Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Jun 2011
Posts: 134

If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
16 Jun 2012, 14:48
Question Stats:
58% (01:20) correct 42% (01:41) wrong based on 291 sessions
HideShow timer Statistics
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a? (1) The remainder when a is divided by 40 is 0 (2) The remainder when 40 is divided by a is 40
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
16 Jun 2012, 15:00
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80. (1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient. (2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient. Answer: B. Hope it's clear.
_________________
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



Manager
Joined: 02 Jun 2011
Posts: 134

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
17 Jun 2012, 07:36
Bunuel wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear. Dear Bunuel, i am not able to understand the st. 2 analysis. (ofcourse i understood what you have written.) one doubt remains like: if it is said x/y leaves a remainder of 10, can i consider values of x/y as 10/20 and like that?



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
17 Jun 2012, 07:40
kashishh wrote: Bunuel wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear. Dear Bunuel, i am not able to understand the st. 2 analysis. (ofcourse i understood what you have written.) one doubt remains like: if it is said x/y leaves a remainder of 10, can i consider values of x/y as 10/20 and like that? Yes, 10 divided by 20 yields the remainder of 10. THEORY: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor).For example positive integer n is divided by 25 yields the remainder of 13 can be expressed as: \(n=25q+13\). Now, the lowest value of \(q\) can be zero and in this case \(n=13\) > 13 divided by 25 yields the remainder of 13. Generally when divisor (25 in our case) is more than dividend (13 in our case) then the reminder equals to the dividend. For example: 3 divided by 24 yields a reminder of 3 > \(3=0*24+3\); or: 5 divided by 6 yields a reminder of 5 > \(5=0*6+5\), Hope it's clear.
_________________
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: 13 Mar 2011
Posts: 8

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
17 Jun 2012, 21:17
B. But is it a 700+ level question??i doubt!
_________________
How about some KUDOS...ey??!!



Intern
Joined: 14 May 2013
Posts: 11

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
24 Jun 2013, 12:02
Bunuel wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear. Thanks for the solution I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ? can you please explain this also ..
_________________
Chauahan Gaurav Keep Smiling



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
24 Jun 2013, 12:16
ichauhan.gaurav wrote: Bunuel wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear. Thanks for the solution I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ? can you please explain this also .. Yes, "the remainder when 40 is divided by a is 40" can be written as \(40=ap+40\) > \(ap=0\). What is the point of confusion here?
_________________
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: 14 May 2013
Posts: 11

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
25 Jun 2013, 05:24
Bunuel wrote: ichauhan.gaurav wrote: Bunuel wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) > \(qa=80\) > so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 > this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 > this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear. Thanks for the solution I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ? can you please explain this also .. Yes, "the remainder when 40 is divided by a is 40" can be written as \(40=ap+40\) > \(ap=0\). What is the point of confusion here? thanks I got it ...
_________________
Chauahan Gaurav Keep Smiling



Senior Manager
Joined: 14 Dec 2017
Posts: 378

Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
21 Jun 2018, 23:14
kashishh wrote: If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
(1) The remainder when a is divided by 40 is 0 (2) The remainder when 40 is divided by a is 40 Given a > 0 & 81 = ak + 1 a = ? Statement 1: The remainder when a is divided by 40 is 0 a = 40p = 40 or 80 to satisfy 81 = ak + 1 Statement 1 is Not Sufficient. Statement 2: The remainder when 40 is divided by a is 40 40 = aq + 40, hence a > 40 & has to satisfy 81 = ak + 1 Hence a = 80 Statement 2 is Sufficient. Answer B. Thanks, GyM




Re: If a is a positive integer and 81 divided by a results in a
[#permalink]
21 Jun 2018, 23:14






