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Math Expert V
Joined: 02 Sep 2009
Posts: 56275
If p and q are positive integers and pq = 24, what is the va  [#permalink]

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2
5 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:29) correct 15% (01:24) wrong based on 671 sessions

### HideShow timer Statistics 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

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Math Expert V
Joined: 02 Sep 2009
Posts: 56275
Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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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.

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

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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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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)

Intern  Joined: 12 Aug 2014
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Re: If p and q are positive integers and pq = 24, what is the va  [#permalink]

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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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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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