January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52284

When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 01:32
Question Stats:
75% (01:53) correct 25% (02:08) wrong based on 257 sessions
HideShow timer Statistics




Director
Joined: 04 Dec 2015
Posts: 738
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 03:17
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 Required number is in form; \(y = 7k + 2\)  (k is the quotient) The same number when divided by 11 leaves remainder 3. ie; dividing \((7k + 2)\) by \(11\) has remainder \(3\). Subtracting this remainder \(3\) from the the number \((7k +2)\) gives number which would be divisible by \(11\). Therefore; \(7k + 2  3 = (7k 1)\) is divisible by \(11\). Try out values \(0, 1, 2\) ... for k. \(k = 8\) \(7 *8 1 = 55\) \(\frac{55}{11} = 5\)
When \(k = 8\), number is divisible by \(11\). Substitute \(k = 8\) in original number form \((7k +2)\) to get the number. \(7 * 8 +2 = 56 + 2 = 58.\) Sum of digits of \(58 = 13\). Answer E...




Manager
Joined: 03 Feb 2017
Posts: 75
Location: Australia

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 03:32
Is it E?
Given: y=7x+2 and y=11x+3.
From this it follows that (y3) should be divisible by 11.
Substituting the first equation for y, we get \(\frac{(7x+2)3}{11}\) should be an integer.
When x=8, it is the smallest number where the above equation divisible by 11.
Therefore y=7x+2=7(8)+2=58 Sum of digits is 13 (E)



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 06:19
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 When positive integer y is divided by 7, the remainder is 2 i.e. y may be {2, 9, 16, 23, 30, 37, 44, 51, 58... etc} When positive integer y is divided by 11, the remainder is 3 i.e. y may be {3, 14, 25, 36, 47, 58, 69, 80, 91, 102... etc} First Common value = 58 Sum of digits = 5+8 = 13 answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8790
Location: Pune, India

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 07:12
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 y = 7a + 2 y = 11b + 3 Look for the first such value by hit and trial. If b = 1, y = 14 but it is not of the form 7a + 2 If b = 2, y = 25 but it is not of the form 7a + 2 If b = 3, y = 36 but it is not of the form 7a + 2 If b = 4, y = 45 but it is not of the form 7a+2 If b = 5, y = 58 = 7*8 + 2 So 58 is first such value. The sum of its digits is 5+8 = 13 Answer (E) For more on this, check: https://www.veritasprep.com/blog/2011/0 ... unraveled/https://www.veritasprep.com/blog/2011/0 ... emainders/https://www.veritasprep.com/blog/2011/0 ... spartii/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



VP
Joined: 07 Dec 2014
Posts: 1151

When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 09:24
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 let x=difference between y/7 and y/11 quotients x=(y2)/7(y3)/11 y=(77x+1)/4 3 is the least value of x giving a multiple of 4 y=(77*3+1)/4=58 5+8=13 E



Current Student
Joined: 18 Jun 2016
Posts: 36
Location: India
GPA: 3.85

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 12:24
gracie wrote: Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 let x=difference between y/7 and y/11 quotients x=(y2)/7(y3)/11 y=(77x+1)/4 3 is the least value of x giving a multiple of 4 y=(77*3+1)/4=58 5+8=13 E I reached the same answer (E) by listing down all possible values of y for y=7q+2 and for y=11k+3. The first common value was 58. Your approach seems straightforward but I could not understand it. Can you help explain? How did you get the value of x here as 3 ? What does "3 is the least value of x giving a multiple of 4 " mean?



VP
Joined: 07 Dec 2014
Posts: 1151

When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
12 Jun 2017, 13:38
anupama000 wrote: gracie wrote: Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 let x=difference between y/7 and y/11 quotients x=(y2)/7(y3)/11 y=(77x+1)/4 3 is the least value of x giving a multiple of 4 y=(77*3+1)/4=58 5+8=13 E I reached the same answer (E) by listing down all possible values of y for y=7q+2 and for y=11k+3. The first common value was 58. Your approach seems straightforward but I could not understand it. Can you help explain? How did you get the value of x here as 3 ? What does "3 is the least value of x giving a multiple of 4 " mean? hi anupama, looking at the equation y=(77x+1)/4, it's clear that, if y is an integer, then the dividend, 77x+1, must be a multiple of the divisor, 4 testing possible values of 0, 1, and 2 for x, none of these work 3 is the least value of x that gives 77x+1 divisibility by 4 I hope this helps, gracie



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4547
Location: United States (CA)

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
14 Jun 2017, 15:17
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 We are given that when positive integer y is divided by 7, the remainder is 2, and that when y is divided by 11, the remainder is 3. Let’s first determine the values of y that produce a remainder of 2 when divided by 7: y could be: 2, 9, 16, 23, 30, 37, 44, 51, 58, ... Next let’s determine the values of y that produce a remainder of 3 when divided by 11: y could be: 3, 14, 25, 36, 47, 58, ... Thus, we see that the smallest value is 58 and the sum of the digits of 58 is 13. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 13 Mar 2017
Posts: 697
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
15 Jun 2017, 03:32
sashiim20 wrote: Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 Required number is in form; \(y = 7k + 2\)  (k is the quotient) The same number when divided by 11 leaves remainder 3. ie; dividing \((7k + 2)\) by \(11\) has remainder \(3\). Subtracting this remainder \(3\) from the the number \((7k +2)\) gives number which would be divisible by \(11\). Therefore; \(7k + 2  3 = (7k 1)\) is divisible by \(11\). Try out values \(0, 1, 2\) ... for k. \(k = 8\) \(7 *8 1 = 55\) \(\frac{55}{11} = 5\)
When \(k = 8\), number is divisible by \(11\). Substitute \(k = 8\) in original number form \((7k +2)\) to get the number. \(7 * 8 +2 = 56 + 2 = 58.\) Sum of digits of \(58 = 13\). Answer E... sashiim20... Your approach to this problem is very nice. But to make it shorter Lets say y = 11 k + 3 So , y2 = 11k +3 2 = 11k+1 is divisible by 7 Now we check by putting the values of k as 0, 1, 2...... k=0, 11k+1 = 1 k=1, 11k+1 = 12 k=2, 11k+1 = 23 k=3, 11k+1 = 34 k=4, 11k+1 = 45 k=5, 11k+1 = 56 So y = 11k+3 = 58...... If we take y w.r.t bigger number, we can solve in little less time thatn if we would have considered y=7k+2.. Answer E..
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Current Student
Joined: 18 Jun 2016
Posts: 36
Location: India
GPA: 3.85

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
15 Jun 2017, 06:18
[/quote]I reached the same answer (E) by listing down all possible values of y for y=7q+2 and for y=11k+3. The first common value was 58. Your approach seems straightforward but I could not understand it. Can you help explain? How did you get the value of x here as 3 ? What does "3 is the least value of x giving a multiple of 4 " mean?[/quote]
hi anupama, looking at the equation y=(77x+1)/4, it's clear that, if y is an integer, then the dividend, 77x+1, must be a multiple of the divisor, 4 testing possible values of 0, 1, and 2 for x, none of these work 3 is the least value of x that gives 77x+1 divisibility by 4 I hope this helps, gracie[/quote]
Thanks gracie. Its clear now. I think I was reading it wrong as it wasn't obvious to me immediately that x needs to be an integer( as it is the difference in quotients). This is a much cleaner and faster approach I must say.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4330
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
15 Jun 2017, 06:35
Bunuel wrote: When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
A. 9 B. 10 C. 11 D. 12 E. 13 Possible values of y = { 9 , 16 , 23 , 30 , 37 , 44 , 51 , 58................} Possible values of x = { 14, 25, 36 , 47 , 58................} Sum of the digits is 5 + 8 = 13 Thus, answer will be (E) 13
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Intern
Joined: 03 Nov 2018
Posts: 3

Re: When positive integer y is divided by 7, the remainder is 2. When y is
[#permalink]
Show Tags
04 Nov 2018, 23:24
First case Y=7p+2 Y=11q+3 7p=11q+1(1)
7*8=11*5+1=56
So, p+q=8+5=13 Answer:E
Posted from my mobile device




Re: When positive integer y is divided by 7, the remainder is 2. When y is &nbs
[#permalink]
04 Nov 2018, 23:24






