GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 02 Mar 2021, 00:41
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If x + y > 1 and y - x < 3, which of the following must be true?
7 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

avatar
B
akshayuberoi
Intern
Intern
Joined: 09 Jan 2020
Posts: 7
Location: India
GPA: 3.17
If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  31 Jan 2021, 08:49
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

61% (01:49) correct 39% (02:17) wrong based on 59 sessions

Hide Show timer Statistics

If x + y > 1 and y - x < 3, which of the following must be true?

I. x < -1
II. x > -1
III. y > 2

(A) I only
(B) II only
(C) III only
(D) I and III
(E) None
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
User avatar
V
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 18 Jan 2020
Posts: 2415
Location: India
Schools: HEC MiM "23, ESSEC MiM "23
GPA: 4
Premium Member CAT Tests
Re: If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  31 Jan 2021, 11:40
1
Kudos
x + y > 1 and y - x < 3
Y > 1-x and Y < 3+x
1-x < Y < 3+x
1-x < 3+x
-2 < 2x
-1 < x

Further can be solved, but only B option satisfies the proven inequality.
So answer is B

Posted from my mobile device
User avatar
G
TestPrepUnlimited
GMAT Tutor
Joined: 16 Sep 2014
Posts: 921
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  31 Jan 2021, 15:46
Expert Reply
akshayuberoi wrote:
If x + y > 1 and y - x < 3, which of the following must be true?

I. x < -1
II. x > -1
III. y > 2

(A) I only
(B) II only
(C) III only
(D) I and III
(E) None


We can add inequalities facing the same direction. Thus rewrite the 2nd inequality as 3 > y - x, add the first inequality to get \(x + y + 3 > 1 + y - x\).

\(2x > -2\) and \(x > -1\). Since we got no info on y this means y can be anything.

Ans: B
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Signature Read More
avatar
B
Palak74
Intern
Intern
Joined: 17 Sep 2019
Posts: 15
Re: If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  19 Feb 2021, 23:32
Hi
This is how I solved it and I am not getting the right answer .
Can someone help me understand where have I gone wrong

To make both the equation to greater than ,
Multiplied (y-x<3) by -1
and get x-y>-3

Now i add both equations
x+y>1
x-y>-3
i eliminate y and get x>-1

Now I solve further by subtracting the 2 equations to eliminate x
and get Y>2 also

What am I doing wrong ?
User avatar
V
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10584
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  20 Feb 2021, 06:28
Expert Reply
If x + y > 1 and y - x < 3

=> y - x < 3 [Multiply the inequality by (-1) and reverse the sign]: - y + x > -3

=> Add both inequalities: x + y - y + x > 1 - 3

=> 2x > -2

=> x > -1

I. x < -1 - NO
II. x > -1 - YES
III. y > 2 - NO

Answer B
_________________
MathRevolution: The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $69 for on-demand and $60 for tutoring per hour.
Signature Read More
User avatar
G
TestPrepUnlimited
GMAT Tutor
Joined: 16 Sep 2014
Posts: 921
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  20 Feb 2021, 09:43
1
Kudos
Expert Reply
Hi Palak74 ,

We cannot subtract two inequalities facing the same direction. We can for opposite direction but it's the same as reversing one inequality then adding. The easy way to put it is we should only add inequalities in the same direction. You may also see we can handpick x = 2 and y = 1 so y > 2 is not always true.
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Signature Read More
avatar
B
Palak74
Intern
Intern
Joined: 17 Sep 2019
Posts: 15
Re: If x + y > 1 and y - x < 3, which of the following must be true? [#permalink] New post  22 Feb 2021, 05:56
TestPrepUnlimited wrote:
Hi Palak74 ,

We cannot subtract two inequalities facing the same direction. We can for opposite direction but it's the same as reversing one inequality then adding. The easy way to put it is we should only add inequalities in the same direction. You may also see we can handpick x = 2 and y = 1 so y > 2 is not always true.



Ok ok Understood. Thankyou
GMAT Club Bot
gmatclubot
[#permalink]
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9507 posts
Bunuel
Math Expert
72189 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2415 posts
generis
Senior SC Moderator
4550 posts
Feedback

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions