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# The remainder when dividing the expression (X + Y) by 5 is

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The remainder when dividing the expression (X + Y) by 5 is [#permalink]

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06 Aug 2004, 01:18
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The remainder when dividing the expression (X + Y) by 5 is 4.
The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

1.
2.
3.
4.
5.
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06 Aug 2004, 03:06
X + Y = 5q1 + 4
X = 10q2 + 2

==> (10q2 + 2) + Y = 5q1 + 4
==> Y = (5q1 - 10q2) + 2
==> Y = 5 (q1-q2) + 2

So the remainder for Y is 2.

Note: q1 and q2 are quotients.
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06 Aug 2004, 03:08
the guest was me...sorry did not login..also correcting a typo

X + Y = 5q1 + 4
X = 10q2 + 2

==> (10q2 + 2) + Y = 5q1 + 4
==> Y = (5q1 - 10q2) + 2
==> Y = 5 (q1-2q2) + 2

So the remainder for Y when divided by 5 is 2.

Note: q1 and q2 are quotients
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06 Aug 2004, 03:20
Got 2 also.

1) x+y=5k+4

2) x=10j+2

3) y=5m+R. (Looking for R)

4) [1&2] y=5k+4 - 10j - 2 = 5(k-2j) + 2

Look at equation 3: y= (Some Integer)*5 + R
And this is what we get in equation 4.

Therefore the remainder R must be 2.
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06 Aug 2004, 04:02
Got to the same point.. but confused myself by trying to solve for q1+2q2. Careless me..
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06 Aug 2004, 07:45
Got B too.

If X + Y when divided by 5 leaves rem 4, it should be *4 or *9 (Eg: 24 or 29)
If X when divided by 10 leaves rem 2, it should be *2 (Eg: 12)
Therefore, Y should be a *2 or *7 number (Eg: 12, 17)

Hence, Y when divided by 5 should leave a rem 2.

(* = some integer)
06 Aug 2004, 07:45
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