Multiple

[Deepthi Subbu]

If x and y are integers greater than 1 , then is x a multiple of y?

1. 3y^2 + 7y =x
2. x^2 - x is a multiple of y.

OA A

[goyalsau]

If x and y are integers greater than 1 , then is x a multiple of y?

1. 3y^2 + 7y =x
2. x^2 - x is a multiple of y.

OA A

I did this one by plugging some integral values of y in the first statement.

You can put in any +ve value for y , Value of x will always be multiple of y,

I know this is not the best way to solve a problem i was not able to figure out any other approach.



II ) statement is not giving much information. ( x^2 - x ) / y is a integer

=== x ( x - 1 ) / y is also an integer, plug in some values and answer is yes sometimes and No at time as well.

[Rahul@gurome]

If x and y are integers greater than 1 , then is x a multiple of y?

1. 3y^2 + 7y =x
2. x^2 - x is a multiple of y

Given: x and y are integers greater than 1

Statement 1: 3y² + 7y = x
Implies, x = y(3y + 7)
Now as y is an integer greater than 1, (3y + 7) is also an integer. Thus x is a product of two integers and one of them is y i.e. x is a multiple of y.

Sufficient.

Statement 2: (x² - x) is a multiple of y
(x² - x) = x(x - 1) = A multiple of y
Implies either x or (x - 1) is a multiple of y.

Not sufficient.

The correct answer is A.

[Deepthi Subbu]

Great answer , thanks Rahul .

@goyalsu - Even i tried the same approach by plugging in values . I was just curious to check for alternate methods.