Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47221

If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
03 Jan 2014, 06:12
Question Stats:
72% (00:45) correct 28% (00:45) wrong based on 730 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 47221

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
03 Jan 2014, 06:12



Director
Joined: 27 May 2012
Posts: 514

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
Updated on: 10 May 2015, 17:43
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ? (1) x = 5 (2) y = 2 We can see that 10^x + y will always be of the form 10+y , or 100 +y or 1000+y etc depending on the power of x so 1 is always going to be carried forward from the 10^x side to y e.g. if x= 1 and y = 1 then 10^x+y will give 10+1 =11, divided by 3 remainder 2 if x= 2 and y = 1 then we have 100+1 =101,divided by 3 remainder 2 if x=2 and y =2 then we have 100+2 =102,divided by 3 remainder 0 etc hence the remainder really depends on the value of y 1) if y = 1 remainder is 2, if y is 2 remainder is 0, since no info about y hence insuff. 2)Y =2 , just what we were looking for , no matter what ever is the value of x remainder will always be 0. as 10^x+y will always be of the form: 12 102 1002 10002 etc remainder in all cases is 0 hence B is suff answer is B
_________________
 Stne
Originally posted by stne on 04 Jan 2014, 02:05.
Last edited by stne on 10 May 2015, 17:43, edited 1 time in total.



Director
Joined: 03 Feb 2013
Posts: 903
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
05 Jan 2014, 11:46
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ? (1) x = 5 (2) y = 2 Before diving into the statements, lets try to simplify the expression. (10^x + y) rem by 3 = (1^x + y) rem by 3 = y rem by 3. The rule of simplification is applicable only in case of remainders. So clearly Statement is Sufficient. hence Option B)
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
07 Feb 2015, 07:09
Great, but it should be (10^x) + y. Otherwise it is as if x+y is the power of 10.



Math Expert
Joined: 02 Sep 2009
Posts: 47221

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
07 Feb 2015, 07:15



Senior Manager
Joined: 02 Dec 2014
Posts: 351
Location: Russian Federation
Concentration: General Management, Economics
WE: Sales (Telecommunications)

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
10 May 2015, 14:51
stne wrote: Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ? (1) x = 5 (2) y = 2 We can see that 10^x + y will always be of the form 10+y , or 100 +y or 1000+y etc depending on the power of x so 1 is always going to be carried forward from the 10^x side to y e.g. if x= 1 and y = 1 then 10^x+y will give 10+1 =11, divided by 3 remainder 2 if x= 2 and y = 1 then we have 100+1 =101,divided by 3 remainder 2 if x=2 and y =2 then we have 100+2 =102,divided by 3 remainder 0 etc hence the remainder really depends on the value of y 1) if y = 1 remainder is 2, if y is 2 remainder is 0, since no info about y hence insuff. 2) X=2 , just what we were looking for , no matter what ever is the value of x remainder will always be 0. as 10^x+y will always be of the form: 12 102 1002 10002 etc remainder in all cases is 0 hence B is suff answer is B Not X=2, Y=2. Please correct a typo=))
_________________
"Are you gangsters?"  "No we are Russians!"



Manager
Joined: 05 Oct 2014
Posts: 60
Location: India
Concentration: General Management, Strategy
GPA: 3.8
WE: Project Management (Energy and Utilities)

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
21 Oct 2017, 02:58
Bunuel wrote: SOLUTION
If x and y are positive integers, what is the remainder when 10^x +y is divided by 3?
Since, the sum of the digits of 10^x is always 1 then the remainders when 10^x+y is divided by 3 is only dependant on the value of the number added to 10^x, so on y. If y is a multiple of 3 then 10^x+y will yield the remainder of 1 (since the sum of the digits of 10^x+y will be one more than a multiple of 3), if y is one more than a multiple of 3 then 10^x+y will yield the remainder of 2 and finally if y is two more than a multiple of 3 then 10^x+y will yield the remainder of 0,
(1) x = 5. Not sufficient. (2) y = 2. Sufficient.
Answer: B. Bunuel〖10〗^(x+y)/3 => 〖10〗^x/3 X 〖10〗^y/3 => 10/3 X 10/3 => 1 X 1 => 1 (Remainder)  (1) 〖10〗^x/3+y/3 => 〖10〗^ /3+y/3 => 1 + (y/3) , given y=2 => 1 + 2 = 3 ( Remainder)  (2) Please tell which one above the question is referring to and also please if my approach is wrong. Considering (2) , answer shall be B.



Math Expert
Joined: 02 Sep 2009
Posts: 47221

Re: If x and yare positive integers , what is the remainder when
[#permalink]
Show Tags
21 Oct 2017, 03:05
merajul wrote: Bunuel wrote: SOLUTION
If x and y are positive integers, what is the remainder when 10^x +y is divided by 3?
Since, the sum of the digits of 10^x is always 1 then the remainders when 10^x+y is divided by 3 is only dependant on the value of the number added to 10^x, so on y. If y is a multiple of 3 then 10^x+y will yield the remainder of 1 (since the sum of the digits of 10^x+y will be one more than a multiple of 3), if y is one more than a multiple of 3 then 10^x+y will yield the remainder of 2 and finally if y is two more than a multiple of 3 then 10^x+y will yield the remainder of 0,
(1) x = 5. Not sufficient. (2) y = 2. Sufficient.
Answer: B. Bunuel〖10〗^(x+y)/3 => 〖10〗^x/3 X 〖10〗^y/3 => 10/3 X 10/3 => 1 X 1 => 1 (Remainder)  (1) 〖10〗^x/3+y/3 => 〖10〗^ /3+y/3 => 1 + (y/3) , given y=2 => 1 + 2 = 3 ( Remainder)  (2) Please tell which one above the question is referring to and also please if my approach is wrong. Considering (2) , answer shall be B. It's \(10^x + y\) not \(10^{x + y}\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: If x and yare positive integers , what is the remainder when &nbs
[#permalink]
21 Oct 2017, 03:05






