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If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is

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If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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New post 11 Jun 2015, 03:53
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E

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Question Stats:

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If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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New post 11 Jun 2015, 04:44
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Bunuel wrote:
If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is equivalent to x + y?

A. \(\sqrt{a+b}\)

B. \(2\sqrt{ab}\)

C. \(\frac{a+b}{\sqrt{2}}\)

D. \(2\sqrt{a}-2\sqrt{b}\)

E. \(\frac{\sqrt{a+b}}{2}\)

Kudos for a correct solution.



Given : a = 4x^2 + 4xy and b = 4y^2 + 4xy

Let's add the two a and b because their addition resembles with the property (a+b)^2

i.e. (a+b) = 4x^2 + 4xy + 4y^2 + 4xy

i.e. (a+b) = 4x^2 + 8xy + 4y^2 = 4*(x^2 + 2xy + y^2)

i.e. \((a+b) = 4*(x + y)^2\)

i.e. \(\sqrt{\frac{(a+b)}{4}} = (x+y)\)

i.e. \(\sqrt{(a+b)}/2 = (x+y)\)

Answer: Option
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Re: If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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New post 13 Jun 2015, 16:48
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Hi All,

While this question is certainly complex-looking, it can be be solved by TESTing VALUES and taking advantage of how the answer choices are written (to avoid some of the work).

We're told that...
A = 4(X^2) + 4XY
B = 4(Y^2) + 4XY

We're asked for the value of X+Y.

IF....
X=1
Y=2
A = 4(1^2) + 4(1)(2) = 4+8 = 12
B = 4(2^2) + 4(1)(2) = 16+8 = 24

The value of X+Y = 1+2 = 3, so we're looking for an answer that equals 3 when A=12 and B=24.

Answer A: root(12+24) = root(36) = 6. NOT a match

Answer B: 2[root(12)(24)] = BIGGER than 3. Not a match

Answer C: (12+24)/Root2 = 36/Root2 = BIGGER than 3. Not a match.

Answer D: 2(root12) - 2(root24) = NEGATIVE. Not a match.

Answer E: root(12+24)/2 = 6/2 = 3. This IS a MATCH.

Final Answer:

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Re: If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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New post 14 Jun 2015, 05:29
1
Bunuel wrote:
If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is equivalent to x + y?

A. \(\sqrt{a+b}\)

B. \(2\sqrt{ab}\)

C. \(\frac{a+b}{\sqrt{2}}\)

D. \(2\sqrt{a}-2\sqrt{b}\)

E. \(\frac{\sqrt{a+b}}{2}\)

Kudos for a correct solution.


a+b=4x^2 + 4xy+4y^2 + 4xy=4(x^2+y^2+2xy)
a+b=4(x+y)^2
a+b/4=(x+y)^2
Taking square root on both sides
\sqrt{a+b}/2=x+y
Answer E
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If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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New post 15 Jun 2015, 04:33
1
Bunuel wrote:
If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is equivalent to x + y?

A. \(\sqrt{a+b}\)

B. \(2\sqrt{ab}\)

C. \(\frac{a+b}{\sqrt{2}}\)

D. \(2\sqrt{a}-2\sqrt{b}\)

E. \(\frac{\sqrt{a+b}}{2}\)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

If we add a and b, we get a + b = 4x^2 + 8xy + 4y^2 = 4(x^2 + 2xy + y^2).

The right side is of the “square of a sum,” so we can factor and solve:
a + b = 4(x + y)^2.
\(\frac{\sqrt{a+b}}{2}=x+y\)

Note that we could safely take the square root of both sides, since we know any square is nonnegative.

The correct answer is E.
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Re: If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is  [#permalink]

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Re: If a = 4x^2 + 4xy and b = 4y^2 + 4xy, which of the following is   [#permalink] 29 Mar 2018, 23:55
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