Modulus

[reply2spg]

If n is a positive integer, which of the following is a possible value of |56 - 5n|?
A. 7
B. 9
C. 12
D. 15
E. 20

SPOILER: OA B, am I suppose to expand equation ^{(56-5n)^2}?

[adi_800]

When you put value of n as 13...the value of the expression is 9...so B is the answer...
No need to solve the expression you mentioned...

[Attack]

Try for some values of n=1,2,3....
we get the value of expression with units digit as 1 or 6 till 5n<55. none of the options confrom to that.

starting again from n= 12,13,14.... we get for n = 13 ,
|56-65|= |-9|= 9.

[Lock]

(56+X)=5n (1) and (56-X)=5n (2), where X represents the possible answer choice listed. Only B satisfies one of these conditions: 56+9=5n. Hence, B.

[Fiver]

|56 - 5n| could be considered as 56-5n or 5n-56
5n, with n as a integer, will have the last digit as either '0' or '5'.
Hence with '56-5n' the last digit of the result will either be 6 or 1 e.g. 56-30=26 or 56-15=41

With '5n-56' the last digit of the result will either be 9 or 4 e.g. 85-56= 29 or 70-56=14.

Now look for options with last digits as 6,1,9 0r 4 and straightaway mark B as the correct response.

[r2kins]

Originally Posted by Fiver

|56 - 5n| could be considered as 56-5n or 5n-56
5n, with n as a integer, will have the last digit as either '0' or '5'.
Hence with '56-5n' the last digit of the result will either be 6 or 1 e.g. 56-30=26 or 56-15=41

With '5n-56' the last digit of the result will either be 9 or 4 e.g. 85-56= 29 or 70-56=14.

Now look for options with last digits as 6,1,9 0r 4 and straightaway mark B as the correct response.

nice approach!