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What is the value of a + b?
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Updated on: 21 Oct 2013, 07:50
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What is the value of a + b? A) 30 B) 50 C) 55 D) 65 E) 90
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Originally posted by AccipiterQ on 21 Oct 2013, 07:15.
Last edited by Bunuel on 21 Oct 2013, 07:50, edited 1 time in total.
Edited the question.



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Re: What is the value of a + b?
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21 Oct 2013, 08:09
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 2b10+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 2b10 are opposite, they have to add to 180, yes? so why doesnt 2a+2b10=180 also yield the correct answer; in this case you would get: 2a+2b10=180 2a+2b=190 a+b=95 No. 2a and 2b10 are opposite angles. Opposite angles are equal. Attachment:
Vertical_Angles.svg.png [ 4.87 KiB  Viewed 4847 times ]
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Re: What is the value of a + b?
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21 Oct 2013, 07:35
here's my question:
I solved it by taking 2a+5a+5=180, and solving for a, and then taking 2b10+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 2b10 are opposite, they have to add to 180, yes? so why doesnt 2a+2b10=180 also yield the correct answer; in this case you would get:
2a+2b10=180 2a+2b=190 a+b=95



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Re: What is the value of a + b?
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14 Jan 2015, 15:00
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=2b10 a=b5 [1]
And:
4b+10=5a+5  substituting [1] 4b+10=5(b5)+5 4b+10= 5b25+5 b=40 [2]
Substituting [2] into [1]: a=b5 a=405 a=35
a+b= 35+40=75.



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Re: What is the value of a + b?
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14 Jan 2015, 16:06
Hi pacifist85, You did make a small math mistake. Double check this line (and watch your "signs")... 4b+10= 5b25+5 What does b equal? The rest of your logic and your overall approach are correct though. GMAT assassins aren't born, they're made, Rich
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Re: What is the value of a + b?
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14 Jan 2015, 16:54
YUP, I SEE IT NOW THANX!



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Re: What is the value of a + b?
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17 Jun 2017, 17:15
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 Answer: C



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Re: What is the value of a + b?
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17 Jun 2017, 17:33
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?
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18 Jun 2017, 07:51
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 Answer will be (C)
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Re: What is the value of a + b?
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04 Jun 2020, 04:19
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