Carcass wrote:

The operation * is deﬁned for all integers x and y as x * y = xy − y. If x and y are positive integers, which of the following CANNOT be zero?

A) X*Y

B) Y*X

C) (X-1)*Y

D) (X+1)*Y

E) X*(Y-1)

Let's take the formula x * y = xy − y, and rewrite is as x * y = y(x − 1)

Now let's check each answer choice (BEGINNING WITH E, since the test-makers like to place the correct answer

for these questions near the end, since most test-takers will check the answers from A to E.)

E) X*(Y-1)

Apply the formula to get: (Y-1)(X-1)

Can this expression ever equal 0?

Sure, if Y = 1 and X = 1, then (Y-1)(X-1) = (1-1)(1-1) = 0

ELIMINATE E

D) (X+1)*Y

Apply the formula to get: (Y)(X+1-1)

Simplify to get (Y)(X)

Can this expression ever equal 0?

NO.

If X and Y are positive integers, then (Y)(X) can NEVER equal zero

Answer:

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Brent Hanneson – Creator of greenlighttestprep.com

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