Bunuel wrote:
For any integers a, b, c, and d, sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered list. For example sechigh(2, 5, 4, 6) = 5 and sechigh(6, 5, 3, 6) = 6 . For the integer y, what is the value of sechigh(6, 7, 11, y)?
(1) y = sechigh (7, 13, 12, x) for some integer x.
(2) y = sechigh (7, 13, 8, z) for some integer z.
The understanding of the
sechigh() function is crucial before jumping on the statements. This function returns the 3rd integer from the left or the second highest integer when the integers are sorted in ascending order with the smallest integer positioned at the extreme left.
S1: y = sechigh (7, 13, 12, x) for some integer x [Sufficient]1. Arranging the terms in ascending order yields 7, 12, 13, x
2. If \(x >= 13\) then the output of the function will be 13 E.g.
sechigh(7, 12, 13, 14) \(= 13\) or E.g.
sechigh(7, 12, 13, 13) \(= 13\)
3. If \(x < 13\) then the output will be \(12\) E.g.
sechigh(7, 12, 12, 13) \(= 12\) or E.g.
sechigh(7, 11, 12, 14) \(= 12\)
4. So, we get only two values of \(y\) i.e. \(12\) and \(13\) from this statement
5. Plugging them into
sechigh(6, 7, 11, y) we get
sechigh(6, 7, 11, 12) \(= 11\) or
sechigh(6, 7, 11, 13) \(= 11\)
6. We get a single definitive answer \(11\)
S2: y = sechigh (7, 13, 8, z) for some integer z [Insufficient]1. Arranging the terms in ascending order yields 7, 8, 13, z
2. If \(x >= 13\) then the output of the function will be \(13\) E.g.
sechigh(7, 8, 13, 14) \(= 13\) or E.g.
sechigh(7, 12, 13, 13) \(= 13\)
3. If \(x < 13\) then the output can range from \(8\) to \(12\) E.g.
sechigh(7, 8, 8, 13) \(= 8\) or E.g.
sechigh(7, 8, 12, 13) \(= 12\)
4. So, we get only \(y\) values ranging from \(8\) to \(13\) from this statement
5. Plugging them into sechigh(6, 7, 11, y) we get
sechigh(6, 7, 8, 11) \(= 8\) or
sechigh(6, 7, 11, 13) \(= 11\)
6. We do not get a single definitive answer
Ans. A
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