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# A number when divided by 5 gives a number which is 8 more

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Manager
Joined: 20 Nov 2009
Posts: 114
A number when divided by 5 gives a number which is 8 more  [#permalink]

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22 Mar 2011, 23:39
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Difficulty:

75% (hard)

Question Stats:

61% (02:29) correct 39% (02:39) wrong based on 221 sessions

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A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

A. 74
B. 75
C. 175
D. 680
E. 690

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27 May 2011, 14:16
13
9
kajolnb wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is
A. 74
B. 75
C. 175
D. 680
E. 690

Back solving is a good technique but I like to keep it as the last option. Reasons for that:
1. It involves a lot of calculations so chances of error are relatively higher.
2. Sometimes, it is not possible to take an educated guess even after trying a couple of values so it could certainly be time consuming if the first numbers you try do not fall in place.

So, as an alternative approach, let me give you an equation that you can use.

Let the number be N.

"A number when divided by 5"
That is N/5

" gives a number which is 8 more than"
N/5 = 8 +

"the remainder obtained on dividing the same number by 34."
N = 34Q + R
So remainder obtained when N is divided by 34 is R which is (N - 34Q)
N/5 = 8 + (N - 34Q)
Isolate N from this equation to get:
N = 85Q/2 - 10

N will take the smallest value when Q = 2 (so that we get an integer value)
N = 85 - 10 = 75
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##### General Discussion
Manager
Joined: 14 Feb 2011
Posts: 144
Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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22 Mar 2011, 23:46
3
1
aiming4mba wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is
A. 74
B. 75
C. 175
D. 680
E. 690

Since the number has to be divisible by 5 and not divisible by 34, we can surely eliminate 74 and 680 from choices.

Lets check the remaining three options

75 - divided by 5 gives 15 and divided by 34 gives 7 as remainder and when 8 is added to 7, it yields 15, so this one satisfies and hence is the answer.
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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23 Mar 2011, 02:02
75/34 = rem 7 and 75/5 = 15, so Answer is B.
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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07 Apr 2011, 18:03
Why do we assume that the number needs to evenly divide by 5? Without that assumption the answer would be 74.
74/5 = 14 + reminder (4)
74/34 = 2 + reminder (6)
6+8 = 14
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27 May 2011, 11:23
1
kajolnb wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is
A. 74
B. 75
C. 175
D. 680
E. 690

I have one approach that is back solving.
see you have find out a number which divided by 5 but not by 34. and x/5=n will be 8 more than the remainder left after dividing an option by 34.
so 74 and is out because is not divided by 5.
Let 75. 75/5=15, and 75/34=2+remainder 7, which is 8 less than 15.
so ans is B.
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27 May 2011, 14:00
I would also go for B. This is a clasic Back Solving, as Baten80 said. The only one not worth trying is the first on, 74, since it is not a multiple of 5.
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29 May 2011, 03:08
VeritasPrepKarishma wrote:
kajolnb wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is
A. 74
B. 75
C. 175
D. 680
E. 690

Back solving is a good technique but I like to keep it as the last option. Reasons for that:
1. It involves a lot of calculations so chances of error are relatively higher.
2. Sometimes, it is not possible to take an educated guess even after trying a couple of values so it could certainly be time consuming if the first numbers you try do not fall in place.

So, as an alternative approach, let me give you an equation that you can use.

Let the number be N.

"A number when divided by 5"
That is N/5

" gives a number which is 8 more than"
N/5 = 8 +

"the remainder obtained on dividing the same number by 34."
N = 34Q + R
So remainder obtained when N is divided by 34 is R which is (N - 34Q)
N/5 = 8 + (N - 34Q)
Isolate N from this equation to get:
N = 85Q/2 - 10

N will take the smallest value when Q = 2 (so that we get an integer value)
N = 85 - 10 = 75

Excellent karishma
loved your approach its always simple and self explanatory.........
kudos to you.........
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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18 Sep 2015, 02:44
Best way pick minimal number in list because we look for this number

74/5=14+4/5, 74/34=2+6/34, so 14+4/5-6=8+4/5, it is more than 8. Out
75/5=15, 75/34=2+7/34, so 15-7=8. correct

B
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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25 Sep 2015, 01:37
VeritasPrepKarishma wrote:
kajolnb wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is
A. 74
B. 75
C. 175
D. 680
E. 690

Back solving is a good technique but I like to keep it as the last option. Reasons for that:
1. It involves a lot of calculations so chances of error are relatively higher.
2. Sometimes, it is not possible to take an educated guess even after trying a couple of values so it could certainly be time consuming if the first numbers you try do not fall in place.

So, as an alternative approach, let me give you an equation that you can use.

Let the number be N.

"A number when divided by 5"
That is N/5

" gives a number which is 8 more than"
N/5 = 8 +

"the remainder obtained on dividing the same number by 34."
N = 34Q + R
So remainder obtained when N is divided by 34 is R which is (N - 34Q)
N/5 = 8 + (N - 34Q)
Isolate N from this equation to get:
N = 85Q/2 - 10

N will take the smallest value when Q = 2 (so that we get an integer value)
N = 85 - 10 = 75

i followed exactly the same procedure. but initially lil bit nervous and confused in the wording of this question.
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Joined: 24 May 2013
Posts: 77
Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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18 Mar 2016, 06:18
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

Let the no be ' n' .
n=34p+r (assume r is the remainder)
n=5* (r+8)=5* (n-34p+8) = 5n -170p+40
4n=170p-40
n=(85/2)*p - 10

p=1 =>n is a fraction.
p=2 => n = 75

A. 74
B. 75
C. 175
D. 680
E. 690
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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21 Mar 2016, 03:29
Nice one... Here we are told that a number divided by 5 gives a quotient with is 8 more than the remainder when number is divided by 34
hence let quotient be p
hence the remainder will be p+8
checking by plugging in the values we get that B is sufficient.
hence B
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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05 Jun 2016, 15:42
I solved this question by plugging in numbers from the answer choices.

A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.

B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer is B
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A number when divided by 5 gives a number which is 8 more  [#permalink]

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Updated on: 06 Nov 2017, 16:10
aiming4mba wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

A. 74
B. 75
C. 175
D. 680
E. 690

let q=quotient for n/34
n/5-8=n-34q→
34q=4n/5+8
test values of 0 and 1 for q
lowest possible value for q=2
lowest possible value for n=75
B

Originally posted by gracie on 14 Sep 2017, 14:21.
Last edited by gracie on 06 Nov 2017, 16:10, edited 1 time in total.
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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20 Sep 2017, 15:49
aiming4mba wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

A. 74
B. 75
C. 175
D. 680
E. 690

The best way to solve this problem is to try each given answer choice. However, the information given in the problem suggests that the number is divisible by 5 but not by 34. Thus, we can eliminate 74 and 680, since the former is not divisible by 5 and the latter is divisible by 34. Since the problem asks for the least possible number, let’s try the smallest number from the remaining three numbers.

B) 75

75/5 = 15

75/34 = 2 R 7

Since 15 is indeed 8 more than 7, 75 is the correct answer.

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A number when divided by 5 gives a number which is 8 more  [#permalink]

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17 Oct 2017, 13:43
aiming4mba wrote:
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

A. 74
B. 75
C. 175
D. 680
E. 690

let r=n/34 remainder
q=n/5
q=r+8
n/5=r+8
n=5r+40
n must be a multiple of 5
looking at 75, the least multiple of 5,
r=7; q=7+8=15
15*5=75=n
B
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Re: A number when divided by 5 gives a number which is 8 more  [#permalink]

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