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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 08 Sep 2021, 05:00
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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.
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A
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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 08 Sep 2021, 12:29
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Bunuel
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.
Show more

Basically, it says that we have a sechigh function that picks the second highest number when the list is ordered.

1)y = second_highest(7, 12, 13, x)
Case1:
x = 13, second highest = 12
Case2:
x = any integer less than or equal to 12, second highest = 12 - Sufficient!
2)y = second_highest(7, 8, 13, z)
Case1:
z = 13, second highest = 8
Case2:
z = 14, second highest = 13 - Insufficient!

IMO, (A)!
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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 25 Sep 2021, 07:17
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Bunuel
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.
Show more

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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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 03 Nov 2021, 07:14
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Bunuel
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.
Show more


This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 05 Nov 2021, 09:38
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Bunuel
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.
Show more

Breaking Down the Info:

When y is the highest value, \(sechigh(6, 7, 11, y) = 11\). When y is the 2nd highest, \(sechigh(6, 7, 11, y) = y\). If y is 7 or lower, \(sechigh(6, 7, 11, y) = 7\). Putting this together, we have the function:

\(sechigh(6, 7, 11, y) = 11 \) if \(y \geq 11\).
\(sechigh(6, 7, 11, y) = y \) if \(y = {10, 9, 8}\).
\(sechigh(6, 7, 11, y) = 7 \) if \(y \leq 7\).


Statement 1 Alone:

The lowest possible value of this function is 12. The highest possible value of this function is 13. So we have \(y \geq 12\). This gives us \(sechigh(6, 7, 11, y) = 11 \), therefore this statement is sufficient.

Statement 2 Alone:

The lowest possible value of this function is 8. The highest possible value of this function is 13 We may have y = 8 or y = 13. That is two different cases, so this statement is insufficient.

Answer: A
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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second hig 03 Nov 2025, 07:05
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