Bunuel wrote:

The average of two numbers is X*Y. If the first number is Y, what is the other number?

(A) 2XY-Y

(B) XY-2Y

(C) 2XY-X

(D) Z

(E) XY-Y

AlgebraLet the second number = Q

The average of two numbers is X*Y. The first number is Y.

\(\frac{Q+Y}{2} = XY\)

\(Q+Y = 2XY\) (Subtract Y)

\(Q = 2XY - Y\)Answer A

Assign valuesFor this question, assigning values may not feel intuitive. Answer D, "Z," is a trap.

If we set up the equation with Z as "the other number," by definition, Z is the answer. That's circular reasoning. There is no "content" to the answer. What is Z's value? We have no idea.

All we need is the RHS of the equation once "other number" is isolated.

Let X = 1

Let Y = 2

Let other number = ?

\(\frac{(? + Y)}{2} = (X*Y)\)

\(\frac{(? + 2)}{2} = (1*2)\)

\(? + 2 = 2(2)\)

\(? = 4 - 2\)

\(? = 2\)The other number (?) is 2

With X=1 and Y=2, find the answer choice that yields 2

(A) 2XY-Y:

\((2(1*2) - 2) = (4 - 2) = 2.\) MATCH

(B) XY-2Y:

\((1*2) - (2*2) = (2 - 4) = -2.\) NO

(C) 2XY-X:

\((2*(1*2)) - 1) = (4 - 1) = 3.\) NO

(D) Z: we have no idea what Z equals. NO

(E) XY-Y:

\(((1*2) - 2) = (2 - 2) = 0.\) NO

Answer A

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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"