Need help with this . Any solution apart from pure number substitution
X&Y are positive integers, what is the remainder when x is divided by y?
1. when x is divided by 2y , the remainder is 4
2. when x+y is divided by y, the remainder is 4
Thanks in advance
X&Y are positive integers
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Consider statement (1) alone first.
Remainder is 4.
Remainder should always be less than the divisor.
So 4<2y
Or y >2. So y can be 3, 4, 5...
Let the quotient be "a" when x is divided by 2y.
So x = a*2y+4.
Or x/y = 2*a + 4/y.
Hence the remainder depends on the value 4/y.
If y is 3, the remainder is 1 . If y is 4 remainder is 0 and if y is more than 4 say 5, 6.. remainder is 4.
Since nothing definite can be said, (1) alone is not sufficient.
Next consider (2) alone.
Since remainder is less than the divisor, 4<y or y is 5, 6....
Let the quotient when (x+y) is divided by y be "b".
So x+y =b*y+4.
Or x = (b-1)*y+4.
Or x/y = (b-1) + 4/y.
Since y is more than 4 say 5, 6.. remainder is hence 4.
So statement (2) alone is sufficient to answer the question.
The correct answer is hence (B).
Remainder is 4.
Remainder should always be less than the divisor.
So 4<2y
Or y >2. So y can be 3, 4, 5...
Let the quotient be "a" when x is divided by 2y.
So x = a*2y+4.
Or x/y = 2*a + 4/y.
Hence the remainder depends on the value 4/y.
If y is 3, the remainder is 1 . If y is 4 remainder is 0 and if y is more than 4 say 5, 6.. remainder is 4.
Since nothing definite can be said, (1) alone is not sufficient.
Next consider (2) alone.
Since remainder is less than the divisor, 4<y or y is 5, 6....
Let the quotient when (x+y) is divided by y be "b".
So x+y =b*y+4.
Or x = (b-1)*y+4.
Or x/y = (b-1) + 4/y.
Since y is more than 4 say 5, 6.. remainder is hence 4.
So statement (2) alone is sufficient to answer the question.
The correct answer is hence (B).
Last edited by Rahul@gurome on Tue Jul 13, 2010 10:31 pm, edited 1 time in total.
Rahul Lakhani
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@rahul
Remainder should always be less than quotient.
Let x=13,y=11
x/y;q=1,r=2
Here r>q
Let x=13,y=12
x/y;q=1;r=1
Here r=q
Remainder cannot be always less than quotient
Can you pl confirm...
Remainder should always be less than quotient.
Let x=13,y=11
x/y;q=1,r=2
Here r>q
Let x=13,y=12
x/y;q=1;r=1
Here r=q
Remainder cannot be always less than quotient
Can you pl confirm...
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That was a mistake. It should be divisor. I have corrected in my earlier post.
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)