Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45360

Re: m16 #35 [#permalink]
Show Tags
07 Nov 2013, 05:50
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
ankit41 wrote: Bunuel wrote: If \(x\), \(a\), and \(b\) are positive integers such that when \(x\) is divided by \(a\), the remainder is \(b\) and when \(x\) is divided by \(b\), the remainder is \(a2\), then which of the following must be true?
A. \(a\) is even B. \(x+b\) is divisible by \(a\) C. \(x1\) is divisible by \(a\) D. \(b=a1\) E. \(a+2=b+1\)
When \(x\) is divided by \(a\), the remainder is \(b\) > \(x=aq+b\) > \(remainder=b<a=divisor\) (remainder must be less than divisor); When \(x\) is divided by \(b\), the remainder is \(a2\) > \(x=bp+(a2)\) > \(remainder=(a2)<b=divisor\).
So we have that: \(a2<b<a\), as \(a\) and \(b\) are integers, then it must be true that \(b=a1\) (there is only one integer between \(a2\) and \(a\), which is \(a1\) and we are told that this integer is \(b\), hence \(b=a1\)).
Answer: D. Hi Bunuel, I solved this problem with a bit different approach x = p*a + b..........eqn(1) and x = q*b + (a2)..............eqn(2) now, equating eqn(1) and eqn(2) p*a + b = q*b + (a2) a(p1) = b(q1)  2 if we put p = q = 3 we get, 2a = 2b  2 or a = b  1 or a + 2 = b + 1 which is option E would pl tell me where am i wrong with my approach?? Thanks. You cannot assign arbitrary values to p and q and say that p = q = 3.
_________________
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: 11 Aug 2011
Posts: 12
Location: India
GPA: 3
WE: Engineering (Other)

Re: m16 #35 [#permalink]
Show Tags
07 Nov 2013, 06:02
Bunuel wrote: ankit41 wrote: Bunuel wrote: If \(x\), \(a\), and \(b\) are positive integers such that when \(x\) is divided by \(a\), the remainder is \(b\) and when \(x\) is divided by \(b\), the remainder is \(a2\), then which of the following must be true?
A. \(a\) is even B. \(x+b\) is divisible by \(a\) C. \(x1\) is divisible by \(a\) D. \(b=a1\) E. \(a+2=b+1\)
When \(x\) is divided by \(a\), the remainder is \(b\) > \(x=aq+b\) > \(remainder=b<a=divisor\) (remainder must be less than divisor); When \(x\) is divided by \(b\), the remainder is \(a2\) > \(x=bp+(a2)\) > \(remainder=(a2)<b=divisor\).
So we have that: \(a2<b<a\), as \(a\) and \(b\) are integers, then it must be true that \(b=a1\) (there is only one integer between \(a2\) and \(a\), which is \(a1\) and we are told that this integer is \(b\), hence \(b=a1\)).
Answer: D. Hi Bunuel, I solved this problem with a bit different approach x = p*a + b..........eqn(1) and x = q*b + (a2)..............eqn(2) now, equating eqn(1) and eqn(2) p*a + b = q*b + (a2) a(p1) = b(q1)  2 if we put p = q = 3 we get, 2a = 2b  2 or a = b  1 or a + 2 = b + 1 which is option E would pl tell me where am i wrong with my approach?? Thanks. You cannot assign arbitrary values to p and q and say that p = q = 3. But p and q are integers. Would you elaborate your point? Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 45360

Re: m16 #35 [#permalink]
Show Tags
07 Nov 2013, 06:14
ankit41 wrote: Bunuel wrote: ankit41 wrote: If \(x\), \(a\), and \(b\) are positive integers such that when \(x\) is divided by \(a\), the remainder is \(b\) and when \(x\) is divided by \(b\), the remainder is \(a2\), then which of the following must be true?
A. \(a\) is even B. \(x+b\) is divisible by \(a\) C. \(x1\) is divisible by \(a\) D. \(b=a1\) E. \(a+2=b+1\)
When \(x\) is divided by \(a\), the remainder is \(b\) > \(x=aq+b\) > \(remainder=b<a=divisor\) (remainder must be less than divisor); When \(x\) is divided by \(b\), the remainder is \(a2\) > \(x=bp+(a2)\) > \(remainder=(a2)<b=divisor\).
So we have that: \(a2<b<a\), as \(a\) and \(b\) are integers, then it must be true that \(b=a1\) (there is only one integer between \(a2\) and \(a\), which is \(a1\) and we are told that this integer is \(b\), hence \(b=a1\)).
Answer: D. Hi Bunuel, I solved this problem with a bit different approach x = p*a + b..........eqn(1) and x = q*b + (a2)..............eqn(2) now, equating eqn(1) and eqn(2) p*a + b = q*b + (a2) a(p1) = b(q1)  2 if we put p = q = 3 we get, 2a = 2b  2 or a = b  1 or a + 2 = b + 1 which is option E would pl tell me where am i wrong with my approach?? Thanks. But p and q are integers. Would you elaborate your point? Thanks. What does p and q being integers has to do with it? The question asks which of the following MUST be true. Again, you cannot assign arbitrary values to p and q. For example, what you get if you assume that p=q=1 to p=q=10?
_________________
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: 21 Apr 2014
Posts: 39

Re: If x, a, and b are positive integers such that when x is [#permalink]
Show Tags
21 Oct 2014, 18:26
1
This post received KUDOS
So the thing to keep in mind with remainder problems like this is that it usually involves finding a value from knowing that the remainder must be smaller than the quotient. From this, we know that a>b and that b>a2, put these two together and we get: a>b>a2 and since these are all positive integers then there b must equal a2
_________________
Eliza GMAT Tutor bestgmatprepcourse.com



Intern
Joined: 30 May 2013
Posts: 4

Re: If x, a, and b are positive integers such that when x is [#permalink]
Show Tags
22 Oct 2014, 02:44
Hello Everyone,
How is option B wrong?



Math Expert
Joined: 02 Sep 2009
Posts: 45360

Re: If x, a, and b are positive integers such that when x is [#permalink]
Show Tags
22 Oct 2014, 03:50



Intern
Joined: 21 Apr 2014
Posts: 39

Re: If x, a, and b are positive integers such that when x is [#permalink]
Show Tags
13 Nov 2014, 15:20
1
This post received KUDOS
Since we know that the remainder is b when x is divided by a we know that b is smaller than a. We also know that a2 is smaller than b, because a2 is the remainder when x is divided by b. If we put those two together we know that: a2<b<a Because we know that x, a and b are all positive integers we also know that b must be a1, because it is an integer that is bigger than a2 and smaller than a
_________________
Eliza GMAT Tutor bestgmatprepcourse.com



NonHuman User
Joined: 09 Sep 2013
Posts: 6832

Re: If x, a, and b are positive integers such that when x is [#permalink]
Show Tags
25 Jan 2018, 03:12
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x, a, and b are positive integers such that when x is
[#permalink]
25 Jan 2018, 03:12



Go to page
Previous
1 2
[ 28 posts ]



