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If n is a positive integer, which of the following is a poss [#permalink]
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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
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Originally posted by puma on 19 Jun 2008, 13:57.
Last edited by Bunuel on 29 Jul 2013, 05:41, edited 2 times in total.
Edited the question and moved to PS forum.



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Re: possible value [#permalink]
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Updated on: 19 Jun 2008, 14:49
puma wrote: If n is a positive integer, which of the following is a possible value of I565nI?
A) 7 B) 9 C) 12 D) 15 E) 20 565n can be written as 2 equations > 565n = a AND 565n = 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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Originally posted by brokerbevo on 19 Jun 2008, 14:10.
Last edited by brokerbevo on 19 Jun 2008, 14:49, edited 4 times in total.



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Re: possible value [#permalink]
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19 Jun 2008, 14:20
brokerbevo wrote: puma wrote: If n is a positive integer, which of the following is a possible value of I565nI?
A) 7 B) 9 C) 12 D) 15 E) 20 I just set up an equation and tested all choices > Answer Emy answer B 9 565n First thing when I looked at this eq. I realized , unit digit of 5*n can be 0 or 5 let's assume 56> 5n ...subtract unit digits of both the values (60 ) =6 or (65) =1 ; none of the answer choice has unit digit of 6 or 1 second possibility 5n>56 (06)= (106)=4 , (56) =(156) = 9 (Bingo , 9 is one of the answer choice)



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Re: possible value [#permalink]
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19 Jun 2008, 18:14
puma wrote: If n is a positive integer, which of the following is a possible value of I565nI?
A) 7 B) 9 C) 12 D) 15 E) 20 it's either 1+5*k or 4+5*k > B is the answer



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Re: possible value [#permalink]
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19 Jun 2008, 20:02
puma wrote: If n is a positive integer, which of the following is a possible value of l565nl?
A) 7 B) 9 C) 12 D) 15 E) 20 it should be B as it is either 5n+1 or 5n1.
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If n is a positive integer, which of the following is a possible value [#permalink]
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11 Feb 2011, 01:10
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



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Re: If n is a positive integer, which of the following is a possible value [#permalink]
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11 Feb 2011, 06:09
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 565n are: 6: 60=6 {for all 5n where units place of 5n is 0 and 5n<56 or n<12} 1: 65=1 {for all 5n where units place of 5n is 5 and 5n<56 or n<12} 9: 56=156=9 {for all 5n where where units place of 5n is 5 and 5n>56 or n>=12} 4: 06=106=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"
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Re: If n is a positive integer, which of the following is a possible value [#permalink]
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15 Feb 2011, 04:15
Hi subhashghosh Can you pls tell how did you proceed by plugging values.because other method is bit lengthy and ill take time with the possibility of inaccuracy. Thanks
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Re: If n is a positive integer, which of the following is a possible value [#permalink]
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15 Feb 2011, 06:27
Observe that 565n is given, and the values given in answer choices are 720, so pick some number for n which will be making the value 565n one of the choice among the ones given, e.g., 565*10 = 6, but we don't have 6 here. So I decided to move upwards and tried again 23 more and saw that 565 * 13 = 56  65 = 9 = 9, which is the choice B.
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Re: If n is a positive integer, which of the following is a [#permalink]
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29 Jul 2013, 03:45
So in these questions we have take into consideration positive and negative scenarios? Any alternative approach
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Re: possible value [#permalink]
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29 Jul 2013, 05:05
brokerbevo wrote: puma wrote: If n is a positive integer, which of the following is a possible value of I565nI?
A) 7 B) 9 C) 12 D) 15 E) 20 565n can be written as 2 equations > 565n = a AND 565n = 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.



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Re: possible value [#permalink]
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29 Jul 2013, 05:41
sophietrophy wrote: brokerbevo wrote: puma wrote: If n is a positive integer, which of the following is a possible value of I565nI?
A) 7 B) 9 C) 12 D) 15 E) 20 565n can be written as 2 equations > 565n = a AND 565n = 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 = (555n) + 1 = {multiple of 5} + 1 When 56<=5n, then 56  5n = (56  5n) = (5n55)  1 = {multiple of 5}  1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B. Hope it's clear.
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Re: possible value [#permalink]
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16 Dec 2013, 11:01
^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.



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Re: If n is a positive integer, which of the following is a poss [#permalink]
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21 Feb 2015, 18:29
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 leapfrog 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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If n is a positive integer, which of the following is a poss [#permalink]
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25 Aug 2015, 00:30
My answer is B ,though my analysis is flawed.Thanks Bunnel for transformation technique here.Is there any way to find this kind of Questions? Thanks
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If n is a positive integer, which of the following is a poss [#permalink]
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13 Feb 2016, 08:42
How I would do that in exam conditions: organize the chart, it must be accurate and neat not to lose time. 1st column: 565n= [plug in answers) 2nd column: 56+5n= [] Without actual calculation just quickly figure out whether we get a positive integer n.
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Re: If n is a positive integer, which of the following is a poss [#permalink]
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10 Mar 2018, 11:00
puma wrote: 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 Look for multiples of 5 which is nearest of 56 and match with one of the answer choice. Try n = 11, we have 56  5n = 56  5* 11 = 56  55 = 1 Not given in answer choice. Try n = 12, we have 56  5n = 56  5* 12 = 56  60 = 5 Not given in answer choice. Try n = 13, we have 56  5n = 56  5* 13 = 56  65 = 9 Correct match (B) All these steps can be done mental maths
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