Is 4Q/11 is positive integer? (1) Q is prime number. (2) 2Q

Question

Is 4Q/11 is positive integer?

(1) Q is prime number.
(2) 2Q is divisible by 11.

Juaz · Answer

OA is not C.

Ravshonbek · Answer

1. Q can be  negative  and  positive  at the same time it can be prime number other than 11 which makes whole product  non integer  so insuff.

2. 2Q is divisible by 11. that's fine. but Q can be  negative  and  positive  so insuff.

combined still nothing about negative and positive. cuz. primes can be either.

E

IrinaOK · Answer

I also vote for C,

1st INSUFF. 

if Q=11 YES, if Q=any other prime number NO.

2nd INSUFF.

(2Q)/11=Intenger, then 4Q/11=2*(2Q/11)=2*Intenger=Intenger, however can be both +ve or -ve.

Both combined, SUFF,

only positive intengers can be prime numbers, thus 

2*(2Q/11)=2*Positive Intenger=Positive Intenger

I can`t see how Q can be  not  11, and still satisfy the 1st and 2nd statements..
 
C....

bkk145 · Answer

B

(1) if Q=11, then 4Q/11 is a positive integer
if Q=3, then 4Q/11 is not a positive integer
INSUFFICIENT

(2) 2Q/11 = integer
Q = (11*integer) / 2
Plug this back in what we are trying to find:
  / 11 =  /11 = 2*integer
This will always be an integer.
SUFFICIENT

varunk · Answer

Can primes be either i.e. -11 is prime number and so is 11?

If a prime number can be negative or position (I thought they could only be positive) then I think the answer is E. 

If only a positive number can be a prime number then I think the answer is C.

Fistail · Answer

hmmm............

seems OA is wrong. I still say it should be C:

  remember the question says positive integer  

1: q could be 2, 3, 5, 7, 11 and so on. nsf. 
2: 2Q could be 22, 11, 0, -11, -22, -33, -44 or so on. nsf. 

from 1 and 2: since q is a prime, q can only be +ve. so 2q is divisible by 11, 4q/11 should be +ve. 

if still not C, i like to see OE.

Fistail · Answer

nope. E as OA is incorrect. Q is a prime, which can not be -ve and is always +ve. 

so should be C.

IrinaOK · Answer

disagree with OA. prime number can not be negative by definition. prime number is a intenger that has only two factors: itself and one. if a number is negative it has at least three factors, which is more than 2. for more detailed explanations: https://mathforum.org/library/drmath/view/55940.html

Ferihere · Answer

A prime number is a positive integer that has exactly two different positive divisors, 1 and itself. 

Reference: GMAT OG11 the Ed, author GMAC, page 108

 ANS: C

Ravshonbek · Answer

hmm, interesting, i got some info from those pages. really intersting question. can negative be prime?

it is E I think

https://primes.utm.edu/notes/faq/negative_primes.html
https://mathforum.org/library/drmath/set ... ative.html
https://www.madsci.org/posts/archives/20 ... .Cs.r.html

Ravshonbek · Answer

stem says is the integer positive, but really intersting question.

Ravshonbek · Answer

I had the idea of primes as positive numbers but after viewing several web pages i changed my mind. After a long discussion with my friend who is doing math studies at the moment we came up with the idea that prime cannot be negative. actually the definition itself says it cannot be negative. The OA should be rebutted then.
what is the source, is there any OE for the DS.

really intersting question

GMATBLACKBELT · Answer

Tricky:

S1: Q is prime. Q can be any prime insuff.

S2: 2Q/11= integer so 2(2Q)/11 --> 2*integer. 

This is simple, but so easy to miss. 2*integer could be + or -.

Insuff.

1&2
Since S1 establishes that Q is + and S2 establishes that 4Q/11 is an integer.

Then 4Q/11 is a + integer.

C

Is 4Q/11 is positive integer? (1) Q is prime number. (2) 2Q

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards