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Re: If x and y are positive integers such that x/y=33.375,
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07 May 2012, 23:36
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3
alexpavlos wrote:
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?
A. 8 B. 21 C. 25 D. 44 E. 47
I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed. Thanks!
\(x\) 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.
Re: f x and y are positive integers such that x / y = 33.375, wh
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07 May 2012, 20:38
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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
Re: If x and y are positive integers such that x/y=33.375,
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09 May 2012, 14:05
alexpavlos wrote:
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?
A. 8 B. 21 C. 25 D. 44 E. 47
I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed. Thanks!
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.
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.
close
70% (01:35) correct 
