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If x and y are integers greater than 1, is x a multiple of y?
(1)3y^2 + 7y = x (2)x^2 -x is a multiple of y
(1) x=3y^2+7y= y ( 3y+7) , since y is an integer---> 3y+7 is an integer ---> x is a multiple of y
---->suff
(2) x^2-x is a multiple of y
pick number x = 3 ,y =6 ---> x^2-x= 6 is a multiple of 6 but x=3 isn't
x=3, y=3, x^2-x= 6 is a multiple of y=3 , x=3 is a multiple of 3
--> insuff.
(1) can be written as y(3y+1)=x
y.m=x
as we know that y is an integer....3Y+1 is also an integer thus X is a multiple of Y...Sufficient
(2) x(x-1)=y
xm=y
hmm this lets see if x=4, y=2...then 4(3)=12...works fine and x is a multiple of Y...if x=5 y=4 then 5(4)=20=which is a multiple of y however x=5 is not a multiple of y=4
If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = X 2) X^2 - X is a multiple of y
let me correct myself and change to A.
what i overlooked with (ii) is I assumed (X^2 - X) is a multiple of y, which is given. ststement (ii) doesnot tell that x is a multiple of y. if suppose x = 5 and y = 2.
(X^2 - X) = yk
25-5=2k
k=10.
but x=5 is not a multiple of y=2. so ii is not suff.
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