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A positive integer n has a remainder
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15 Apr 2021, 03:57
15 Apr 2021, 03:57
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Question Stats:
54% (01:56) correct
45% (02:02) wrong based on 68 sessions
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A positive integer \(n\) has a remainder of 5 when is divided by 7.
\(\frac{m+3}{5}\) is an integer greater than 1.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
\(\frac{m+3}{5}\) is an integer greater than 1.
Quantity A |
Quantity B |
The remainder when \((5n+3)\) is divided by 7 |
The remainder when \(m\) is divided by 5 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: A positive integer n has a remainder
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15 Apr 2021, 19:54
15 Apr 2021, 19:54
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\(n\) has a remainder of 5 when is divided by 7. so \(n\) can be - 5 , 12 , 19 , 26 , ...
\(\frac{m+3}{5}\) \(> 1\)
if we take \(\frac{m+3}{5}\) = 2 --> \(m = 7\)
if we take \(\frac{m+3}{5}\) = 3 --> \(m = 12\)
so \(m\) can be - 7 , 12 , 19 , 24 , ...
Qt A
The remainder when \((5n+3)\) is divided by 7
in every case it will be \(0\) (Try out the values of \(n\) from above)
Qt B
The remainder when \(m\) is divided by 5
It will always be \(2\) (Try out the values of \(m\) from above)
Qt B > Qt A
Answer B
\(\frac{m+3}{5}\) \(> 1\)
if we take \(\frac{m+3}{5}\) = 2 --> \(m = 7\)
if we take \(\frac{m+3}{5}\) = 3 --> \(m = 12\)
so \(m\) can be - 7 , 12 , 19 , 24 , ...
Qt A
The remainder when \((5n+3)\) is divided by 7
in every case it will be \(0\) (Try out the values of \(n\) from above)
Qt B
The remainder when \(m\) is divided by 5
It will always be \(2\) (Try out the values of \(m\) from above)
Qt B > Qt A
Answer B
Re: A positive integer n has a remainder
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31 Jul 2022, 07:55
31 Jul 2022, 07:55
1
Maybe this is a simpler and more practical way to look at this question during the test:
7k+5=n
5n+3=5(7k+5)+3=5*7k+28
Because the remainder of 5n+3 by 7 is the sum of the remainder of 5*7k by 7 (which is 0) and 28 by 7 (also 0)
Now we know 5n+3 is divided by 7, with the remainder being 0.
Given that (m+3)/5 is an integer > 1, m+3 is a multiple of 5. So, m isn't a multiple of 5 and that m/5 must have a remainder greater than 0.
Hence, A<B.
7k+5=n
5n+3=5(7k+5)+3=5*7k+28
Because the remainder of 5n+3 by 7 is the sum of the remainder of 5*7k by 7 (which is 0) and 28 by 7 (also 0)
Now we know 5n+3 is divided by 7, with the remainder being 0.
Given that (m+3)/5 is an integer > 1, m+3 is a multiple of 5. So, m isn't a multiple of 5 and that m/5 must have a remainder greater than 0.
Hence, A<B.
