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# What is the value of (a*5^(1/2) + b*5^(1/2))^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
What is the value of (a*5^(1/2) + b*5^(1/2))^2?  [#permalink]

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02 Apr 2018, 22:01
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Difficulty:

35% (medium)

Question Stats:

75% (01:43) correct 25% (01:58) wrong based on 41 sessions

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What is the value of $$(a\sqrt{5} + b\sqrt{5})^2$$?

(1) a - b = 5
(2) a(a + b) = 81 - b(b + a)

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Intern
Joined: 28 Apr 2014
Posts: 49
GMAT 1: 640 Q50 V25
Re: What is the value of (a*5^(1/2) + b*5^(1/2))^2?  [#permalink]

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02 Apr 2018, 22:26
IMO B
5(a-b)^2=?

St1
a-b=5
doesn't help

St2
(a+b)^2=81
Hence sufficient
examPAL Representative
Joined: 07 Dec 2017
Posts: 1140
Re: What is the value of (a*5^(1/2) + b*5^(1/2))^2?  [#permalink]

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02 Apr 2018, 23:18
Bunuel wrote:
What is the value of $$(a\sqrt{5} + b\sqrt{5})^2$$?

(1) a - b = 5
(2) a(a + b) = 81 - b(b + a)

As all we're given is equations, we'll look for a simplification-based approach.
This is a Precise methodology.

We'll simplify the data in our question stem:
$$(a\sqrt{5} + b\sqrt{5})^2=(\sqrt{5}(a+b))^2=5(a+b)^2$$

(1) This lets us substitute b instead of a into the equation which is not enough to calculate its value.
Insufficient.

(2) Moving -b(b+a) to the LHS and extracting (a+b) as common factor gives (a+b)(a+b)=81 so (a+b)^2 = 81
Then our answer is 5*81.
Sufficient.

(B) is our answer.
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Re: What is the value of (a*5^(1/2) + b*5^(1/2))^2?  [#permalink]

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03 Apr 2018, 01:36

Solution

Given:
• We are given an expression $$(a \sqrt{5}+b \sqrt{5}) ^2$$

To find:

• We need to find the value of the expression $$(a \sqrt{5}+b \sqrt{5}) ^2$$.
o $$(a \sqrt{5}+b \sqrt{5}) ^2$$ = $$[ \sqrt{5}(a + b)] ^2$$
o = $$5(a + b) ^2$$

Thus, we only need to find the value of (a + b) to find the value of the expression $$(a \sqrt{5}+b \sqrt{5}) ^2$$.

Statement-1: a - b =5

The value of a-b can be 5 for various values of a and b. And, different values of a and b will result in a different value of a + b.

Let us see some examples:
• For, a=6 and b=1, a-b=5 and a + b = 7
• For, a=7 and b=2, a-b=5 and a + b = 9

Thus, Statement 1 alone is not sufficient to answer the question.

Statement-2:a (a + b) = 81- b (a + b)

Let us simplify the expression “a (a + b) = 81- b (a + b)”.
• $$a^2+ ab = 81- b^2-ab$$
• $$a^2+b^2+2ab= 81$$
• $$(a + b) ^2 = 9^2$$
• $$a + b= 9$$

We can find the value of (a + b) from statement 2. Hence, we can also find the value of $$(a \sqrt{5}+b \sqrt{5}) ^2$$.

Thus, Statement 2 alone is sufficient to answer the question.

Hence, the correct answer is option B.

_________________
Re: What is the value of (a*5^(1/2) + b*5^(1/2))^2?   [#permalink] 03 Apr 2018, 01:36
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# What is the value of (a*5^(1/2) + b*5^(1/2))^2?

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