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Retired Moderator Joined: 06 Jul 2014
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 18% (02:39) correct 82% (02:48) wrong based on 371 sessions

### HideShow timer Statistics 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

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Re: When 120 is divided by positive single-digit integer m the remainder  [#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$$\sqrt{n}$$..

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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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: When 120 is divided by positive single-digit integer m the remainder  [#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

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GMAT 1: 740 Q49 V42 Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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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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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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roopika2990 wrote:

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 positive single-digit integer m the remainder  [#permalink]

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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 positive single-digit integer m the remainder  [#permalink]

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4
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

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

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

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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 positive single-digit integer m the remainder  [#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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GMAT 1: 590 Q49 V20 GMAT 2: 730 Q50 V38 Re: When 120 is divided by positive single-digit integer m the remainder  [#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

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 positive single-digit integer m the remainder  [#permalink]

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Harley1980 wrote:
roopika2990 wrote:

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 positive single-digit integer m the remainder  [#permalink]

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Can someone explain how 120^2 would leave a remainder of 120?
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Re: When 120 is divided by positive single-digit integer m the remainder  [#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

Man! What does <> mean in m<>n?
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Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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talismaaniac wrote:
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

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

Not equal: ≠. Edited to avoid confusion.
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Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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I really haven't been able to understand how 120^2 is an option at all...If n= 120^2, then we are dividing 120/14400. This no way can ever give the remainder of 120..
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Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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1
menonpriyanka92 wrote:
I really haven't been able to understand how 120^2 is an option at all...If n= 120^2, then we are dividing 120/14400. This no way can ever give the remainder of 120..

Hello

When we divide a smaller number by a bigger number, then the smaller number (dividend) itself becomes the remainder, while the quotient becomes 0.

Eg, if we divide 4 by 7, quotient is 0 and remainder is 4 only.
Similarly if we divide 120 by 14400, remainder will be 120 only
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Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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amanvermagmat fair point! Did not think about it in that way. Thank you so much!
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Re: When 120 is divided by positive single-digit integer m the remainder  [#permalink]

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It's been a long time since this question is posted: My 2 cents:

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

So, 120 = np + √n ---- (1)
This can be split into 3 cases:

(i) n = 120 ---> This is not valid as the remainder would be zero.

(ii) n > 120 ----> The only case where (1) is valid is when n = (120)^2

(iii) n < 120 ----> Since we know n is a positive integer, √n < √120 and √120 ~ 11

So, √n < 11

That means √n could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. But, n has to be a square of √n. The only value that satisfies this is when √n = 3 i.e. n = 9.

So, we get 2 values for n from (ii) and (iii). So this statement is NOT SUFFICIENT.

2) n is a single-digit integer

This is fairly straightforward. Since, m & n are single digit positive intergers, the only possibility is 7 & 9. So this statement is SUFFICIENT.

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

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chetan2u wrote:
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

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

I am changing the OA. Please revert if any query..

I did everything and managed to find out each statement is sufficient. And that too is wrong How do we come up 120^2 being a possible solution. It's just too much _________________
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Kudos are always appreciated  Re: When 120 is divided by positive single-digit integer m the remainder   [#permalink] 20 Jul 2019, 13:02
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