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In the figure above, m + n = 110. What is the value of o + p ?

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In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 04 Dec 2014, 07:50
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A
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C
D
E

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Tough and Tricky questions: Geometry.



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In the figure above, m + n = 110. What is the value of o + p ?

A) 70
B) 110
C) 250
D) 270
E) 330

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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 04 Dec 2014, 10:41
As m and n add upto 110 degrees, the third angle in the triangle must be 70 degrees.

We can see the the angle just above this is a vertical angle, so it must also be 70 degrees. So now we know the two angles next to angles O and P (let's call them O' and P') add upto 110 degrees. Also note that all angles making up a straight line must add upto 180 degrees. So, O + O' and P + P' must each add upto 180 degrees--all four add upto 360 degrees. Know this and know that O' + P' add upto 110 yields O + P = 250 degrees.

Choice C
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 04 Dec 2014, 10:54
1
1
let r be the point of intersection of two lines.
since, m+n= 110
therefore r= 180-110
r=70
Therefore degree of opposite angle= 70
In triangle ORP,
angle POR = 180-o
angle OPR = 180-p
angle ORP = 70

180-o+180-p+70=180
-o-p=-250
o+p=250

Ans = C

PS :- I have used O and P as vertices of triangle just for the sake of explanation.
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 04 Dec 2014, 11:25
1
In the figure below, a=b
a=180-(m+n) = 180-110 = 70
therefore b= 70
O = b+ 180-P

O+P= b+180 = 70+180 = 250

answer: C
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 05 Dec 2014, 00:39
1
Answer = C) 250

As vertically opposite angles are same,\(\angle{ACB} = 70^{\circ}\)

Attachment:
2014-12-04_1849.png
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Sum of remaining angles would also be the same

180-o + 180-p = 110

o+p = 360-110 = 250
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 05 Dec 2014, 07:27
Bunuel wrote:

Tough and Tricky questions: Geometry.



Attachment:
2014-12-04_1849.png
In the figure above, m + n = 110. What is the value of o + p ?

A) 70
B) 110
C) 250
D) 270
E) 330

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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New post 18 Apr 2016, 11:53
Well, since the opposites of O and P add up to 110, and these four angles together must measure up to 180+180=360, you just substract 110 from 360 to get 250.

Ans c
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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Re: In the figure above, m + n = 110. What is the value of o + p ? &nbs [#permalink] 30 Sep 2017, 07:57
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