If a and b are both positive integers a/b = 34.06

Question

If a and b are both positive integers  \frac{a}{b}=34.06 , what is the probability that the remainder of  \frac{a}{b}  is a multiple of 6?

A. 1/3
B. 9/20
C. 1/2
D. 2/3
E. 3/4

bv8562 · Accepted Answer

a/b = 34.06 = 3406/100 = 1703/50

Thus, there are only two possible values of a/b i.e  a/b  could either be  3406/100  or  1703/50

When a/b = 3406/100, remainder is 6 (A multiple of 6)
When a/b = 1703/50, remainder is 3 (Not a multiple of 6)

P(Remainder to be a multiple of 6) = Favorable options/Total options =  1/2 (C)

chetan2u · Answer

a=34b+0.06b

So, the remainder is 0.06b. This means 0.06b is also an integer. 
 0.06b=\frac{6b}{100}=\frac{3b}{50} 
Thus b is a multiple of 50. => b=50x

If x is odd, the remainder =  \frac{3b}{50}=\frac{3*50x}{50}=3x=3*odd=odd 
If x is even, the remainder =  \frac{3b}{50}=\frac{3*50x}{50}=3x=3*even=even

As the probability of x to be odd and to be even is same. So the probability of remainder to be even or odd is the same.

P=  \frac{1}{2}

C

arjunnath · Answer

a=34.06b { a=bq+r ; where q is the quotient and r is the remainder; here, q=34.06, r=0}

a=34b+0.06b

When we divide a by b, any remainder will finally only be divided from the decimal portion of the equation (i.e. 0.06b) and not from the term before the decimal (i.e. 34b).

Now consider only 0.06b the portion that determines the value of the remainder.

Hence, 0.06b could be any integer 1,2,3,4,5,6,7,8 or 9.

Now, as per the question, we are given that b is a positive integer
The only values that satisfy this are 3 and 6.

0.06b = 3 or 6.

This gives us 2 outcomes.

The probability of selecting 6 as a multiple of  \frac{a}{b}  among 3 and 6 is  \frac{1}{2} .

Answer is C  \frac{1}{2}

OP1001 · Answer

A = 34b + 0.06b. Therefore 0.06b = the remainder = an integer. 
What are the possibilities of b so that 0.06b becomes an integer: b = 50 -> 0.06b = 3 / b = 100 -> 0.06b = 6 / b =150 -> 0.06b = 9 and so on. 
What is the relation? All the remainders are multiples of 3. 
Since 1/2 of all multiples of 3 are multiples of 6. This means that the probability of the remainder being a multiple of 6 is 1/2.

Adit_ · Answer

The point is that all the remainders are multiple of 3 and no that there are only 2 options.

If a and b are both positive integers a/b = 34.06

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If a and b are both positive integers a/b = 34.06

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