Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 May 2015, 06:57

# Today:

Wharton Round 3 Decisions.   |   Join Chat Room for Live Updates

### 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

# Perfect Squares

Author Message
TAGS:
Intern
Joined: 12 Jun 2009
Posts: 1
Followers: 0

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

Perfect Squares [#permalink]  12 Jun 2009, 22:52
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
Hi, I'm struggling to understand the concept behind a particular perfect squares question. Could anybody help?

If 375y = x^2, and x and y are positive integers then which of the following must be an integer?

I. y/15
II. y/30
III. y^2/25

As I'm new to this forum, please do advise if I've used incorrect symbols or haven't laid everything out as per standard practice. Thanks in advance.
Founder
Affiliations: AS - Gold, UA - Silver, HH-Diamond
Joined: 04 Dec 2002
Posts: 12743
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2635

Kudos [?]: 12502 [0], given: 3832

Re: Perfect Squares [#permalink]  12 Jun 2009, 23:09
Expert's post
Welcome to GMAT Club!
There are easier ways to write the math symbols here - I have edited your expression below. You can learn how to post math symbols here: writing-mathematical-symbols-in-posts-72468.html. Usually, all you have to do is to highlight the text and hit the M button. Bu there are exceptions such as fractions.

If $$375y = x^2$$, and x and y are positive integers then which of the following must be an integer?

I. $$\frac{y}{15}$$

II. $$\frac{y}{30}$$

III. $$\frac{y^2}{25}$$

Let me add another twist - a Stopwatch

_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 08 Jan 2009
Posts: 329
Followers: 2

Kudos [?]: 88 [0], given: 5

Re: Perfect Squares [#permalink]  13 Jun 2009, 02:07
if 375 * y = x ^2

x and y are integers u can write it as (5^3 * 3) * y = x^2

since x is an integer x ^2 is a perfect square . so to make LHS a perfect square y = 5 *3

so u can see y/15 and y^2/25 is an integer.

i would go for i and iii.
Manager
Joined: 04 Dec 2008
Posts: 108
Followers: 1

Kudos [?]: 77 [0], given: 2

Re: Perfect Squares [#permalink]  13 Jun 2009, 02:56
3121gmat wrote:
Hi, I'm struggling to understand the concept behind a particular perfect squares question. Could anybody help?

If 375y = x^2, and x and y are positive integers then which of the following must be an integer?

I. y/15
II. y/30
III. y^2/25

As I'm new to this forum, please do advise if I've used incorrect symbols or haven't laid everything out as per standard practice. Thanks in advance.

Welcome on board!
1. Looking 375y=x^2 tells us that y has to also be 375 in order for x to be a perfect square.
2. Breakdown 375 to its prime factor---- (5*5*5*3)=y
3. Now it's much easier to compare each statement.
I. y/15----> Yes (quotient=25)
II.y/30----> No (quotient=25/2)
III.y^2/25----> Yes (quotient=5625)
Senior Manager
Joined: 20 Mar 2008
Posts: 454
Followers: 1

Kudos [?]: 73 [0], given: 5

Re: Perfect Squares [#permalink]  13 Jun 2009, 22:25
3121gmat wrote:
Hi, I'm struggling to understand the concept behind a particular perfect squares question. Could anybody help?

If 375y = x^2, and x and y are positive integers then which of the following must be an integer?

I. y/15
II. y/30
III. y^2/25

As I'm new to this forum, please do advise if I've used incorrect symbols or haven't laid everything out as per standard practice. Thanks in advance.

Just as 3121gmat, I'm having some difficulty in understanding this problem.

Here's my 2 cents:

y doesn't have to be 375. For example, if we had a statment like 9y = x^2, which will be valid if y=4 & x=6.

In this case, if y=15, x^2 = 375*15,
or x=75.

I will go with (I)
Director
Joined: 05 Jun 2009
Posts: 852
WE 1: 7years (Financial Services - Consultant, BA)
Followers: 9

Kudos [?]: 207 [0], given: 106

Re: Perfect Squares [#permalink]  14 Jun 2009, 09:50
Let me give my shot

$$375y=x^2$$
splitting the 375 = $$5^2*5*3$$
now as 375y is a square of positive integer and y is also a positive integer
implies that y has to be = 5*3*a^2, where a is an integer too

Why? let me show
375y=$$5^2*5*3*[5*3*a^2]$$ = $$25^2*3^2*a^2$$

$$a^2$$ is added so as to generale the possible values of y.
If you don't understand till here try different values of 'a' such as {2,3,4} to get y and x. It will give you different set of values to understand the reason of using a.

1) $$y/15 = 15*a^2/15 = a^2$$
definitely a integer that too positive

2) $$y/30 = 15*a^2/30 = a^2/2$$
not necessary an integer if a^2 is not a multiple of 2.

3) $$y^2/25 = 15*15*a^4/25 = 9a^4$$
definitely an integer.

(i) and (iii)
_________________

Consider kudos for the good post ...
My debrief : journey-670-to-720-q50-v36-long-85083.html

Senior Manager
Joined: 07 Jan 2008
Posts: 418
Followers: 3

Kudos [?]: 91 [0], given: 0

Re: Perfect Squares [#permalink]  14 Jun 2009, 09:56
3121gmat wrote:
Hi, I'm struggling to understand the concept behind a particular perfect squares question. Could anybody help?

If 375y = x^2, and x and y are positive integers then which of the following must be an integer?

I. y/15
II. y/30
III. y^2/25

As I'm new to this forum, please do advise if I've used incorrect symbols or haven't laid everything out as per standard practice. Thanks in advance.

375y= 3.5.5.5.y = x^2 ==> the number of 3 is even number, the number of 5 is even number ==> y contains both 3 and 5.

Clearly, (I) and (III) meet requirement.
Re: Perfect Squares   [#permalink] 14 Jun 2009, 09:56
Similar topics Replies Last post
Similar
Topics:
Perfect square 2 08 Jan 2012, 20:19
1 Perfect Square 13 21 May 2011, 04:45
Perfect square.... 1 29 Oct 2010, 06:07
1 Perfect square 8 05 Mar 2009, 22:50
Display posts from previous: Sort by