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

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.

chetan2u · 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..

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

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards