OG Verbal review 135

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massi2884: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Sep 13, 2011 3:19 pm; Thanked: 3 times; GMAT Score:710

by massi2884 » Tue Apr 17, 2012 10:53 am

In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

144
216
324
360
396

OA is B Please explain

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Source: Beat The GMAT — Problem Solving | Tue Apr 17, 2012 10:53 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Tue Apr 17, 2012 10:59 am

Area of MPRS = Area of MPQT + Area of TQRS

540 = a*a + 12*a

(where 'a' is the side of the square MPQT or the breadth of rectangle MPRS)

a^2 + 12*a - 540 = 0

(a + 30)*(a - 18) = 0

a = 18 is the only positive root and hence the only possible value.

Area of TQRS = 18*12 = 216 sq. units

(B) is the answer

Aneesh Bangia
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massi2884: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Sep 13, 2011 3:19 pm; Thanked: 3 times; GMAT Score:710

by massi2884 » Tue Apr 17, 2012 11:05 am

Thanks Aneesh, however how can you quickly go from a^2 + 12*a - 540 = 0 to (a + 30)*(a - 18) = 0 ? I spent a lot of time on this point.

Thanks.

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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Tue Apr 17, 2012 11:14 am

Well, that largely comes from practice. So, I'd suggest you to solve a lot of quadratic equations.

Anyway, for this problem, let me try to explain my thought-process.

a^2 + 12*a - 540 = 0

I knew that I had to split 12*a into two parts such that they multiply to -540*a^2. Since -540*a^2 is a negative number, one of the two parts should be positive and one should be negative. Then I went on looking for two numbers that multiply to 540 and whose difference is 12.

I tried out these pairs which multiply to 540:

20 and 17, doesn't work because the difference is 3.
30 and 18, Voila! It works! So, the two parts must be 30*a - 12*a.

It might look like a long procedure, but when you've practiced hundreds of quadratic expressions, it is a 5-second thing. So, Practice!

Aneesh Bangia
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massi2884: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Sep 13, 2011 3:19 pm; Thanked: 3 times; GMAT Score:710

by massi2884 » Wed Apr 18, 2012 12:17 am

Thanks Aneesh, However, I don't get when you take 20 and 17: in fact, they multiply to 340 instead of 540. Can you please clarify your steps? Thanks.

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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Wed Apr 18, 2012 1:34 am

Correction:
I meant 20 and 27

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jan 11, 2018 1:54 pm

massi2884 wrote:In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

144
216
324
360
396

Since PQMT is a square, we can let PQ = PM = n. Since QR = 12, PR = n + 12. Finally, since the area of rectangle MPRS is 540, we have:

n(n + 12) = 540

n^2 + 12n = 540

n^2 + 12n - 540 = 0

(n + 30)(n - 18) = 0

n = -30 or n = 18

Since n can't be negative, n = 18, and the area of square MPQT is 18 x 18 = 324. Thus, the area of rectangle TQRS is 540 - 324 = 216,

Answer: B

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