BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Inequalities

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 210
Joined: Thu Mar 08, 2012 11:24 pm
Thanked: 62 times
Followed by:3 members

by niketdoshi123 » Sat Aug 11, 2012 8:50 pm
shivanigs wrote:If x^3 y^4= 5,000, is y = 5?


(1) y is a positive integer.
(2) x is an integer.
Find the prime factors of 5000
5000 = 5*5*5*5*2*2*2 = 2^3 * 5^4 = x^3 y^4
=> y^4 = 5^4
=> y = ±5
So , if y is a positive integer then only it will be equal to 5.

statement 1:
y is a positive integer .
This statement is sufficient to answer the question.

Statement 2:
x is an integer.
Looking at this statement we should check whether x can be a non integer number.
As the factors are prime numbers and both the prime numbers have different powers. There is no other possibility, which satisfies the equation.

the correct answer is A
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 12, 2012 6:39 am
shivanigs wrote:If x^3 y^4= 5,000, is y = 5?

(1) y is a positive integer.
(2) x is an integer.
5000 = 5*5*5*5*2*2*2
= (2^3)(5^4)

Statement 1: y is a positive integer.
This one looks promising, but we aren't told whether or not x is an integer.
So, we have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=1 and x= the cube root of 5000. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: x is an integer.
We have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=-5 and x=3. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2:
If x and y are both integers and y is a positive integer, it must be the case that x=3 and y=5
SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Thu Aug 16, 2012 2:14 am

by shatyasree » Thu Aug 16, 2012 3:03 am
I agree with Brent
Top
Legendary Member
Posts: 512
Joined: Mon Jun 18, 2012 11:31 pm
Thanked: 42 times
Followed by:20 members

by sana.noor » Wed May 08, 2013 9:59 pm
how C is the right choice, what if y=3 and x=5?...
Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button. :)
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 149
Joined: Wed May 01, 2013 10:37 pm
Thanked: 54 times
Followed by:9 members

by Atekihcan » Thu May 09, 2013 2:06 am
sana.noor wrote:how C is the right choice, what if y=3 and x=5?...
That's not possible as (x^3)*(y^4) = (5^3)*(3^4) = a multiple of 3 but 5000 is not a multiple of 3.
Top
Post new topic Post Reply
• Page 1 of 1