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If r is the remainder when the positive integer n is divided

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If r is the remainder when the positive integer n is divided  [#permalink]

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New post 21 Sep 2010, 21:39
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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?  [#permalink]

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New post 21 Sep 2010, 22:12
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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 non-negative 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?  [#permalink]

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New post 22 Sep 2010, 16:32
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?  [#permalink]

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New post 22 Sep 2010, 17:50
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?  [#permalink]

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New post 23 Sep 2010, 11:58
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  [#permalink]

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New post 15 Aug 2013, 22:33
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  [#permalink]

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New post 03 Apr 2016, 14:13
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 non-negative 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  [#permalink]

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New post 03 Apr 2016, 21:23
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 non-negative 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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Resources:
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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  [#permalink]

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