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

Question

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

chetan2u · Accepted Answer

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

chetan2u · Answer

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..
Second value of n, therefore, is 120^2..
At least two possible values of n: 9 and 120^2..
Insuff

2)  n  is a single-digit integer 
 When we divide  120  by single-digit positive integer only two numbers give remainder:  9  and  7  and we know that  m 
eq n  so we can infer that there are two possible cases
1)  m = 7  and  n =9 
2)  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..

roopika2990 · Answer

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

Harley1980 · Answer

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≤r0 ." 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.

Harley1980 · Answer

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

ashakil3 · Answer

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.

MathRevolution · Answer

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.

menonpriyanka92 · Answer

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..

amanvermagmat · Answer

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

bumpbot · Answer

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

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