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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 \(Y.\)

1st statement - Y(3Y+1) = X implies that... X is a multiple of Y... - sufficient

2nd Statement - i am not sure the best way... but i tried to use some arbitrary smart #s which will give me X>1. X(X-1) is multiple of Y... so ex- if Y=6, then X =3.. so X is not a multiple of Y. or Y = 12, then X = 4 again X is not a multiple of Y.

The answer should be (A) - statement (1) alone is sufficient to answer the question.

Consider statement (1) first: X = 3Y^2 + 7Y => X = Y (3Y + 7) => X = Y * some number Therefore X is a multiple of Y. So statement (1) alone is sufficient.

Next consider statement 2: X^2 - X is a multiple of Y => kY = X(X-1) where k is any integer >= 1 => X = kY/(X-1) = [k/(X-1)]Y Therefore X is a multiple of Y depending on whether k/(X-1) is an integer or not. For k = 4 and X = 5, this works. For k=5, X=5 it does not work. Therefore statement (2) alone is insufficient to answer the question.

Hence (A) is the correct answer choice.
_________________

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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