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The length of arc AXB is twice

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 Post subject: The length of arc AXB is twice
 Post Posted: Wed Oct 05, 2011 7:23 am 
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Students


Posts: 23
Location: Bangalore
The length of arc AXB is twice the length of arc BZC, and the length of arc AYC is three times the length of arc AXB. What is the measure of angle BCA?
    1) 20
    2) 40
    3) 60
    4) 80
    5) 120

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Source: Manhattan CAT II

According to the question,
Length of arc AXB is twice the length of arc BZC => arc AXB = 2 times arc BZC ----> (1)
Length of arc AYC is three times the length of arc AXB => arc AYC = 3 times AXB ---->(2)

From (1), it could be said that 3 * arc AXB = 6 * arc BZC ---->(3)

From (2) & (3), arc AYC : arc AXB : arc BZC = 1 : 3 : 6

Manhattan Explanation Given:
According to the question, the ratio of the lengths of arc AYC to arc AXB to arc BZC is 6: 2: 1.

Could you please tell me what I'm doing wrong over here.
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tim
 Post subject: Re: The length of arc AXB is twice
 Post Posted: Thu Nov 17, 2011 12:24 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
According to your calculations, AYC is the smallest arc and BZC is the largest. This goes against the information in the problem. Check your work and let us know if you need any further help..

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Tim Sanders
Manhattan GMAT Instructor
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nick21
 Post subject: Re: The length of arc AXB is twice
 Post Posted: Thu Nov 24, 2011 9:40 pm 
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Students


Posts: 1
Hi all
I'm ending up with BZC=40=====> <Z=20
since AXB = 2BZC ===> AXB=80
AYC=6BZC=====> AYC=240
if BCA=BZC+AYC====>BCA=280 ===>> c=140 which is far above any answer choice
where am I wrong please???
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tim
 Post subject: Re: The length of arc AXB is twice
 Post Posted: Tue Dec 13, 2011 2:46 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
Nick, i hate to do this, but there are in fact SO many errors in your calculations that i’m going to ask you to take a look at this one again before we help you. The main reason i say this is because most of your mistakes appear to involve a lack of attention to detail – writing incorrect letters that then propogate through your work and make the answers wrong. Please try again and we’ll be glad to help you..

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Tim Sanders
Manhattan GMAT Instructor
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