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Which of the following can be a remainder of X/Y if both X

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Manager
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Which of the following can be a remainder of X/Y if both X [#permalink]

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New post 11 Sep 2008, 04:09
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C
D
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Which of the following can be a remainder of X/Y if both X and Y are positive integers and X/Y =2.625?

a) 2
b) 4
c) 5
d) 8
e) 9

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Re: remainder PS [#permalink]

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New post 11 Sep 2008, 04:49
2.625=2+625/1000 = 21/8 .

21/8 leaves a remainder of 5.
ans = C

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Re: remainder PS [#permalink]

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New post 11 Sep 2008, 05:14
X/Y = 2.625
or, X = 2.625 x Y
or, X = 2Y + 0.625Y
or, X = 2Y + 625/1000 x Y
or X = 2Y + 5/8Y

remainder will be 5 .
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Manager
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Location: Toronto, Canada
Re: remainder PS [#permalink]

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New post 11 Sep 2008, 06:47
OA is C


Thanks guys... all clear answers. I unfortunately make a silly mistake on this one... did 6/8 instead... grr.

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Re: remainder PS [#permalink]

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New post 11 Sep 2008, 07:50
Quoting Ian Stewart's explanation on a similar problem :
IanStewart wrote:
Quote:
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

(a) 2
(b) 4
(c) 8
(d) 20
(e) 45

When we divide s by t we can always write:

s/t = q + r/t

where q is the 'quotient', and r is the 'remainder', where 0 <= r < t (so 0 <= r/t < 1). That's essentially the definition of the remainder, so is quite important to understand- many remainder questions will be difficult to answer otherwise. If

s/t = 64.12 = 64 + 12/100

then 64 is the quotient, while the fractional part, 12/100, is equal to r/t (compare with the other equation above). This doesn't mean 12 is the remainder, however- that would only be true if t was equal to 100. Still, we can find what values r might take. Rewriting:

r/t = 12/100
r/t = 3/25
25r = 3t

and if r and t are integers, the primes that divide the right side of this equation must also divide the left- in particular r must be divisible by 3. Only one answer choice is divisible by 3- E, or 45- so it's the only possible value of r among the answer choices.

There are many other possible values for r- any multiple of 3 would have been a possible answer, in fact.

Here in our question we have

x/y = 2.625 = 2 + (625/1000) = 2 + (5/8)

if r is remainder then , r/y = 5/8
8r = 5y (and we know from the question that r and y are integers)

Only one choice is a multiple of 5 here. So the answer is C

Thanks Ian
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Re: remainder PS   [#permalink] 11 Sep 2008, 07:50
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Which of the following can be a remainder of X/Y if both X

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