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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.
Remainder.JPG [ 73.19 KiB | Viewed 24058 times ]
(1) When n is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.
Attachment:
Remainder.JPG [ 73.19 KiB | Viewed 24058 times ]
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.
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.
27 Oct 2014, 09:36
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Bunuel
Tough and Tricky questions: Remainders.
If r is the remainder when 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
solution: From #1, if n = 5, remainder is 5 and is odd.
if n = 7, remainder is 7 and is odd.
However, remainder when n(5 or 7) is divided by 7 is different. Hence not sufficient
From #2, n=3, or 31, or 59 etc, remainder is 3,
Even when the above numbers are divided by 7, the remainder is still 3
Answer should be B
