BTGmoderatorRO 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
Please help me out on how you solve this.
qa is b

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, then 75 is the correct answer.

Alternate Solution:

Let n be the number. Thus, the remainder when n is divided by 34 is n/5 - 8. We have:

n = 34s + n/5 - 8

where s is some positive integer.

4n/5 = 34s - 8

Let's multiply each side by 5:

4n = 34*5*s - 40

Let's divide each side by 4:

n = (34*5*s)/4 - 10

n = (17*5*s)/2 - 10

As n is required to be an integer, the smallest value of s is s = 2. Thus, the smallest value of n is (17 * 5 * 2)/2 - 10 = 17 * 5 - 10 = 85 - 10 = 75.

Answer: B

BTGmoderatorRO 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
Please help me out on how you solve this.
qa is b

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

gives a number??

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