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

 It is currently 13 Dec 2018, 10:04

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y

Author Message
TAGS:

### Hide Tags

MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1439
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

28 Sep 2018, 20:13
00:00

Difficulty:

95% (hard)

Question Stats:

30% (02:03) correct 70% (02:03) wrong based on 53 sessions

### HideShow timer Statistics

x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y. What is the positive difference between the minimum possible value of x and the minimum value of y?

A. -6

B. 0

C. 1

D. 4

E. 6

_________________
Manager
Joined: 23 Nov 2017
Posts: 58
Location: India
GMAT 1: 720 Q51 V36
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

28 Sep 2018, 23:50
Given conditions: x + 2y > 20 and 3x - 30 < -y; x and y are positive integers
Objective: To find the difference between the minimum possible value of x and the minimum value of y

3x - 30 < -y can be written as 3x + y < 30

Please refer to the following 3 graphs.

The area that satisfies the first inequality x + 2y > 20 is the region above the red line.

The area that satisfies the second inequality 3x + y < 30 is the region below the green line.

Because x and y are positive integers, the area of interest is restricted to I quadrant and the area enclosed in the triangle ABC are values of x and y that satisfy both the inequalities.

Let us find the coordinates of point C
Solve the two equations x + 2y = 20 and 3x + y = 30
3x + 6y = 60
3x + y = 30
-----------
5y = 30
---------
Or y = 6. Substituting y = 6 in equation (1), we get x = 8.
So, coordinates of point C are (8, 6)

It is evident from the graph that lowest point among the three from y coordinates is C, So, the minimum value of y enclosed in the triangle is an integer greater than 6. So, it has to be 7.
From the graph, we can also deduce that the minimum value of x enclosed in the triangle is an integer greater than 0. So, it has to be 1.

The positive difference between the minimum value of x and minimum value of y is 6.
Attachments

Inequalties-3.png [ 28.26 KiB | Viewed 675 times ]

Inequalties-2.png [ 18.19 KiB | Viewed 676 times ]

Inequalties-1.png [ 9.25 KiB | Viewed 675 times ]

_________________

An IIM C Alumnus - Class of '94
GMAT Tutor at Wizako GMAT Classes & Online Courses

Manager
Joined: 12 Mar 2018
Posts: 84
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

29 Sep 2018, 04:01
seems 1 as 0 is not possible which question limits
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2303
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

29 Sep 2018, 04:19

Solution

Given:
• x and y are positive integers
• x + 2y > 20 and 3x – 30 < -y

To find:
• The positive difference between minimum value of x and minimum value of y

Approach and Working:
• x + 2y > 20
• 3x – 30 < -y
Or, 3x + y < 30
Or, -3x – y > -30
Or, -6x – 2y > -60

Adding the above two inequalities, we get,
• x – 6x + 2y – 2y > 20 – 60
Or, -5x > -40
Or, 5x < 40
Or, x < 8

As x is positive integer, minimum possible value of x is 1
• also, if x < 8, we can say from x + 2y > 20,
2y > 20 – x
Or, 2y > 12
Or, y > 6

As y is positive integer, minimum possible value of y is 7

Therefore, the positive difference = 7 – 1 = 6

Hence, the correct answer is option E.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Joined: 12 Nov 2016
Posts: 4
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

29 Sep 2018, 04:39
2y > 20 – x
Or, 2y > 12

As X<8, how can we consider x=8

Posted from my mobile device
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2303
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

29 Sep 2018, 04:46
1
Siddharthachepuri@gmail.com wrote:
2y > 20 – x
Or, 2y > 12

As X<8, how can we consider x=8

Posted from my mobile device

Hi,
we did not consider x = 8. As x is less than 8, we used this to conclude that y is greater than 12.
(For example, if x can be maximum 7, then y should be minimum 7 (we wrote it as y > 6).
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

12 Dec 2018, 19:49
workout wrote:
x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y. What is the positive difference between the minimum possible value of x and the minimum value of y?

A. -6

B. 0

C. 1

D. 4

E. 6

Let us get the range of one variable first and for that we will have to cancel out the other variable.
So x+2y>20....(I)
3x-30<-y..... multiply by 2, so 6x-60<-2y...(II)
x+2y-2y>20+6x-60.......5x<40.....x<8
Now since x is positive integer and x<8, the minimum possible value of x is 1..

Now take the equation for getting the range of the values of y..
x+2y>20...2y>20-x.... higher the X, lower the y
So take max possible value of x, so 2y>20-7....y>6.5
3x-30<-y....y<30-3x....if you add max value of X, we will get least possible value of y
So y<30-3*7.....y<9
So least possible value is less than 9 but greater than 6.5..
So minimum value of y is 7..

Difference is 7-1=6
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 08 Jul 2018
Posts: 59
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

12 Dec 2018, 20:53
EgmatQuantExpert wrote:

Solution

Given:
• x and y are positive integers
• x + 2y > 20 and 3x – 30 < -y

To find:
• The positive difference between minimum value of x and minimum value of y

Approach and Working:
• x + 2y > 20
• 3x – 30 < -y
Or, 3x + y < 30
Or, -3x – y > -30
Or, -6x – 2y > -60

Adding the above two inequalities, we get,
• x – 6x + 2y – 2y > 20 – 60
Or, -5x > -40
Or, 5x < 40
Or, x < 8

As x is positive integer, minimum possible value of x is 1
• also, if x < 8, we can say from x + 2y > 20,
2y > 20 – x
Or, 2y > 12
Or, y > 6

As y is positive integer, minimum possible value of y is 7

Therefore, the positive difference = 7 – 1 = 6

Hence, the correct answer is option E.

Once we calculate value for x, while calculating value for y using first equation we get y>6 and with second equation, we get y<6. How to know which one to take?
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y  [#permalink]

### Show Tags

12 Dec 2018, 21:40
ritu1009 wrote:
EgmatQuantExpert wrote:

Solution

Given:
• x and y are positive integers
• x + 2y > 20 and 3x – 30 < -y

To find:
• The positive difference between minimum value of x and minimum value of y

Approach and Working:
• x + 2y > 20
• 3x – 30 < -y
Or, 3x + y < 30
Or, -3x – y > -30
Or, -6x – 2y > -60

Adding the above two inequalities, we get,
• x – 6x + 2y – 2y > 20 – 60
Or, -5x > -40
Or, 5x < 40
Or, x < 8

As x is positive integer, minimum possible value of x is 1
• also, if x < 8, we can say from x + 2y > 20,
2y > 20 – x
Or, 2y > 12
Or, y > 6

As y is positive integer, minimum possible value of y is 7

Therefore, the positive difference = 7 – 1 = 6

Hence, the correct answer is option E.

Once we calculate value for x, while calculating value for y using first equation we get y>6 and with second equation, we get y<6. How to know which one to take?

second equation $$y<30-3x$$... This will give us the upper limit as we are getting y is less than something.
So this should give you the maximum value of y..
and you will get maximum value for y when x is minimum in y<30-3x, so y<30-3*1....y<27
so range of values of y is 6<y<27.....
Minimum value is 7 and max value is 26

Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y &nbs [#permalink] 12 Dec 2018, 21:40
Display posts from previous: Sort by

# x and y are positive integers such that x + 2y > 20 and 3x – 30 < -y

 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®.