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# If x + 2y = a and x – 2y = b, which of the following express

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Founder
Joined: 18 Apr 2015
Posts: 12642
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If x + 2y = a and x – 2y = b, which of the following express [#permalink]  24 Jan 2019, 06:52
Expert's post
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Question Stats:

75% (02:05) correct 25% (01:32) wrong based on 32 sessions
If $$x + 2y = a$$ and $$x – 2y = b$$, which of the following expressions is equal to $$xy$$?

A. $$ab$$

B. $$\frac{a+b}{2}$$

C. $$\frac{a-b}{2}$$

D. $$\frac{a^2-b^2}{4}$$

E. $$\frac{a^2-b^2}{8}$$
[Reveal] Spoiler: OA

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Intern
Joined: 24 Jan 2019
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: If x + 2y = a and x – 2y = b, which of the following express [#permalink]  24 Jan 2019, 07:47
1
KUDOS
elimination is the best way to solve it,
options (b) and (c) is eliminated as they have solution only in terms of x, not xy which the question is about. Thus they are eliminated
for last 2 option, evaluate a^2-b^2 which is 8xy. Therefore, option d is the correct answer
Founder
Joined: 18 Apr 2015
Posts: 12642
Followers: 269

Kudos [?]: 3178 [0], given: 11677

Re: If x + 2y = a and x – 2y = b, which of the following express [#permalink]  26 Jul 2020, 11:05
Expert's post
$$x=a-2y$$ and $$x=b+2y$$

$$a-2y=b+2y$$

$$a-b=4y$$

$$y=\frac{a-b}{4}$$

$$2y=a-x$$

$$2y=x-b$$

$$a-x=x-b$$

$$x=\frac{a+b}{2}$$

$$x \times y$$

$$\frac{a-b}{4} \times \frac{a+b}{2}$$

$$\frac{(a-b)^2}{8}$$

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Re: If x + 2y = a and x – 2y = b, which of the following express   [#permalink] 26 Jul 2020, 11:05
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