · Answer

There is the missing link. You are right. That is why we need both conditions. (C) is the OA.

Ravshonbek · Answer

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

ywilfred · Answer

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

engel · Answer

Little confused guys, prime numbers cannot be negative ? It means -11 is not qualified as a prime number ?

GMAT TIGER · Answer

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....

danielduq · Answer

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.

Rosser · Answer

https://mathforum.org/library/drmath/view/55940.html - Explanation as to why there are no negative prime numbers.

GoToHaas2016 · Answer

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

Bunuel · Answer

(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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