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If r is the remainder when the positive integer n is divided
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21 Sep 2010, 20:39
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If r is the remainder when the positive integer n is divided by 7, what is the value of r ? (1) When n is divided by 21, the remainder is an odd number (2) When n is divided by 28, the remainder is 3
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Re: What is the remainder?
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21 Sep 2010, 21:12
If r is the remainder when the postive integer n is divided by 7, what is the value of r ? 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). (1) when n is divided by 21 the remainder is an odd number > \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient. Or try two different numbers for \(n\): If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1; If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3. Two different answers, hence not sufficient. (2) when n is divided by 28, the remainder is 3 > \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient. Answer: B.
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Re: What is the remainder?
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22 Sep 2010, 15:32
Yep...Followed the same approach while reviewing and got it rite... I think I am pushing the panic button even during my practice tests.. Can you please advice or refer to some other link where people discuss about this topic?
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Re: What is the remainder?
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22 Sep 2010, 16:50
You may consider taking some pain in typing the questions. It will make searches to work in forum. I normally search with start of the question text and hit the discussion for that question
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Re: What is the remainder?
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23 Sep 2010, 10:58
saxenashobhit wrote: You may consider taking some pain in typing the questions. It will make searches to work in forum. I normally search with start of the question text and hit the discussion for that question Sure buddy...going forward I will do it. !!
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Re: If r is the remainder when the positive integer n is divided
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15 Aug 2013, 21:33
n=7A+r
What is r?
(1).
n=21B +R (Odd)
R can be anything 7,9,11,13,...,19
INsufficient
(2).
n=28C + 3 n= 7(4C) +3 . Since 3<7
REM (n/7)=3 Sufficient
(B) it is !



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Re: If r is the remainder when the positive integer n is divided
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03 Apr 2016, 13:13
Bunuel wrote: If r is the remainder when the postive integer n is divided by 7, what is the value of r ?
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).
(1) when n is divided by 21 the remainder is an odd number > \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.
Or try two different numbers for \(n\): If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1; If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3. Two different answers, hence not sufficient.
(2) when n is divided by 28, the remainder is 3 > \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient.
Answer: B. Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 > \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient." ?



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Re: If r is the remainder when the positive integer n is divided
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03 Apr 2016, 20:23
Keysersoze10 wrote: Bunuel wrote: If r is the remainder when the postive integer n is divided by 7, what is the value of r ?
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).
(1) when n is divided by 21 the remainder is an odd number > \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.
Or try two different numbers for \(n\): If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1; If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3. Two different answers, hence not sufficient.
(2) when n is divided by 28, the remainder is 3 > \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient.
Answer: B. Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 > \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient." ? 28p gives the remainder of 0, when divided by 7 and 3 gives the remainder of 3 when divided by 7.
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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.
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Re: If r is the remainder when the positive integer n is divided
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02 Jul 2018, 22:11
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