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

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30 Jun 2015, 09:51

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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

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

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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.

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

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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.

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

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30 Jun 2015, 23:23

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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

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.

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..

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

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..
_________________

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.
_________________

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

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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?
_________________

You have to have the darkness for the dawn to come.

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

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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.

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?
_________________

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

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19 Dec 2017, 22:52

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

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

Man! What does <> mean in m<>n?

Not equal: ≠. Edited to avoid confusion.
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