\(x\) divided by \(y\) yields the remainder of \(r\) can always be expressed as: \(\frac{x}{y}=q+\frac{r}{y}\) (which is the same as \(x=qy+r\)), where \(q\) is the quotient and \(r\) is the remainder.

\(\frac{x}{y}=33.375=33\frac{375}{1,000}=33\frac{3}{8}=33+\frac{3}{8}\), so according to the above \(\frac{r}{y}=\frac{3}{8}\), which means that \(r\) must be a multiple of 3. Only option B offers answer which is a multiple of 3.

Answer: B.

Hope it's clear.
_________________

IMO B

You are correct upto b/y, where b is the remainder..

0.375 can be represented as 3/8, so in our case, b must be the multiple of 3.. from the options given, only B(21) matches this criteria, hence B is the answer

The answer is B - 21 because 21/0.375 yields an integer (= 56) and none of the other options does

x/y = Integer + Remainder
=> x/y = 33 + 0.375

Multiplying both sides by 56,
56(x/y) = 56*33 + 21

ALTERNATIVELY,you may calculate as follows:
x/y = 33.375
=> x/y = 33375/1000 = 267/8 = (33*8 + 3)/8

Multiply both sides by 7 to get
x/y = (33*56 + 21)/8 which can be written as 33*56/8 + 21/8

Once we know that we can get 3 as a remainder, we can select the answer choice that is a multiple of 3 (21 in this case)

The answer is therefore choice (B)
_________________

x/y=33.375 or x/y=33 + 375/1000

remainder/y=375/1000=5*5*5*3/5*5*5*2*2*2=3/8
R/y=3/8
8R=3y

so, ur remainder must be divisible by 3. only answer choice B is divisible by 3.
_________________

x/y=33.375
x = 33y + 0.375y

quotient (q) = 33
reminder (r) = 0.375y

Since x and y are positive integers, quotient and reminder are always integers or whole numbers. Then, r must be one of these whole numbers from the answer choices. We need to find which one of these answer choices is divisible by 0.375.
r = 0.375y
r = 3y/8

A. If r = 8, 3y/8 = 8, y = 64/3
B. If r = 21, 3y/8 = 21, y = 56
C. If r = 25, 3y/8 = 25, y = 200/3
D. If r = 44, 3y/8 = 44, y = 353/3
E. If r = 47, 3y/8 = 47, y = 376/3

So only, B has integer value/whole number. So its B.

[Decimal of the Quotient] = \(\frac{Remainder}{Divisor}\)

Now, x/y = 33.375

\(\frac{R}{Y}\) = \(\frac{375}{1000}\)=\(\frac{3}{8}\)

Hence, R (remainder) will always be a multiple of 3. Ans is B => 21

\(\frac{x}{y} = \frac{33.375}{1} =\frac{33.375 *2}{2} =\frac{66.75}{2} = \frac{66.75 * 2}{4} = \frac{133.5}{4}= \frac{133.5 * 2}{8} =\frac{267}{8}\)

One of the numbers given in the options is left as a remainder when x is divided by y. So if these numbers are added to x, then they should be divisible by y.

267+8 = 275 --> Not divisible by 8.
267+21 = 288 --> divisible by 8. --> Required answer. (we are lucky that in the 2nd option itself we got such a number. Otherwise we might have to test all given options)

B is the answer.

Another way

(267/8) --> remainder is 3. IF I add 5 to it then it will be divisible by 8

Select such a number which when divided by 8, leaves a remainder 5. B is again the option.

Hello everyone!

Just to clarify concepts,

\(\frac{x}{y}=q+\frac{r}{y}\)

\(\frac{x}{y}=33.375=33\frac{375}{1,000}=33\frac{3}{8}=33+\frac{3}{8}\)

Does the above means that y is a multiple of 8 and the remainder must be a multiple of 3?

Kind regards!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________