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When 120 is divided by single-digit integer m the remainder is

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When 120 is divided by positive single-digit integer \(m\) the remainder is positive. When 120 is divided by positive integer \(n\) the remainder is also positive. If \(m<>n\) what is the remainder when 120 is divided by \(|n-m|\)?

1) When 120 divided by integer \(n\) the remainder equal to \(\sqrt{n}\)
2) \(n\) is a single-digit integer
[Reveal] Spoiler: OA

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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 30 Jun 2015, 19:54
Can you please explain the answer?

1) When 120 divided by integer n the remainder equal to n√

This can be a number between -120 and 120, and only 9 and -9 satisfies this condition, every other square in between those numbers fails - INSUFFICIENT.

2) n is a single-digit integer

Can be any number between -9 to 9.
INSUFFICIENT

Both put together the answer can be anything remainder of division of 120 by an integer between 0 and 18 INSUFFICIENT.

Ans - E

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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 30 Jun 2015, 23:17
roopika2990 wrote:
Can you please explain the answer?

1) When 120 divided by integer n the remainder equal to n√

This can be a number between -120 and 120, and only 9 and -9 satisfies this condition, every other square in between those numbers fails - INSUFFICIENT.

2) n is a single-digit integer

Can be any number between -9 to 9.
INSUFFICIENT

Both put together the answer can be anything remainder of division of 120 by an integer between 0 and 18 INSUFFICIENT.

Ans - E


Hello roopika2990.
According to this I always think that divider can be only positive if we talk about remainders:
"GMAT Prep definition of the remainder:
If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a=qd+r\) and \(0≤r<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\)."
finding-the-remainder-when-dividing-negative-numbers-88839.html#p670603

But I add corrections to my question to exclude any ambiguity and now it says that \(m\) and \(n\) are positive numbers.
Thanks for reprimand.

----

2) n is a single-digit integer

Can be any number between -9 to 9.
INSUFFICIENT


It can't be any number because 2 for example gives remainder that equal 0 and this is not positive remainder.
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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Harley1980 wrote:
When 120 is divided by positive single-digit integer \(m\) the remainder is positive. When 120 is divided by positive integer \(n\) the remainder is also positive. If \(m<>n\) what is the remainder when 120 is divided by \(|n-m|\)?

1) When 120 divided by integer \(n\) the remainder equal to \(\sqrt{n}\)
2) \(n\) is a single-digit integer




1) From this statement we know that \(n = 9\)
\(120 = 13*9+3\)
And from the task we know that \(120 = m*x + R\) where \(R>0\)
also we know that \(m<>n\) so \(m <> 9\)

When we divide \(120\) on single-digit positive integer only two numbers gives remainder: \(9\) and \(7\) so we can infer that \(m = 7\)
\(|9-7| = 2\) --> \(120/2 = 60\) Remainder is \(0\)
Sufficient

2) When we divide \(120\) on single-digit positive integer only two numbers gives remainder: \(9\) and \(7\) and we know that \(m <> n\) so we can infer that there is two possible variants:
\(m = 7\) and \(n =9\)
or \(m=9\) and \(n = 7\)
\(|9-7| = 2\)
\(|7-9| = 2\)
\(120/2 = 60\) Remainder is \(0\)
Sufficient

Answer is D
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 21 Feb 2016, 16:53
Harley1980

How do you know that for statement 1, that there is no other positive integer that would satisfy the requirement for when 120/n the remainder is sqrt(n). I know that 9 satisfies it, but when your writing the GMAT, and you want to ensure that there is no other possibility, how should one do so? The question stem doesn't state that n has to be a positive single digit.

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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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ashakil3 wrote:
Harley1980

How do you know that for statement 1, that there is no other positive integer that would satisfy the requirement for when 120/n the remainder is sqrt(n). I know that 9 satisfies it, but when your writing the GMAT, and you want to ensure that there is no other possibility, how should one do so? The question stem doesn't state that n has to be a positive single digit.



Hi,
the originator has not been online for some time, so let me answer your Q..

1) When 120 divided by integer n the remainder equal to\(\sqrt{n}\)..
as you have written, we cannot straightway jump to answer 9.
but 9 is an answer..

there is one more value of n that I can give you without thinking is 120^2...
the remainder will be 120 here..
so you have two answer possible..
Insuff..

2) n is a single-digit integer
now we know only that n is a single digit ..
Only 7 and 9 leave remainder..
so Suff..

B


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Harley1980 wrote:
When 120 is divided by positive single-digit integer \(m\) the remainder is positive. When 120 is divided by positive integer \(n\) the remainder is also positive. If \(m<>n\) what is the remainder when 120 is divided by \(|n-m|\)?

1) When 120 divided by integer \(n\) the remainder equal to \(\sqrt{n}\)
2) \(n\) is a single-digit integer

Source: self-made


Hi Harley1980,

the solution given by you along with OA is not correct..

The solution is as follows..

1) When 120 divided by integer \(n\) the remainder equal to \(\sqrt{n}\)
From this statement we know that N is 9 as found by you..
But is 9 the only value possible..

The second value is staring at us right in the Q..
Any value of n >120 will leave a remainder 120..
so 120^2 will also leave a remainder 120..
so second value of n is 120^2..
Atleast two possible values of n: 9 and 120^2..
Insuff

2) \(n\) is a single-digit integer
When we divide \(120\) on single-digit positive integer only two numbers gives remainder: \(9\) and \(7\) and we know that \(m <> n\) so we can infer that there is two possible variants:
\(m = 7\) and \(n =9\)
or \(m=9\) and \(n = 7\)
\(|9-7| = 2\)
\(|7-9| = 2\)
\(120/2 = 60\) Remainder is \(0\)
Sufficient

Answer is B


I am changing the OA. Please revert if any query..
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 16 May 2016, 08:22
I believe n can also be 11. We get the same answer [B] from the absolute value difference between 9 and 7, anyway.

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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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If we look at the original condition, there are 2 variables (m and n) and 1 equation (as 120=2^3*3*5, only m=7 and 9 are possible). In order to match the number of variables to the number of equations we need 1 equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer choice.
In the case of the condition 1), since n=9, 120^2, the answers are not unique and the condition is not sufficient.
In the case of the condition 2), since m=n=7,9 is the only possibility, only |n-m|=2 is possible. Hence, the remainder becomes 0 and the answer becomes unique. The condition, hence is sufficient, and the correct answer choice is B.

- For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 02 Jul 2017, 09:31
Harley1980 wrote:
When 120 is divided by positive single-digit integer \(m\) the remainder is positive. When 120 is divided by positive integer \(n\) the remainder is also positive. If \(m<>n\) what is the remainder when 120 is divided by \(|n-m|\)?

1) When 120 divided by integer \(n\) the remainder equal to \(\sqrt{n}\)
2) \(n\) is a single-digit integer



This problem is basically a modifed version of a MGMAT Adavanced problem

The remainder when 120 is divided by single-digit integer m is positive, as is the remainder when 120
is divided by single-digit integer n. If m > n, what is the remainder when 120 is divided by m – n?
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 05 Jul 2017, 03:13
Harley1980 wrote:
roopika2990 wrote:
Can you please explain the answer?

1) When 120 divided by integer n the remainder equal to n√

This can be a number between -120 and 120, and only 9 and -9 satisfies this condition, every other square in between those numbers fails - INSUFFICIENT.

2) n is a single-digit integer

Can be any number between -9 to 9.
INSUFFICIENT

Both put together the answer can be anything remainder of division of 120 by an integer between 0 and 18 INSUFFICIENT.

Ans - E


Hello roopika2990.
According to this I always think that divider can be only positive if we talk about remainders:
"GMAT Prep definition of the remainder:
If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a=qd+r\) and \(0≤r<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\)."
http://gmatclub.com/forum/finding-the-r ... ml#p670603

But I add corrections to my question to exclude any ambiguity and now it says that \(m\) and \(n\) are positive numbers.
Thanks for reprimand.

----

2) n is a single-digit integer

Can be any number between -9 to 9.
INSUFFICIENT


It can't be any number because 2 for example gives remainder that equal 0 and this is not positive remainder.


7 and 9 are the two single digit integers that give remainders while dividing 120.
I think the answer should be E because alsthpugh combinig both statements gives n=9, but what about m?
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Re: When 120 is divided by single-digit integer m the remainder is [#permalink]

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New post 13 Oct 2017, 12:16
Can someone explain how 120^2 would leave a remainder of 120?

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Re: When 120 is divided by single-digit integer m the remainder is   [#permalink] 13 Oct 2017, 12:16
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