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Bunuel
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Bunuel

In circle P, the two chords intersect at point X, with the lengths as indicated in the figure. Which could not be the sum of lengths a and b, if a and b are integers?

A. 49
B. 30
C. 26
D. 16
E. 14

Attachment:
2016-02-14_1430.png

Hi Bunuel,

Should D be 19?

We know that the triangle is having a defined ratio

6 -> b = 3 or 2 or 1 (divide by 2, 3 and 6 respectively since b must be int)
8 -> a = 16 or 24 or 48 ( times by 2, 3 and 6 following the above)

hence possible values 14, 19, 26 or 49... I don't see how we can get a+b=16 and the other possible answer is 30...
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Answered this by substitution in 20 seconds.

6x8=48
So now get the combinations for 48:

1 and 48; sum is 49
2 and 24; sum is 26
3 and 16; sum is 19
4 and 12; sum is 16
6 and 8 ;sum is 14

The only one missing is 30 > Answer B
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Hi,

use Power of Point Theorem:

a*b=48

-> (a,b) e {(48,1), (29,2), (16,3), (12,4), (8,6), (4,12), (3,16)...}

Taking the sums, we see that (B) is the outlier
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