Author 
Message 
TAGS:

Hide Tags

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4225
Location: Canada

If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
10 Sep 2019, 13:25
Question Stats:
59% (02:41) correct 41% (03:15) wrong based on 69 sessions
HideShow timer Statistics
If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y? A) 12 B) 16 C) 26 D) 30 E) 34
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Test confidently with gmatprepnow.com



SVP
Joined: 26 Mar 2013
Posts: 2344
Concentration: Operations, Strategy

If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
10 Sep 2019, 14:25
GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 Let's analyze the equation 15y – 11x = 8 ....we can find simple observation Odd Odd = Even....So x & y must be odd to maintain even number (8). Let's alter the equation: 15y = 11x + 8 x must be have unit digit of 7 or 2 to make the sum equal either to 5 or 0 to divide 15 but as mentioned it x can't be even so focus on 7,17,...etc Let x=7.....15y = 85...not divisible by 15 (as we need number to be divisible by 3 too) Let x=17....15y = 195....bingo...We can Eliminate A & B directly. Use choice C that represented x+y......2617 =9 but 9 * 15 does not equal to 195 Use choice D that represented x+y......3017 =13..... 13 * 15 equal to 195 Answer: D



VP
Joined: 19 Oct 2018
Posts: 1294
Location: India

If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
Updated on: 11 Sep 2019, 05:18
15y11x=8 15y=11x+8 8=8 mod 15 Hence, 11x=7 mod 15 4*x=8 x=2 At x=2, y=2 x,y>3 As slope of 15y=11x+8 is 11/15, there is 11 units increment in y coordinates for every 15 increment in x coordinates. Next integral solution is x=2+15=17 and y=2+11=13 x+y=17+13=30 GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34
Originally posted by nick1816 on 11 Sep 2019, 02:07.
Last edited by nick1816 on 11 Sep 2019, 05:18, edited 1 time in total.



VP
Joined: 19 Oct 2018
Posts: 1294
Location: India

Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
11 Sep 2019, 02:12
Highlighted(Red) portion in your solution is not correct. x and y can be both even or both odd. (2,2) is a solution of the equation. Mo2men wrote: GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 Let's analyze the equation 15y – 11x = 8 ....we can find simple observation Odd Odd = Even.... So x & y must be odd to maintain even number (8). Let's alter the equation: 15y = 11x + 8 x must be have unit digit of 7 or 2 to make the sum equal either to 5 or 0 to divide 15 but as mentioned it x can't be even so focus on 7,17,...etc Let x=7.....15y = 85...not divisible by 15 (as we need number to be divisible by 3 too) Let x=17....15y = 195....bingo...We can Eliminate A & B directly. Use choice C that represented x+y......2617 =9 but 9 * 15 does not equal to 195 Use choice D that represented x+y......3017 =13..... 13 * 15 equal to 195 Answer: D



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4225
Location: Canada

Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
11 Sep 2019, 05:45
GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 Given: 15y – 11x = 8 Subtract 4y from both sides to get: 11y – 11x = 8 – 4y ASIDE: Why did I subtract 4y from both sides? This allows me to factor the expression 11y – 11x, which may help reveal some useful relationship. Continuing along…. Factor both sides to get: 11(y – x) = 4(2 – y) KEY CONCEPT: Since x and y are INTEGERS, we know that (y – x) is an INTEGER, which means 11(y – x) is a multiple of 11From this, we can conclude that 4(2 – y) is a multiple of 11What is the smallest value of y (given that y is an integer greater than 3) such that 4(2 – y) is a multiple of 11? If y= 13, then 4(2 – y) = 4(2 – 13) = 4(11) = 44. Perfect! So, y= 13 is the smallest value of y to meet the given conditions. To find the corresponding value of x, take 15y – 11x = 8 and plug in y=13 to get: 15(13) – 11x = 8 Simplify : 195 – 11x = 8 Subtract 195 from both sides: 11x = 187 Solve: x = 17So, the LEAST possible value of x+y = 17 + 13 = 30 Answer: D Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4859
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
11 Sep 2019, 08:38
GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 \(15y – 11x = 8\) Or, \(15y = 11x + 8\) , now here RHS must be divisible by 15 = RHS must be divisible by both 3 & 5 Now, try pugging in values for x > 3 For the number to be divisible by 5 the number must end either in 5 or 0 Now , try x = 12 first as units digit will end in 0 11*12 + 8 = 140 , not divisible by 3 Next try x = 17 , as units digit will end in 11*17 + 8 = 195 , Divisible by both 3 and 5 So, we get x = 17 and y = 13 Thus, x + y = 17 + 13 = 30, Answer must be (D)
_________________



SVP
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34

Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
11 Sep 2019, 08:50
GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 Given: 1. x and y are integers greater than 3 2. 15y – 11x = 8 Asked: What is the least possible value of x+y? 15y11x = 8 15y = 11x + 8 x =2; y = 2; 30=22+8; Is a solution but x,y>3 y=13;x=17; 15*13 = 195 = 187+8 x + y = 13 + 17 = 30 IMO D



Manager
Joined: 18 Jul 2015
Posts: 104
GMAT 1: 530 Q43 V20
WE: Analyst (Consumer Products)

If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
29 Sep 2019, 00:51
While all the above methods are to the point and clear, in a case you are not able to think about these methods then this question can be solved backwards from the answer choices by using the method of solving a system of two linear equations and looking for a solution in which y is an integer as x and y are integers as per question stem. Eq1: \(15y11x=8\) Eq2: \(x+y=\) Any of the answer options In case of D, Eq1: \(15y11x=8\) Eq2: \(x+y=30\) Multiplying the second equation with 11 we get  \(11x+11y=330\) Solving both the equations we get \(26y=338\) > \(y=13\) which is an integer and satisfies the condition provided in the question stem. Ans. D
_________________
Cheers. Wishing Luck to Every GMAT Aspirant!



Manager
Joined: 09 May 2018
Posts: 77

Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
Show Tags
30 Sep 2019, 05:37
nick1816 wrote: 15y11x=8 15y=11x+8 8=8 mod 15 Hence, 11x=7 mod 15 4*x=8 x=2 At x=2, y=2 x,y>3 As slope of 15y=11x+8 is 11/15, there is 11 units increment in y coordinates for every 15 increment in x coordinates. Next integral solution is x=2+15=17 and y=2+11=13 x+y=17+13=30 GMATPrepNow wrote: If x and y are integers greater than 3, and 15y – 11x = 8, what is the least possible value of x+y?
A) 12 B) 16 C) 26 D) 30 E) 34 nick1816  Could you please explain to me arithmetic modulus part? I am not familiar with the concept but I have heard of it. Where can I read this from?




Re: If x and y are integers greater than 3, and 15y – 11x = 8,
[#permalink]
30 Sep 2019, 05:37






