If a+b=âˆ’8, and a=20/b, what is the value of a^2+b^2?

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Mon Nov 20, 2017 7:25 am

If $$a+b=âˆ’8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

The OA is A.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Mon Nov 20, 2017 7:25 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Nov 20, 2017 9:16 am

AAPL wrote:If $$a+b=âˆ’8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

The OA is A.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Given: a+b=âˆ’8 and a=20/b

Take a=20/b and multiply both sides by b to get: ab = 20

Take a + b = âˆ’8 and SQUARE both sides to get (a+b)Â² = (âˆ’8)Â²
Expand and simplify left side to get: aÂ² + 2ab + bÂ² = 64
Now replace ab with 20 to get: aÂ² + 2(20)+ bÂ² = 64
Simplify: aÂ² + 40 + bÂ² = 64
Subtract 40 from both sides to get: aÂ² + bÂ² = 24

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Mon Nov 20, 2017 11:05 am

If $$a+b=-8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

The OA is A.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Hi AAPL,
Let's take a look at your question.

$$a+b=-8$$
$$a=\frac{20}{b}$$
$$a^2+b^2=?$$

Starting from,
$$a+b=-8$$
Squaring both sides,
$$\left(a+b\right)^2=\left(-8\right)^2$$
Evaluating,
$$a^2+b^2+2ab=64...(i)$$

We know that,
$$a=\frac{20}{b}$$
Plugging value of a in (i),
$$a^2+b^2+2\left(\frac{20}{b}\right)b=64$$
$$a^2+b^2+2\left(20\right)=64$$
$$a^2+b^2+40=64$$
$$a^2+b^2=64-40$$
$$a^2+b^2=24$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Nov 22, 2017 12:18 pm

AAPL wrote:If $$a+b=âˆ’8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

We can square the first equation and we have:

a^2 + b^2 + 2ab = 64

Simplifying the second equation, we have:

ab = 20

Thus:

a^2 + b^2 + 40 = 64

a^2 + b^2 = 24

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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