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AccipiterQ
Joined: 26 Sep 2013
Last visit: 03 Sep 2020
Posts: 144
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
GMAT 2: 730 Q49 V41
Posts: 144
Updated on: 21 Oct 2013, 07:50
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.
Last edited by Bunuel on 21 Oct 2013, 07:50, edited 1 time in total.
Edited the question.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:54) correct
19%
(02:08)
wrong
based on 322
sessions
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Attachment:
crisscross.jpg [ 34.28 KiB | Viewed 13290 times ]
A) 30
B) 50
C) 55
D) 65
E) 90
AccipiterQ
Joined: 26 Sep 2013
Last visit: 03 Sep 2020
Posts: 144
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
GMAT 2: 730 Q49 V41
Posts: 144
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
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
AccipiterQ
No. 2a and 2b-10 are opposite angles. Opposite angles are equal.
Attachment:
Vertical_Angles.svg.png [ 4.87 KiB | Viewed 11796 times ]
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pacifist85
Joined: 07 Apr 2014
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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 [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.
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.
EMPOWERgmatRichC
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Expert reply
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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
pacifist85
Joined: 07 Apr 2014
Last visit: 20 Sep 2015
Posts: 321
Status:Math is psycho-logical
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Posts: 321
YUP, I SEE IT NOW THANX!
Mo2men
Joined: 26 Mar 2013
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AccipiterQ
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
sashiim20
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Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
AccipiterQ
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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AccipiterQ
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)
_________________
Posts: 137
pretty straightforward. Use vertically opposite angle property and then its just algebra
b = 30 ; a = 30-5 = 25
a + b = 55
C
b = 30 ; a = 30-5 = 25
a + b = 55
C
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