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Manager  Joined: 26 Sep 2013
Posts: 190
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 What is the value of a + b?  [#permalink]

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1
3 00:00

Difficulty:   15% (low)

Question Stats: 82% (02:00) correct 18% (02:16) wrong based on 194 sessions

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Attachment: crisscross.jpg [ 34.28 KiB | Viewed 4260 times ]
What is the value of a + b?

A) 30
B) 50
C) 55
D) 65
E) 90

Originally posted by AccipiterQ on 21 Oct 2013, 08:15.
Last edited by Bunuel on 21 Oct 2013, 08:50, edited 1 time in total.
Edited the question.
Manager  Joined: 26 Sep 2013
Posts: 190
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: What is the value of a + b?  [#permalink]

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here's my question:

I solved it by taking 2a+5a+5=180, and solving for a, and then taking 2b-10+4b+10=180, and solving for b. I end up with b=30, and a=25.

But I also thought, since the angles 2a and 2b-10 are opposite, they have to add to 180, yes? so why doesnt 2a+2b-10=180 also yield the correct answer; in this case you would get:

2a+2b-10=180
2a+2b=190
a+b=95
Math Expert V
Joined: 02 Sep 2009
Posts: 55609
Re: What is the value of a + b?  [#permalink]

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2
AccipiterQ wrote: What is the value of a + b?

A) 30
B) 50
C) 55
D) 65
E) 90

here's my question:

I solved it by taking 2a+5a+5=180, and solving for a, and then taking 2b-10+4b+10=180, and solving for b. I end up with b=30, and a=25.

But I also thought, since the angles 2a and 2b-10 are opposite, they have to add to 180, yes? so why doesnt 2a+2b-10=180 also yield the correct answer; in this case you would get:

2a+2b-10=180
2a+2b=190
a+b=95

No. 2a and 2b-10 are opposite angles. Opposite angles are equal.
Attachment: Vertical_Angles.svg.png [ 4.87 KiB | Viewed 3685 times ]

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Re: What is the value of a + b?  [#permalink]

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But if you do it with the equal angles it doesn't give 55. Unless I have a mistake in the calculation that I don't see:

2a=2b-10
a=b-5 

And:

4b+10=5a+5 | substituting 
4b+10=5(b-5)+5
4b+10= 5b-25+5
b=40 

Substituting  into :
a=b-5
a=40-5
a=35

a+b= 35+40=75.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of a + b?  [#permalink]

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Hi pacifist85,

You did make a small math mistake. Double check this line (and watch your "signs")...

4b+10= 5b-25+5

What does b equal?

The rest of your logic and your overall approach are correct though.

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Senior Manager  Status: Math is psycho-logical
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Location: Netherlands
GMAT Date: 02-11-2015
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Re: What is the value of a + b?  [#permalink]

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YUP, I SEE IT NOW THANX!
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Joined: 26 Mar 2013
Posts: 2229
Re: What is the value of a + b?  [#permalink]

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AccipiterQ wrote:
Attachment:
crisscross.jpg
What is the value of a + b?

A) 30
B) 50
C) 55
D) 65
E) 90

Opposite angles are equal

2a = 2b - 10.........1

5a + 5 = 4b + 10...2

solving 2 equations

a =25 & b=30

a +b = 55

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Re: What is the value of a + b?  [#permalink]

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AccipiterQ wrote:
Attachment:
crisscross.jpg
What is the value of a + b?

A) 30
B) 50
C) 55
D) 65
E) 90

Opposite Angles are equal.

$$2a = 2b - 10$$

$$a = b - 5$$

$$b = a + 5$$ -------- (i)

Substituting (i) in (ii) we get;

$$5a + 5 = 4b + 10$$ ---------- (ii)

$$5a + 5 = 4(a + 5) + 10$$

$$5a + 5 = 4a + 20 + 10$$

$$5a - 4a = 30 - 5$$

$$a = 25$$

Substituting value of $$a$$ in (i), we get;

$$b = a + 5$$ -------- (i)

$$b = 25 + 5 = 30$$

Therefore, $$a + b = 30 + 25 = 55$$ Answer (C)...
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Re: What is the value of a + b?  [#permalink]

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AccipiterQ wrote:
Attachment:
crisscross.jpg
What is the value of a + b?

A) 30
B) 50
C) 55
D) 65
E) 90

2a + 5a + 5 = 180 = 4b + 10 + 2b - 10

Or, 7a + 5 = 180 = 6b

Or, a = 25 & b = 30

So, a + b = 55

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Re: What is the value of a + b?  [#permalink]

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_________________ Re: What is the value of a + b?   [#permalink] 26 Nov 2018, 09:13
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