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CONQUERING GMAT MATH AND INTEGRATED REASONING

By spartan

 


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 A D C B P X Solution When two chords intersect within a circle, the product of the segments on one chord is equal to the product of the segments on the other chord. Since the segments of the first chord are 6 and 8, the product of the lengths is 48. Thus, the product of the lengths a and b must be 48, and possible lengths are 48 and 1, 24 and 2, 12 and 4, and 8 and 6. So 49, 26, 16, and 14 are possible values for a + b. The correct answer is B, since 30 is not the sum of two integer factors of 48.


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