Last visit was: 12 Sep 2024, 01:53 It is currently 12 Sep 2024, 01:53
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95475
Own Kudos [?]: 657823 [19]
Given Kudos: 87247
Manager
Joined: 13 Jun 2013
Posts: 223
Own Kudos [?]: 1073 [4]
Given Kudos: 14
Manager
Joined: 22 Jan 2014
Posts: 130
Own Kudos [?]: 248 [0]
Given Kudos: 212
WE:Project Management (Computer Hardware)
Intern
Joined: 26 Jul 2014
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 0
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
In order to prove that option B is the right answer we are multiplying the inequality by the LCM (6) without knowing if x+y is positive or negative.

Is there any reason for x+y to be assumed to be positive?
Math Expert
Joined: 02 Sep 2009
Posts: 95475
Own Kudos [?]: 657823 [0]
Given Kudos: 87247
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
pratikshetty123
In order to prove that option B is the right answer we are multiplying the inequality by the LCM (6) without knowing if x+y is positive or negative.

Is there any reason for x+y to be assumed to be positive?

We are multiplying by 6, which is positive. We care about the sign of the value by which we are multiplying an inequality.
Senior Manager
Joined: 02 Dec 2014
Posts: 304
Own Kudos [?]: 306 [1]
Given Kudos: 353
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE:Sales (Telecommunications)
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
1
Kudos
Bunuel

Tough and Tricky questions: Statistics.

If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

Statement 1. If x=4 and y=5 then answer is Yes. But if x=6 and y=14 then answer is No. Insufficient
Statement 2. We have (x+y)/2<(x+y+36)/6 Multiply both sides by 6 to get 3x+3Y<x+y+36 Hence x+y<18 Sufficient
Scoreleap Test Prep Representative
Joined: 08 Mar 2021
Posts: 222
Own Kudos [?]: 125 [0]
Given Kudos: 0
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
Raisakatyal
If set S= (7,y,12,8,x,9), is x+y less than 18?
(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

S = {7, y, 12, 8, x, 9}. Is x + y < 18?

Statement 1:
Range < 9
Case 1: Let x = y = 4
Range = 12 - 4 = 8 < 9
x + y = 8 < 18
Case 2: Let x = y = 15
Range = 15 - 7 = 8 < 9
x + y = 30 > 18
Statement 1 is Not Sufficient.

Statement 2:
$$\frac{x + y}{2} < \frac{7 + y + 12 + 8 + 9 + x}{6}$$
=> 3 * (x + y) < 36 + x + y
=> 2 * (x + y) < 36
=> x + y < 18
Statement 2 is Sufficient.

So, correct answer is option B.
Non-Human User
Joined: 09 Sep 2013
Posts: 34816
Own Kudos [?]: 877 [0]
Given Kudos: 0
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
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: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18? [#permalink]
Moderator:
Math Expert
95463 posts