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If p and q are positive integers and pq = 24, what is the va [#permalink]
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17 Jan 2014, 02:35
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If p and q are positive integers and pq = 24, what is the va [#permalink]
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17 Jan 2014, 02:35
SOLUTIONIf 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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17 Jan 2014, 03:21
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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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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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28 Nov 2014, 12:11
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! 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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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: If p and q are positive integers and pq = 24, what is the va [#permalink]
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17 Oct 2017, 12:42
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