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If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7 B) 9 C) 12 D) 15 E) 20

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5) B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!! C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5) D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5) E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)
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Last edited by brokerbevo on 19 Jun 2008, 13:49, edited 4 times in total.

Re: If n is a positive integer, which of the following is a possible value [#permalink]

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11 Feb 2011, 05:09

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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}

Re: If n is a positive integer, which of the following is a possible value [#permalink]

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15 Feb 2011, 05:27

Observe that |56-5n| is given, and the values given in answer choices are 7-20, so pick some number for n which will be making the value |56-5n| one of the choice among the ones given, e.g., 56-5*10 = 6, but we don't have 6 here. So I decided to move upwards and tried again 2-3 more and saw that |56-5 * 13| = |56 - 65| = |-9| = 9, which is the choice B.
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If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7 B) 9 C) 12 D) 15 E) 20

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5) B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!! C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5) D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5) E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)

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.

If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7 B) 9 C) 12 D) 15 E) 20

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5) B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!! C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5) D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5) E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)

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.

The correct answer must not be a multiple of 5.

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

When 56>5n, then |56 - 5n| = 56 - 5n = (55-5n) + 1 = {multiple of 5} + 1 When 56<=5n, then |56 - 5n| = -(56 - 5n) = (5n-55) - 1 = {multiple of 5} - 1

So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.

^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.

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

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