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filipembribeiro
Joined: 20 Jul 2020
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Schools: Stanford '26 Kellogg '26 INSEAD Jan '26 IESE '26 HBS '26
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25 Jul 2021, 11:19
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:22) correct
53%
(02:07)
wrong
based on 118
sessions
History
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For a finite sequence of nonzero integers, the percentage of variations in parity is defined as the percentage of pairs of consecutive terms of the sequence for which the sum of the two consecutive terms is odd. What is the percentage of variations in parity for an arithmetic sequence of t terms where each term \(t_{n} = t_{n-1} + c\)?
(1) The total number of terms in the sequence is 50.
(2) c is even.
(1) The total number of terms in the sequence is 50.
(2) c is even.
27 Jul 2021, 20:13
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filipembribeiro
We are looking at an AP, where the common difference is c.
Two cases
a) All terms are similar in property, that is all are even or all are odd.
1,3,5,7…. Here c=2
10,20,30,…here c=10
In all the cases as above, the sum of pair of consecutive numbers will always be EVEN.
b) c is odd, that is property changes with alternate term.
5,10,15….c=5
1,2,3,4,5…c=1
Here the sum of pairs of consecutive numbers will always be odd.
We could also just work on the expression given.
\(t_{n} = t_{n-1} + c\)
Sum of pair of consecutive numbers =
\(t_{n}+t_{n-1} = t_{n-1} + c+t_{n-1}=2*t_{n-1}+c\)
Thus the sum depends on c.
If c is odd, the sum is odd, and answer is 0%.
If c is even, the sum is even, and the answer is 100%.
(1) The total number of terms in the sequence is 50.
We cannot get the value of c from it.
(2) c is even.
Answer is 100%.
Sufficient
B
