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# What is the value of a + b?

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

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Updated on: 21 Oct 2013, 07:50
2
4
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Difficulty:

15% (low)

Question Stats:

81% (01:55) correct 19% (02:08) wrong based on 185 sessions

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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, 07:15.
Last edited by Bunuel on 21 Oct 2013, 07:50, edited 1 time in total.
Edited the question.
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Posts: 65765
Re: What is the value of a + b?  [#permalink]

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21 Oct 2013, 08:09
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.
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Vertical_Angles.svg.png [ 4.87 KiB | Viewed 4847 times ]

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

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

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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=2b-10
a=b-5 [1]

And:

4b+10=5a+5 | substituting [1]
4b+10=5(b-5)+5
4b+10= 5b-25+5
b=40 [2]

Substituting [2] into [1]:
a=b-5
a=40-5
a=35

a+b= 35+40=75.
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Re: What is the value of a + b?  [#permalink]

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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= 5b-25+5

What does b equal?

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

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

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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?  [#permalink]

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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

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

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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?  [#permalink]

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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

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

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04 Jun 2020, 04:19
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Re: What is the value of a + b?   [#permalink] 04 Jun 2020, 04:19