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

Question

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

KarishmaB · Accepted Answer

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

beyondgmatscore · Answer

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.

subhashghosh · Answer

75/34 = rem 7 and 75/5 = 15, so Answer is B.

katealpha · Answer

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

MHIKER · Answer

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.

aeros232 · Answer

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.

Warlock007 · Answer

Excellent karishma loved your approach its always simple and self explanatory.........

kudos to you.........

Temurkhon · Answer

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

brs1cob · Answer

i followed exactly the same procedure. but initially lil bit nervous and confused in the wording of this question.

Vinayprajapati · Answer

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

stonecold · Answer

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

JLAR2107 · Answer

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

gracie · Answer

n=5q
n=34p+(q-8)
subtracting 2 from 1→
34p-4q=8
least value of p=2
least value of q=15
least possible value of n=75
B

ScottTargetTestPrep · Answer

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.

Answer: B

gracie · Answer

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

esonrev · Answer

How do you get to 85Q from the above?

CrackverbalGMAT · Answer

First things first, on questions like these, I’ll look at planning a  strategy  that can help me  cut my losses . And the best way to do that is  to use options to back up my concepts .

When we look at the question, the  question is asking us the least possible number that satisfies certain conditions . Logically, I would look at  the first three options as more probable than the last two . This is  not to generalize that the bigger numbers can never be the answers , but only to say that this gives us a way to start off with the solution. If the first three options do not work out, it actually makes your job easier. I hope this makes sense.

The question says that  when the unknown number is divided by 5, it gives a number ; it also says that  when the same unknown number is divided by 34, it gives some remainder . Do you observe the difference in the wordings?

In the first case, you got a number, whereas, in the second case, you obtained a remainder. This is a subtle, but definite clue that  the unknown number is divisible by 5 but not by 34. This is enough for us to eliminate option A and D .

Let us look at the other options now. Since we are trying to find the least number, the next number I’ll pick will be 75.

When 75 is divided by 5, the number (that is the result) is 15. When 75 is divided by 34, the remainder is 7. We can see that 15 is definitely 8 more than 7. This is exactly what the question says; it says that the result in the first case is 8 more than the remainder in the second case.

As such, the required number has to be 75.  The correct answer option is B .

You now see what I meant by saying that bigger numbers like 680 and 690 are highly improbable answers in such questions. Again, I reiterate that I do not want you to generalize this and assume that bigger numbers can never be the answers, instead, what I want you to understand is  it’s better to try smaller numbers first  since they are easier to deal with and also tie in with the concept of finding the least number.

Hope that helps!

bumpbot · Answer

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

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