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

 It is currently 23 May 2019, 10:13 ### 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. ### Request Expert Reply # If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager  G
Joined: 13 May 2017
Posts: 107
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22 GPA: 3.14
WE: Account Management (Entertainment and Sports)
If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

2 00:00

Difficulty:   85% (hard)

Question Stats: 41% (02:30) correct 59% (01:47) wrong based on 51 sessions

### HideShow timer Statistics

If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1
VP  D
Joined: 09 Mar 2016
Posts: 1284
Re: If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

rencsee wrote:
If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1

IMO: E hopefully x+y<11 (if y y < 3 , ie 2 then 8+2<10 but 8-2 is not > 8)

x−y>8

if y<1 i.e. 0 then 10+0<11 and 10-0>8
CEO  V
Joined: 12 Sep 2015
Posts: 3726
Location: Canada
Re: If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

1
Top Contributor
2
rencsee wrote:
If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1

KEY CONCEPT: If the inequality signs of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities to create a new inequality.

We have:
x + y < 11
x − y > 8

Multiply both sides of the bottom inequality by -1 to get:
x + y < 11
-x + y < -8 [since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]

Now we can ADD the inequalities to get: 2y < 3
Divide both sides by 2 to get: y < 1.5
So, if y < 1.5, which of the answer choices MUST be true?
Well, if y < 1.5, then it MUST be the case that y < 2

Answer: D

RELATED VIDEOS FROM OUR COURSE

_________________
VP  D
Joined: 09 Mar 2016
Posts: 1284
If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

GMATPrepNow wrote:
rencsee wrote:
If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1

KEY CONCEPT: If the inequality signs of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities to create a new inequality.

We have:
x + y < 11
x − y > 8

Multiply both sides of the bottom inequality by -1 to get:
x + y < 11
-x + y < -8 [since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]

Now we can ADD the inequalities to get: 2y < 3
Divide both sides by 2 to get: y < 1.5
So, if y < 1.5, which of the answer choices MUST be true?
Well, if y < 1.5, then it MUST be the case that y < 2

Answer: D

RELATED VIDEOS FROM OUR COURSE

GMATPrepNow hi there why are you multiplying both sides by -1 ? whats the logic behind making things "complicated" changing this x − y > 8 into
-x + y < -8

we dont have inaequlity like this for example $$-5>x$$ so as to multiply both sides by -1, i simply didnt see the neccessity to do so and finally whats wrong with my solition Manager  B
Joined: 04 Oct 2017
Posts: 81
If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

GMATPrepNow wrote:
rencsee wrote:
If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1

KEY CONCEPT: If the inequality signs of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities to create a new inequality.

We have:
x + y < 11
x − y > 8

Multiply both sides of the bottom inequality by -1 to get:
x + y < 11
-x + y < -8 [since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]

Now we can ADD the inequalities to get: 2y < 3
Divide both sides by 2 to get: y < 1.5
So, if y < 1.5, which of the answer choices MUST be true?
Well, if y < 1.5, then it MUST be the case that y < 2

Answer: D

RELATED VIDEOS FROM OUR COURSE

Hi,

I subtracted the inequalities
x+ y <11
x-y>8

and got y< 1.5. Y is an integer hence y<2. Option D. Is my approach correct???
CEO  V
Joined: 12 Sep 2015
Posts: 3726
Location: Canada
Re: If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

1
Top Contributor
dave13 wrote:
GMATPrepNow hi there why are you multiplying both sides by -1 ? whats the logic behind making things "complicated" changing this x − y > 8 into
-x + y < -8

we dont have inaequlity like this for example $$-5>x$$ so as to multiply both sides by -1, i simply didnt see the neccessity to do so and finally whats wrong with my solition Hi Dave,

Our goal is to combine the two inequalities so that the x terms are eliminated (this is our goal because the answer choices have y-terms only)
When it comes to combining two inequalities, one option is to ADD the inequalities. HOWEVER, we can only add the inequalities if the inequality symbols are facing the same direction.
In order to get the inequalities facing the same direction, I tool one inequality and multiplied both sides by -1

See the two embedded videos for more on these concepts.

I'm not entirely sure what you are doing in your solution. Can you elaborate on it for me?

Cheers,
Brent
_________________
CEO  V
Joined: 12 Sep 2015
Posts: 3726
Location: Canada
Re: If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f  [#permalink]

### Show Tags

Top Contributor
Kezia9 wrote:
GMATPrepNow wrote:
rencsee wrote:
If x and y are non-negative integers, x+y<11, and x−y>8, which of the following must be true for all the qualified values of x?

A. y < 3
B. y > 2
C. 2 < y < 10
D. y < 2
E. y < 1

Hi,

I subtracted the inequalities
x+ y <11
x-y>8

and got y< 1.5. Y is an integer hence y<2. Option D. Is my approach correct???

In this case, subtracting the inequalities worked, HOWEVER it's a bit of a coincidence (resulting from the fact that the inequality symbols were facing in opposite directions).

Also, when you subtracted the inequalities, you got 2y on one side, and 3 on the other side, but what rationale did you use to decide which direction to make the inequality symbol?
That is, why didn't you write 2y > 3?

IMPORTANT: In many cases, if you SUBTRACT inequalities, the resulting inequality will NOT be true.
For example, if we take...
x < 10
y < 4
...we can't conclude that x - y < 6
For example, it could be the case that x = 9 and y = -10, in which case x - y = 19, which contradicts the conclusion that x - y < 6

To be 100% certain of your solution, I suggest that you stick with the rules/strategies presented in the above videos.

Cheers,
Brent
_________________ Re: If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f   [#permalink] 27 Nov 2018, 09:36
Display posts from previous: Sort by

# If x and y are non-negative integers, x+y<11,andx−y>8 , which of the f

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

#### MBA Resources  