In the figure shown, the measure of angle PRS is how many de

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Zach.J.Dragone: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Wed Nov 20, 2013 5:35 pm; Thanked: 1 times

by Zach.J.Dragone » Wed Dec 04, 2013 2:40 pm

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

(1) The measure of angle QPR is 30Â°.
(2) The sum of the measures of angles PQR and PRQ is 150Â°.

D

Maybe this is a stupid question, but I am trying to figure out how I know to set these problems up. To figure out the unknown angles and to figure out what to subtract from what to get the correct answer. Any similar practice problems would help as well.

Thanks!!!

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Source: Beat The GMAT — Problem Solving | Wed Dec 04, 2013 2:40 pm

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by [email protected] » Wed Dec 04, 2013 3:16 pm

Hi Zach,

In these types of "overlapping shape" questions, it's important to note every deduction that you can before you add in the information form the two Facts.

In this question, since we're dealing with overlapping triangles, there are a bunch of formulas worth noting (3 involving the triangles, 1 involving a straight line.

By noting these equations first, you'll notice that there are 5 variables and 4 equations. IF we are given one more UNIQUE equation, then we'll have a "system" of equations and we'll be able to stop working.

Fact 1 tells us that C = 30, which is a 5th equation

Now we have a "system", we CAN figure out the value of all of the angles and we CAN answer the question.
Fact 1 is SUFFICIENT

Fact 2 tells us that A + B = 150, which is a 5th equation (you can also use it to figure out that C = 30)

Again, we have a "system", so we can figure out everything, just as in Fact 1.
Fact 2 is SUFFICIENT

Final Answer: D

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Rich

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Wed Dec 04, 2013 8:34 pm

Hi Zach,
To Find: Angle(PRS) - Angle(PQR) = ?
Let Angle(PRS) = Y and Angle(PQR) = X

Statement 1: Angle(QPR) = 30
Consider Triangle PQR,

Angle(QPR) + Angle(PRQ) + Angle(RQP) = 180
30 + (180-y) + x = 180 =>> Y-X = 30
Hence Sufficient.

Statement 2: Angle(PQR) + Angle(PRQ) = 150
X + (180-Y) =150 =>> Y-X = 30
Hence Sufficient.

Answer is D

Regards,
Uva.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Dec 04, 2013 9:07 pm

In this figure, we know that Angle PRS = Angle QPR + Angle PQR

to find : (Angle PRS - Angle PQR)

Rephrase = what is angle QPR

Statement 1:
QPR = 30
SUFFICIENT

Statement 2:
PQR + PRQ = 150
Since PQR is a triangle..
QPR + PQR + PRQ = 180
QPR = 30
SUFFICIENT

Answer [spoiler]{D}[/spoiler]

R A H U L

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Thu Dec 05, 2013 2:49 am

Looking at Statement 1 alone:
For every degree that line PR rotates clockwise from line PQ, angle PRS increases 1 degree.
So if QPR is 30Â°, then PRS has increased 30Â°.
SUFFICIENT.

Looking at Statement 2 alone:
[PRS + PRQ] + PQR = [180] + PQR
PRS + (PRQ + PQR) = 180 + PQR
PRS + (150) = 180 + PQR
Difference PRS - PQR = 180 - 150 = 30
SUFFICIENT

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Dec 05, 2013 4:21 am

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The sum of the measures of angles PQR and PRQ is 150 degrees.

To evaluate the statements, test TWO cases.
Be sure to satisfy any constraints in the problem and the rules of geometry:
Angles inside a triangle must add up to 180.
Angles that form a straight line must add up to 180.
And so on.

If the value of PRS-PQR is the SAME in each case, the statement is SUFFICIENT.
If the value of PRS-PQR CHANGES, the statement is INSUFFICIENT.

Statement 1: QPR = 30 degrees

In each case, QPR=30.
In each case, PRS-PQR = 30.
Since the value of PRS-PQR is the same in each case, SUFFICIENT.

Statement 2: PQR + PRQ = 150 degrees
The two cases used to satisfy statement 1 also satisfy statement 2.
In each case, PRS-PQR = 30.
Since the value of PRS-PQR is the same in each case, SUFFICIENT.

The correct answer is D.

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mcdesty: Master | Next Rank: 500 Posts; Posts: 116; Joined: Wed Mar 14, 2012 1:02 pmFollowed by: 11 members; Thanked: 20 times; GMAT Score:760

by mcdesty » Tue Jul 08, 2014 5:38 pm

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Re: In the figure shown, the measure of angle PRS is how many de

by Scott@TargetTestPrep » Sat Jul 11, 2020 12:53 pm

Zach.J.Dragone wrote: ↑
Wed Dec 04, 2013 2:40 pm
In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

(1) The measure of angle QPR is 30Â°.
(2) The sum of the measures of angles PQR and PRQ is 150Â°.

D

Solution:

We need to determine by how many degrees the measure of angle PRS exceeds the measure of angle PQR.

Statement One Only:

The measure of angle QPR is 30°.

Let the measure of RPS be x. Then, the two interior angles of the triangle PQS are 90 and 30 + x. Thus, the third interior angle of the same triangle is 180 - (90 + 30 + x) = 180 - 120 - x = 60 - x. So, in terms of x, the angle PQS measures 60 - x.

Now, look at the triangle PRS. Two of the interior angles of this triangle are 90 and x; thus, the third interior angle (which is angle PRS) is 180 - (90 + x) = 90 - x.

Using the two expressions, we can determine that the angle PRS exceeds the angle PQS by 90 - x - (60 - x) = 90 - x - 60 + x = 30 degrees.

Statement one is sufficient to answer the question.

Statement Two Only:

The sum of the measures of angles PQR and PRQ is 150°.

This means angle QPR is 180 - 150 = 30°. Using the same procedure that we used in statement one, we can determine the difference between the measures of angles PRS and PQR using QPR = 30.

Statement two is sufficient to answer the question.

Answer: D

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Founder and CEO
[email protected]

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