If p and q are positive integers and pq = 24, what is the

Question

If p and q are positive integers and pq = 24, what is the value of p ?

(1) q/6 is an integer.
(2) p/2 is an integer.

Bunuel · Answer

SOLUTION

If p and q are positive integers and pq = 24, what is the value of p ?

(1) q/6 is an integer --> q is a multiple of 6 --> the following pairs of (p, q) satisfy pq = 24: (4, 6), (2, 12) and (1, 24). Not sufficient.

(2) p/2 is an integer --> p is even --> more than one pair of (p, q) satisfy pq = 24: (4, 6), (2, 12), ... . Not sufficient.

(1)+(2) Since from (2) p is even, then two pairs remain from (1): (4, 6) and (2, 12). Therefore p can be 4 or 2. Not sufficient.

Answer: E.

WoundedTiger · Answer

If p and q are positive integers and pq = 24, what is the value of p ?

(1) q/6 is an integer.
(2) p/2 is an integer.

Given

p, q are positive integers and pq=24. What is the value of p
Factors of 24 are : 1,2,3,4,6,8,12,24

St 1: q= 6*I where I is some integer so possible value of q=6,12,24 ---->possible value of p=4,2,1
So A and D ruled out
St 2: p=2*a where a is some integer so possible value of p=2,4,6,8,12 and 24
so B ruled out

Combining we get 
possible value for q: 6,12 (Note 24 cannot be there because q=24 then p=1 and p/2 is not an integer)
Possible value of p: 4 and 2

Ans E

arunspanda · Answer

If p and q are positive integers and pq = 24, what is the value of p ?

(1) q/6 is an integer.
(2) p/2 is an integer.

Given
 pq = 24 
 p  and  q are positive integers:  p > 0  ,  q > 0

Statement 1

q/6  is an integer =>  q = 6k , k is a positve integer as  q > 0

Substituting  q  in  pq = 24 , we obtain  p*6k =24 .
As  6k > 0 , dividing both sides by 6k , we obtain  p = 24/(6k) = 4/k .
 p  can be  4 ,  2  and  1  for  k= 1 ,  2  and  4 .

As p  can not be determined uniquely, statement (1) is not sufficient...................................  .(A), (D)

Statement 2

p/2  is an integer,  p = 2l ,  l is a positve integer as  p > 0 
Substituting  p  in the equation  pq = 24 , we obtain  2l.q =24 .
As  2l > 0 , dividing both sides by 2l , we obtain  q = 24/(2l) = 12/l .
 q  can be  12 ,  6 , 4 , 3 , 2  and  1  for  k= 1 ,  2 ,  3 ,  4 , 6  and  12 .
Or, p  can be  2 , 4 , 6 , 8  and  12  in order to satisfy p*q = 24

As p  can not be determined uniquely, statement (2) is not sufficient...................................  .(B)

Combining statements (1) and (2),  p*6k = 2l*q 
Substituting  3p = q  in equation pq=24 ,
Or,  3p*p=24 
Or, p =\sqrt{8} 
=>  p  is not an integer;thus, both statements (1) and (2) are not sufficient.......................  .(C)

Answer:  (E)

mulhinmjavid · Answer

I solved this question using prime factorization box and got correct answer. But i think that approach is not reasonable for these kind of questions because there could only one single pair which could satisfy both statements. ( even in that case, prime factorization box would still recommend that there is no definitive answer because we dont know all numbers present in prime box). Kindly correct me if i am wrong.

minhaz3333 · Answer

pq = 24 
possible values for p and q 
1*24 = 24 
2*12 = 24
3*8 = 24
4*6 = 24
6*4 = 24 
8*3 = 24
12*2 = 24
24*1 = 24

from stat 1 - 
possible values of p when q/6 is an integer 
1*24 = 24 
2* 12 = 24 
4*6 = 24

p can be 1 or 2 or 4 .not sufficient. 
from stat 2 
when p/2 is and integer then possible values of p itself - 
2*12
4*6
6*4
12*2
24*1
p can be 2 , 4, 6, 12, 24. not sufficient .

now from 1 + 2
possible values of p when q/6 and p/2 are integers
2*12 
4*6 
p can be either 2 or 4. not sufficient

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:
 
We need to determine the value of p, given that pq = 24 and both p and q are positive integers. We see that p (and q) are factors of 24. Therefore, p (and q) can be one of the following integers:

1, 2, 3, 4, 6, 8, 12, and 24

Statement One Alone:

Since q/6 is an integer, q is 6, 12, or 24, and p will then be 4, 2, or 1, respectively. Since p can take on more than one value, statement one alone is not sufficient.

Statement Two Alone:

Since p/2 is an integer, p is 2, 4, 6, 8, 12, or 24. Since p can take on more than one value, statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that p can still be either 2 or 4. Since p can take on more than one value, both statements are not sufficient.

Answer: E

CrackverbalGMAT · Answer

Since pq = 24 and p and q are positive integers, we can conclude that p and q are positive integral factors of 24. The positive integral factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

From statement I alone, q/6 is an integer.

Therefore, q is a multiple of 6. Remember that q is also a factor of 24. Therefore, the possible values for q = 6 or 12 or 24. And because the product of p ad q is 24, there will be 3 corresponding values for p.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, p/2 is an integer.

This means that p is an even factor of 24 and hence p can be any of 2, 4, 6, 8, 12 or 24. 
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:

From statement II, p is even; from statement I alone, q = 6 or 12 or 24. 
For q = 6, p = 4 and for q = 12, p = 2. 
The combination of statements is insufficient to find a unique value for p. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!
Aravind BT

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If p and q are positive integers and pq = 24, what is the

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