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

 It is currently 13 Oct 2019, 18:05

### 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

# If in set S above, x is an integer x is an integer greater than one

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

### Hide Tags

Director
Joined: 12 Feb 2015
Posts: 915
If in set S above, x is an integer x is an integer greater than one  [#permalink]

### Show Tags

15 Oct 2018, 09:51
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:41) correct 25% (02:21) wrong based on 56 sessions

### HideShow timer Statistics

Set S = {$$x$$, $$\frac{x}{4}$$ , $$y^2$$, $$5y$$, $$x^2$$, $$y$$}

If in set S above, $$x$$ is an integer greater than one and $$0 < y ≤ 0.7$$, which of the following represents the range of the set S?

A) $$(x + y)(x − y)$$

B) $$x^2 ​– 3y$$

C) $$y^2$$

D) $$x – y$$

E) $$x^2 − y$$

_________________
"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"
Senior Manager
Joined: 13 Feb 2018
Posts: 454
GMAT 1: 640 Q48 V28
Re: If in set S above, x is an integer x is an integer greater than one  [#permalink]

### Show Tags

15 Oct 2018, 10:43
According to the constraints of the variables, $$x^2$$ will be the greatest value and $$y^2$$ - the lowest
So the range we have got $$x^2-y^2$$

IMO
Ans: A
CEO
Joined: 12 Sep 2015
Posts: 3990
Re: If in set S above, x is an integer x is an integer greater than one  [#permalink]

### Show Tags

15 Oct 2018, 11:01
2
Top Contributor
CAMANISHPARMAR wrote:
Set S = {$$x$$, $$\frac{x}{4}$$ , $$y^2$$, $$5y$$, $$x^2$$, $$y$$}

If in set S above, $$x$$ is an integer greater than one and $$0 < y ≤ 0.7$$, which of the following represents the range of the set S?

A) $$(x + y)(x − y)$$

B) $$x^2 ​– 3y$$

C) $$y^2$$

D) $$x – y$$

E) $$x^2 − y$$

Nice question!

In order to determine the range, we must determine the greatest and smallest values in the set.

Let's start with the expressions with x in them: x, x/4 and x²
Since x > 1, we know that x/4 < x < x²

Now the expressions with y in them: y, 5y and y²
Since 0 < y ≤ 0.7 y² < y < 5y

From these two inequalities, we must determine the greatest and smallest values
We'll do so by finding some EXTREME values.

First, since x is an INTEGER greater than 1, the smallest possible value of x is 2
So, the smallest possible value of x/4 = 2/4 = 1/2

Next, since y ≤ 0.7, the greatest possible value of y is 0.7
So, the greatest possible value of y² = (0.7)² = 0.49

Notice that the greatest possible value of y² is still less than the smallest possible value of x/4
Since y² < y < 5y, we can conclude that y² is the SMALLEST value in the set.
----------------------------------------

Since x is an INTEGER greater than 1, the smallest possible value of x is 2
So, the smallest possible value of x² = 2²= 4
Next, since y ≤ 0.7, the greatest possible value of 5y is 3.5

Notice that the smallest possible value of x² is still greater than the greatest possible value of 5y
Since x/4 < x < x², we can conclude that x² is the GREATEST value in the set.
----------------------------------------

Range = GREATEST value - SMALLEST value
= x² - y²
= (x + y)(x - y)

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Re: If in set S above, x is an integer x is an integer greater than one   [#permalink] 15 Oct 2018, 11:01
Display posts from previous: Sort by

# If in set S above, x is an integer x is an integer greater than one

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne