GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Sep 2018, 01:14

### 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
Your Progress

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

# Is xy an integer?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49277
Is xy an integer?  [#permalink]

### Show Tags

30 Apr 2015, 04:06
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:52) correct 25% (01:33) wrong based on 178 sessions

### HideShow timer Statistics

Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

Kudos for a correct solution.

_________________
Current Student
Joined: 24 Mar 2015
Posts: 35
Concentration: General Management, Marketing
GMAT 1: 660 Q44 V38
GPA: 3.21
WE: Science (Pharmaceuticals and Biotech)
Re: Is xy an integer?  [#permalink]

### Show Tags

30 Apr 2015, 13:15
1
1
Bunuel wrote:
Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

Kudos for a correct solution.

The stem is a yes or no question so as long as we can give a single definite solution to the question we have sufficiency.

1) we have no information on y so not sufficient. Eliminate A and D.
2) we have no information on x so not sufficient. Eliminate B.

Together we know that each x and y are going to be fixed values regardless of the actual size of the shapes being referenced that will be multiplied together which in turn will give us a single definite answer to the question of if it is an integer or not. This provides is enough information to provide sufficiency, select answer C.
_________________

Please pass me a +KUDOS if you liked my post! Thanks!

Do not compare yourself to others, compare yourself to who you were yesterday.

Manager
Joined: 21 Jun 2014
Posts: 136
Location: United States
Concentration: General Management, Strategy
GMAT 1: 630 Q45 V31
GPA: 3.4
WE: Engineering (Computer Software)
Re: Is xy an integer?  [#permalink]

### Show Tags

30 Apr 2015, 19:14
1
Algebra way :
The answer choice is between C or E

A. x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square
It implies radius of circle =squareside/2 i.e. r1=s1/2

B. y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.
It implies diagonal of the square=diameter of the circle i.e. s2=sqrt(2)*r2

Solving for the ratios ,x=(s1/2)^2/(3.14*(s1/2)^2) which results in 4/3.14
similarly, y =(3.14*(r2^2))/((r2^2)*2) which results in 3.14/2
Multiplying together it leads to 2 an integer
_________________

Regards,
Manish Khare
"Every thing is fine at the end. If it is not fine ,then it is not the end "

Manager
Joined: 01 Jan 2015
Posts: 56
Re: Is xy an integer?  [#permalink]

### Show Tags

01 May 2015, 13:58
Answer C
Only combining both we'll get a integer value of XY
Senior Manager
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Re: Is xy an integer?  [#permalink]

### Show Tags

01 May 2015, 14:54
1
Statement 1:
Nothing about y

Statement 2:
Nothing about x

Combined, when the ratios are multiplied together, the pi from both statements cancel and we are left with an integer.
sufficient

Answer: C
Math Expert
Joined: 02 Sep 2009
Posts: 49277
Re: Is xy an integer?  [#permalink]

### Show Tags

04 May 2015, 04:00
Bunuel wrote:
Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

The question asks whether a particular product (xy) is an integer. Note that this is a Yes-No question.

Statement 1: NOT SUFFICIENT. This statement only refers to x. Without knowing anything about y, you cannot know whether xy is an integer.

Statement 2: NOT SUFFICIENT. Likewise, this statement only refers to y, so it cannot be sufficient.

Statements 1 and 2 TOGETHER: SUFFICIENT. The super-fancy way to get the answer is to realize that x is a fixed number, completely determined by its definition in the statements. The same is true of y. Why is this the case? All circles are the same shape, so they are all similar to each other. Likewise, all squares are the same shape and are similar to each other. So when you inscribe a circle inside a square (to touch all four sides of the square), there

There should be only one “shape” to the picture in your mind of a square with a circle inscribed inside it, touching all four walls. All that’s different is how large or small that picture is, so the ratio of the square’s area to the circle’s area is fixed:

The same is true for y, the ratio of the circle’s area to the area of an inscribed square:

So x and y are fixed. You don’t know what their values are, but you don’t care: in theory, you could calculate those values. And then you could determine whether the product is an integer or not.

The longer way to get the answer is to actually figure out these ratios.

Take x first. Call the side of the square 1. Then the radius of the inscribed circle is 1/2, and the area of the circle is $$\pi*r^2= \frac{\pi}{4}$$. The area of the square is 1^2 = 1, so the ratio of the square’s area to the circle’s area is $$1:\frac{\pi}{4}$$, or $$\frac{4}{\pi}$$. That’s the value of x.

Now take y. Call the side of the square 1 again. Then the diameter of the circle is the diagonal of the square, which is $$\sqrt{2}$$. The radius of the circle is $$\frac{\sqrt{2}}{2}$$, and the area of the circle is $$\pi*r^2 = \pi(\frac{\sqrt{2}}{2})^2 = \frac{\pi}{2}$$. That’s the value of y, since the area of the square is just 1, and you want the ratio of the circle’s area to the square’s area.

Finally, the product of x and y is $$(\frac{4}{\pi})(\frac{\pi}{2}) = 2$$, which is indeed an integer.

The correct answer is C.

Attachment:

circle1.gif [ 3.09 KiB | Viewed 1754 times ]

Attachment:

circle2.gif [ 5.87 KiB | Viewed 1752 times ]

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 8107
Re: Is xy an integer?  [#permalink]

### Show Tags

03 Jul 2018, 08:17
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.
_________________
Re: Is xy an integer? &nbs [#permalink] 03 Jul 2018, 08:17
Display posts from previous: Sort by

# Is xy an integer?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.