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

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If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 17 Jan 2014, 02:35
2
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A
B
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D
E

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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 17 Jan 2014, 02:35
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.
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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 17 Jan 2014, 03:21
1
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
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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 18 Jan 2014, 02:31
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)
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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 28 Nov 2014, 12:11
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 45
Category: Arithmetic Arithmetic operations
Page: 156
Difficulty: 600


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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.
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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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New post 11 May 2016, 04:14
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
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Re: f p and q are positive integers and pq =24, what is the  [#permalink]

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Re: f p and q are positive integers and pq =24, what is the   [#permalink] 12 Apr 2018, 04:08
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