If n is a positive integer, which of the following is a poss

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

The units place of 5n will either be 5 or 0.
The units place of 56 is always 6.

So; the possible values for units place of |56-5n| are:

6: 6-0=6 {for all 5n where units place of 5n is 0 and 5n<56 or n<12}
1: 6-5=1 {for all 5n where units place of 5n is 5 and 5n<56 or n<12}
9: 5-6=15-6=9 {for all 5n where where units place of 5n is 5 and 5n>56 or n>=12}
4: 0-6=10-6=4 {for all 5n where where units place of 5n is 0 and 5n>56 or n>=12}

Only number with above criteria is 9.

Ans: "B"

I'm sorry if this is a ridiculous question but how do we know that the answer we're looking for must be a multiple of 5? I understand 5n will be a multiple of 5 but I can't see anywhere a statement regarding the answer being a multiple of 5. I would greatly appreciate it if you could explain. Thank you in advance.

^Yeah.. That was an amazing method which I would never have thought of.

The method I used was that subtraction with multiples of 5 follow a pattern: they either end in 1 or 6 (for positive numbers). My problem was that I din't count the negative subtractions.. But they are either 9 or 4 and thus B) is the only valid choice.

The "good" thing about the method I used is that it covers the same reasoning you used; they are (a multiple of 5) +/- 1 and thus only one of them could be an alternative.

However I do not think this method is wise to employ in general since it doesn't have to work in general for all multiples of integer x.

Hi All,

While it's nice to know an "elegant" approach to solving problems, the practical approach to any question will likely involve the easiest work possible. If you have to stare at this question for 2 minutes to come up with the 'elegant' approach, then your'e wasting time. Here, we can get to the correct answer in under a minute (doing math that children can do) with "brute force":

We're told that N is a POSITIVE INTEGER. We're asked for a possible value of |56 - 5N|.

IF....
N = 1, then the answer is 51
N = 2, then the answer is 46
N = 3, then the answer is 41
N = 4, then the answer is 36

At this point, you might recognize that the pattern (so far) is that the answer will end in 1 or 6. Taking a quick look at the answers, you'll see that NONE of them fits this pattern. We're not wrong though....so there MUST be more work to be done. Remember that absolute value signs turn NEGATIVE results into POSITIVE ones....

Let's leap-frog a few of the numbers and continue working...
IF.....
N = 11, then the answer is 1
N = 12, then the answer is |-4| = 4
N = 13, then the answer is |-9| = 9

And now we have the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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