If x and y are positive integers and 21x=12y : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 16:45

### 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 x and y are positive integers and 21x=12y

Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Feb 2012
Posts: 20
WE: Other (Transportation)
Followers: 0

Kudos [?]: 39 [1] , given: 14

If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

26 Feb 2012, 05:30
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:54) correct 16% (01:51) wrong based on 90 sessions

### HideShow timer Statistics

If x and y are positive integers and 21x=12y what is the least possible value of xy?

(A) 14
(B) 28
(C) 63
(D) 84
(E) 252
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7077

Kudos [?]: 93113 [1] , given: 10552

Re: If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

26 Feb 2012, 05:34
1
KUDOS
Expert's post
tom09b wrote:
If x and y are positive integers and 21x=12y what is the least possible value of xy?

(A) 14
(B) 28
(C) 63
(D) 84
(E) 252

$$21x=12y$$ --> $$\frac{x}{y}=\frac{12}{21}=\frac{4}{7}$$. Now, since x and y are positive integers then the least value of x is 4 and the least value of y is 7 --> $$xy=4*7=28$$.

_________________
Senior Manager
Joined: 10 Nov 2010
Posts: 267
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 300 [0], given: 22

Re: If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

26 Feb 2012, 05:37
tom09b wrote:
If x and y are positive integers and 21x=12y what is the least possible value of xy?

(A) 14
(B) 28
(C) 63
(D) 84
(E) 252

B....

21x=12y
=> x/y = 4/7
=> 7x=4y
7(3)=4(3) => x*y=9 But it is not given
7(4)=4(7) => x*y=28
_________________

The proof of understanding is the ability to explain it.

Intern
Joined: 13 Feb 2012
Posts: 20
WE: Other (Transportation)
Followers: 0

Kudos [?]: 39 [0], given: 14

Re: If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

26 Feb 2012, 09:07
GMATD11 wrote:
tom09b wrote:
If x and y are positive integers and 21x=12y what is the least possible value of xy?

(A) 14
(B) 28
(C) 63
(D) 84
(E) 252

B....

21x=12y
=> x/y = 4/7
=> 7x=4y
7(3)=4(3) => x*y=9 But it is not given
7(4)=4(7) => x*y=28

Sorry, I don't understand your explanation...
Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7077

Kudos [?]: 93113 [0], given: 10552

Re: If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

26 Feb 2012, 11:19
tom09b wrote:
GMATD11 wrote:
tom09b wrote:
If x and y are positive integers and 21x=12y what is the least possible value of xy?

(A) 14
(B) 28
(C) 63
(D) 84
(E) 252

B....

21x=12y
=> x/y = 4/7
=> 7x=4y
7(3)=4(3) => x*y=9 But it is not given
7(4)=4(7) => x*y=28

Sorry, I don't understand your explanation...

This red part is not correct x and y can not equal to 3, since their ratio in this case would be 3/3=1 and not 4/7 as it should be (or simply 7*3=4*3 is not correct).
_________________
Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 992
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 163

Kudos [?]: 1460 [0], given: 227

Re: If x and y are positive integers and 21x=12y [#permalink]

### Show Tags

20 Aug 2013, 04:06
21x=14y ==> 7x=4y ===> x=4y/7

Now we have to calculate xy =
I can substitute value of x from above calculated relationship.

I got ==> (4y^2)/7

Now test for given values
A. 14 ===> Y^2 = 14*7/4 = 24.5
B. 28 ===> Y^2 = 28*7/4 = 49 Thus Y=7 answer is B.
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: If x and y are positive integers and 21x=12y   [#permalink] 20 Aug 2013, 04:06
Similar topics Replies Last post
Similar
Topics:
7 x and y are positive integers such that x < y. If 8 15 Feb 2015, 22:24
26 If x, y, and z are positive integers such that x is a factor 15 18 Mar 2014, 00:36
11 If x and y are positive integers and 6 21 Feb 2012, 13:45
9 If x, y and z are positive integers such that x is a factor 11 08 Feb 2011, 02:34
8 If x, y and z are positive integers such that x is a factor 9 29 Nov 2007, 10:01
Display posts from previous: Sort by