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

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.

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

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.

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.

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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