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Gmanimesh
What is the remainder when X is divided by 8?
(a) x leaves the same remainder when divided by 8,10 and Y.
(b) x is 5 less than the LCM of 8,10 and Y

Statement 1

x leaves the same remainder when divided by 8,10 and Y

x can be anything.

Say x = 1, the remainder is 1.
Say x = 0, the remainder is 0

So the statement is not sufficient.

Statement 2

x is 5 less than the LCM of 8,10 and Y

Let the LCM be z

We know that z is divisible by 8.

The number which is less than z and is divisible by 8 is z - 8

As x is 5 less than z, the remainder will always be 5.

Statement II is sufficient.

Option B
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chetan2u
What is the remainder when X is divided by 8?
(a) x leaves the same remainder when divided by 8,10 and Y.
x could be anything from 1 to 7.
Clearly insufficient.

(b) x is 5 less than the LCM of 8,10 and Y
Thus, x=LCM(8,10,Y)-5
x+5=LCM(8,10,Y), meaning x+5 is divisible by 8.
Hence, x will leave a remainder of 8-5 or 3.
Sufficient.


B
­aren't you assuming Y is a postive integer here, can't Y be a fraction ?
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chetan2u
What is the remainder when X is divided by 8?
(a) x leaves the same remainder when divided by 8,10 and Y.
x could be anything from 1 to 7.
Clearly insufficient.

(b) x is 5 less than the LCM of 8,10 and Y
Thus, x=LCM(8,10,Y)-5
x+5=LCM(8,10,Y), meaning x+5 is divisible by 8.
Hence, x will leave a remainder of 8-5 or 3.
Sufficient.


B
­aren't you assuming Y is a postive integer here, can't Y be a fraction ?

When we talk of LCM of x and y, it means x and y are integers.

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