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# The average of two numbers is XY. If the first number is Y, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
The average of two numbers is XY. If the first number is Y, what is  [#permalink]

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01 Mar 2018, 00:35
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Difficulty:

25% (medium)

Question Stats:

83% (01:10) correct 17% (01:19) wrong based on 56 sessions

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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

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Joined: 12 Nov 2017
Posts: 15
Re: The average of two numbers is XY. If the first number is Y, what is  [#permalink]

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01 Mar 2018, 00:41
(X+Y)/2 =X*Y =>X = 2XY-Y

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The average of two numbers is XY. If the first number is Y, what is  [#permalink]

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01 Mar 2018, 12:11
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

Algebra
Let 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)
$$Q = 2XY - Y$$

Assign values
For 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

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Joined: 23 Sep 2016
Posts: 220
Re: The average of two numbers is XY. If the first number is Y, what is  [#permalink]

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03 Mar 2018, 02:31
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

lets total be T
so average be T/2=xy
t=2xy
if 1st number is Y then second number is 2xy-y
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Joined: 08 Jul 2010
Posts: 2564
Location: India
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Re: The average of two numbers is XY. If the first number is Y, what is  [#permalink]

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03 Mar 2018, 02:42
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

(a+Y)/2 = X*Y

i.e. a+Y = 2X*Y

i.e. a = 2X*Y - Y

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Re: The average of two numbers is XY. If the first number is Y, what is &nbs [#permalink] 03 Mar 2018, 02:42
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