It is currently 13 Dec 2017, 11:01

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135518 [0], given: 12697

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

### Show Tags

17 Jan 2014, 01:35
Expert's post
3
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:05) correct 15% (01:01) wrong based on 477 sessions

### HideShow timer Statistics

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each 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:
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!
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135518 [0], given: 12697

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135518 [0], given: 12697

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

### Show Tags

17 Jan 2014, 01:35
Expert's post
1
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 135518 [0], given: 12697

Director
Joined: 25 Apr 2012
Posts: 721

Kudos [?]: 872 [1], given: 724

Location: India
GPA: 3.21
Re: If p and q are positive integers and pq = 24, what is the va [#permalink]

### Show Tags

17 Jan 2014, 02:21
1
KUDOS
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
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 872 [1], given: 724

Manager
Joined: 04 Oct 2013
Posts: 161

Kudos [?]: 126 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If p and q are positive integers and pq = 24, what is the va [#permalink]

### Show Tags

18 Jan 2014, 01:31
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)

Kudos [?]: 126 [0], given: 55

Intern
Joined: 12 Aug 2014
Posts: 18

Kudos [?]: [0], given: 72

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

### Show Tags

28 Nov 2014, 11:11
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each 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:
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.

Kudos [?]: [0], given: 72

Intern
Joined: 11 Nov 2014
Posts: 40

Kudos [?]: 19 [0], given: 102

Concentration: Marketing, Finance
WE: Programming (Computer Software)
Re: If p and q are positive integers and pq = 24, what is the va [#permalink]

### Show Tags

11 May 2016, 03:14
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

Kudos [?]: 19 [0], given: 102

Non-Human User
Joined: 09 Sep 2013
Posts: 14868

Kudos [?]: 287 [0], given: 0

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

### Show Tags

17 Oct 2017, 11:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 287 [0], given: 0

Re: If p and q are positive integers and pq = 24, what is the va   [#permalink] 17 Oct 2017, 11:42
Display posts from previous: Sort by