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. 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.
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
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New project wSTAT(which Schools To Apply To?)
GMATClub School Ambassador
BSchool app with GRE
New  RC Butler  2 RC's everyday



Manager
Joined: 23 Nov 2017
Posts: 58
Location: India

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
Inequalties3.png [ 28.26 KiB  Viewed 675 times ]
Inequalties2.png [ 18.19 KiB  Viewed 676 times ]
Inequalties1.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



eGMAT 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. Answer: E
_________________
Register for free sessions 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
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 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.egmat.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



eGMAT 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
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).
_________________
Register for free sessions 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
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 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.egmat.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) 3x30<y..... multiply by 2, so 6x60<2y...(II) Add these two equations.. x+2y2y>20+6x60.......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>20x.... higher the X, lower the y So take max possible value of x, so 2y>207....y>6.5 3x30<y....y<303x....if you add max value of X, we will get least possible value of y So y<303*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 71=6
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.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. Answer: EOnce 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. Answer: EOnce 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 \(y<303x\)... 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<303x, so y<303*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/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.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






