December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Jul 2011
Posts: 207
Location: Accra, Ghana

If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
Updated on: 20 Jun 2014, 01:14
Question Stats:
82% (00:52) correct 18% (00:58) wrong based on 479 sessions
HideShow timer Statistics
If x and y are positive integers, what is the remainder when \(10^x +y\) is divided by 3? (1) x = 5 (2) y = 2
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by dzodzo85 on 19 Mar 2012, 23:40.
Last edited by Bunuel on 20 Jun 2014, 01:14, edited 1 time in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
19 Mar 2012, 23:51




Intern
Joined: 14 Dec 2011
Posts: 4

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
09 May 2012, 13:07
So the question should be ((10^x)+y)/3? Posted from GMAT ToolKit



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
09 May 2012, 13:57



Manager
Joined: 13 Feb 2012
Posts: 137
Location: Italy
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Sales (Transportation)

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
05 Sep 2012, 02:17
The OG explanations sometimes really baffle me; I reached the solution simply by realizing that it did not matter what power the 10 was to be elevated to, and to know the value of y was sufficient; just like Bunuel explained above. The OG explanation should not be the primary route, in my opinion.
_________________
"The Burnout"  My Debrief
Kudos if I helped you
Andy



Manager
Joined: 21 Oct 2013
Posts: 186
Location: Germany
GPA: 3.51

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
20 Jun 2014, 01:03
The question is not really understandable. Please post it either in the "formula form" or like this (10^x)+y.



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
20 Jun 2014, 01:14



Senior Manager
Joined: 18 Aug 2014
Posts: 324

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
12 Dec 2015, 10:58
Bunuel wrote: 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 I'm sorry if this is something obvious i'm missing but I'm not quite following what you mean by that; sum of digits 10^x is always 1 as in...10 and x?
_________________
Please help me find my lost Kudo's bird



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
13 Dec 2015, 01:34



Senior Manager
Joined: 18 Aug 2014
Posts: 324

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
13 Dec 2015, 09:07
Bunuel wrote: redfield wrote: Bunuel wrote: 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 I'm sorry if this is something obvious i'm missing but I'm not quite following what you mean by that; sum of digits 10^x is always 1 as in...10 and x? If x = 1, then 10^1 = 10 > the sum of the digits = 1 + 0 = 1; If x = 2, then 10^3 = 100 > the sum of the digits = 1 + 0 + 0 = 1; If x = 3, then 10^3 = 1000 > the sum of the digits = 1 + 0 + 0 + 0= 1; ... Hope it's clear. Sorry I'm still struggling with this; what are you equating the 1 and the 0's to, the 1 being the 10 and the 0's being the power it is risen to?
_________________
Please help me find my lost Kudo's bird



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
13 Dec 2015, 09:13
redfield wrote: Bunuel wrote: redfield wrote: I'm sorry if this is something obvious i'm missing but I'm not quite following what you mean by that; sum of digits 10^x is always 1 as in...10 and x? If x = 1, then 10^1 = 10 > the sum of the digits = 1 + 0 = 1; If x = 2, then 10^3 = 100 > the sum of the digits = 1 + 0 + 0 = 1; If x = 3, then 10^3 = 1000 > the sum of the digits = 1 + 0 + 0 + 0= 1; ... Hope it's clear. Sorry I'm still struggling with this; what are you equating the 1 and the 0's to, the 1 being the 10 and the 0's being the power it is risen to? We are talking about the sum of the digits of a number. For example, the sum of the digits of 17 is 8 because 1 + 7 = 8. Or, the sum of the digits of 2^5 is 5 because 2^5 = 32 and 3 + 2 = 5.
_________________
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



Senior Manager
Joined: 18 Aug 2014
Posts: 324

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
13 Dec 2015, 09:19
Bunuel wrote: We are talking about the sum of the digits of a number. For example, the sum of the digits of 17 is 8 because 1 + 7 = 8. Or, the sum of the digits of 2^5 is 5 because 2^5 = 32 and 3 + 2 = 5.
Ohhhhh; my apologies I was trying to make it some abstract/esoteric concept rather than literally just the sum of the numbers that make up the number!
_________________
Please help me find my lost Kudo's bird



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6667
GPA: 3.82

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
13 Dec 2015, 20:40
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If x and y are positive integers, what is the remainder when 10 x +y is divided by 3? (1) x = 5 (2) y = 2 In the original condition, there are 2 variables(x,y), which should match with the number of equations. So, you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. In 1) & 2), it becomes 10^5+2=100,002. Also, the remainder after divided by 3 is same as the remainder after the sum of all digits divided by 3. That is, 1+0+0+0+0+2=3 can be divided by 3 and therefore it is yes, which is sufficient. So the answer is C. This is an integer question which is one of the key questions. When applying 4(A) of the mistake type, 1) x=5 but y=2 > yes, y=3 > no, which is not sufficient. 2) y=2 > 10^x+2=12,102,1002,10002......... When it comes to number like these, the sum of all digits are 3 and also can be divided by 3 and it is yes, which is sufficient. Therefore, both B and C can be the answer. When both B and C can be the answer, the answer is B. This type of question is given in Math Revolution lectures and you need to get this type of question right to reach the score range 5051. > For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 06 Feb 2016
Posts: 6

if integers x,y > 0, what is the remainder when (10^x + y)/3? Logic?
[#permalink]
Show Tags
Updated on: 20 Feb 2016, 08:09
If x and y are positive integers, what is the remainder when 10^x + y is divided by 3? (1) X=5 (2) y=2 The correct answer is B;
I understood the explanation, and indeed B was my first choice, too. However, I'm struggling with its logic. Because the question asks for a value, so I thought it depends on the power of 10th? I see the similar pattern it follows (33,334.. etc), yet different powers would yield in different results, therefore I won't be able to find out the exact value.
i.e. (10^1 + 2)/ 3 = 4 or (10^2 + 2 /3) = 34)
Could you explain, why in I say B is sufficient, even though there are many values? (Find the question in the 2nd Quant Review)
Originally posted by nilem94 on 20 Feb 2016, 07:50.
Last edited by nilem94 on 20 Feb 2016, 08:09, edited 1 time in total.



Math Expert
Joined: 02 Aug 2009
Posts: 7115

Re: if integers x,y > 0, what is the remainder when (10^x + y)/3? Logic?
[#permalink]
Show Tags
20 Feb 2016, 08:08
nilem94 wrote: If x and y are positive integers, what is the remainder when 10^x + y is divided by 3? (1) X=5 (2) y=2 The correct answer is B;
I understood the explanation, and indeed B was my first choice, too. However, I'm struggling with its logic. Because the questions ask for a value, so I thought it depends on the power of 10th? I see the similar pattern it follows (33,334.. etc), yet different powers would yield in different results, therefore I won't be able to find out the exact value.
i.e. (10^1 + 2)/ 3 = 4 or (10^2 + 2 /3) = 34)
Could you explain, why in I say B is sufficient, even though there are many values? (Find the question in the 2nd Quant Review) Hi, INFO: since the div rule by 3 states that the sum of digits should be div by 3 and the remainder of any integer is same as remainder of the sum of integer.. lets see what is 10^x + y... here irrespective of value of x, the sum of integers will be 1, as it will be 1,10,100,1000... so we require to know y to find the remainder..
lets see the choices.. 1) X=5 nothing about y insuff
(2) y=2 now we know sum = 1+2.. remainder is 0.. Suff B Hope it helped
_________________
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



Intern
Joined: 06 Feb 2016
Posts: 6

Re: if integers x,y > 0, what is the remainder when (10^x + y)/3? Logic?
[#permalink]
Show Tags
20 Feb 2016, 08:13
Ah now I see, the remainder is always 0, no matter what power! Thank you so much!



Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
20 Feb 2016, 13:33
nilem94 wrote: If x and y are positive integers, what is the remainder when 10^x + y is divided by 3? (1) X=5 (2) y=2 The correct answer is B;
I understood the explanation, and indeed B was my first choice, too. However, I'm struggling with its logic. Because the question asks for a value, so I thought it depends on the power of 10th? I see the similar pattern it follows (33,334.. etc), yet different powers would yield in different results, therefore I won't be able to find out the exact value.
i.e. (10^1 + 2)/ 3 = 4 or (10^2 + 2 /3) = 34)
Could you explain, why in I say B is sufficient, even though there are many values? (Find the question in the 2nd Quant Review) Merging topics. Please search before posting.
_________________
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



Intern
Joined: 22 Jul 2018
Posts: 5

Re: If x and y are positive integers, what is the remainder when
[#permalink]
Show Tags
14 Aug 2018, 19:55
dzodzo85 wrote: If x and y are positive integers, what is the remainder when \(10^x +y\) is divided by 3?
(1) x = 5 (2) y = 2 Answer B. \(\frac{10^x +y}{3}\) = \(\frac{10^x}{3}+ \frac{y}{3}\) = \(\frac{(9+1)^x}{3}\) + \(\frac{y}{3}\) For \((9+1)^x\), all the terms will have a factor of 9 (divisible by 3) except the last term \(1^x\) [According to binomial theorem], so the remainder is always 1. Now we just need to know the value of y for the 2nd term \(\frac{y}{3}\) Hence the answer is B.




Re: If x and y are positive integers, what is the remainder when &nbs
[#permalink]
14 Aug 2018, 19:55






