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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second...

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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second...  [#permalink]

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New post 19 Aug 2018, 10:09
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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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For any integers a, b, c, and d, sechigh(a, b, c, d) is the second...  [#permalink]

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New post 19 Aug 2018, 11:38
CAMANISHPARMAR 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.



(1) y = sechigh (7, 13, 12, x) for some integer x.

case 1
x>13
y =13

case 2
x< 12
y=12

in any case sechigh(given set) = 11

sufficient.

(2) y = sechigh (7, 13, 8, z) for some integer z

case 1
z > 13
y = 13

case 2
8< z< 13
y=z

case 3
x < 8
y = 8

insufficient

A
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Re: For any integers a, b, c, and d, sechigh(a, b, c, d) is the second...  [#permalink]

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New post 19 Aug 2018, 16:58
Official Answer:

This problem contains a Formula. Since formulas are rules that apply only in the specific problem, take your time to understand what the formula means: sechigh is equal to the second highest integer in the group. The question asks what the value of sechigh is for a specific group of integers containing one variable. Consider the possible scenarios depending on the value of y because y is the only unknown value in the set.

1) If y ≤ 7 then the sechigh(y, 6, 7, 11) = 7

2) If 7 < y < 11 then sechigh(6, 7, y, 11) = y

3) If y ≥ 11 then sechigh(6, 7, 11, y) = 11


What do these scenarios mean about the information needed to answer the question? If Scenario (1) or (3) applies, you don’t need the exact value of y to answer the question; you just need to know enough to know that scenario applies. If Scenario (2) applies, you need to know the value of y to answer the question.

y ≤ 7 ?

y ≥ 11 ?

if not, y = ?



(1) SUFFICIENT: Think about the different possible values for sechigh (7, 13, 12, x) depending on the value of x.

If x ≤ 12 then sechigh (7, x, 12, 13) = 12.

If x > 12 then sechigh (7, 12, 13, x) = 13.

Since sechigh (7, 13, 12, x) = y it must be true that y = 12 or y = 13. In either of these cases, Scenario (3) applies because y is greater than 11; the answer to the question is 11. Since there is only one value possible, this statement is SUFFICIENT. Eliminate choices (B), (C), and (E).



(2) INSUFFICIENT: Think about the different possible values for sechigh (7, 13, 8, z) depending on the value of z.

If z ≤ 8 then sechigh (7, z, 8, 13) = 8.

If 8 < z < 13 sechigh (7, 8, z, 13) = z.

If z ≥ 13 then sechigh (7, 8, 13, z) = 13.

Since the result of this formula is equal to y that means y could be any integer between 8 and 13 inclusive: 8 ≤ y ≤ 13. These value mean that Scenario (2) or (3) from the question might apply. So the answer to the question could be 11 or y if y < 11. Since more than one value is possible, this statement is INSUFFICIENT. Eliminate choice (D).


The correct answer is (A).
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Re: For any integers a, b, c, and d, sechigh(a, b, c, d) is the second...   [#permalink] 19 Aug 2018, 16:58
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