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13 Dec 2022, 23:48
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (02:12) correct
50%
(01:55)
wrong
based on 94
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An increasing sequence of P consists of 5 consecutive positive multiples of a positive integer. What is the remainder when the largest term of the sequence is divided by 2 ?
S1. The median of the sequence is even.
S2. The second term of the sequence is odd.
S1. The median of the sequence is even.
S2. The second term of the sequence is odd.
14 Dec 2022, 00:00
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PriyamRathor
Assume divisor = d ; d > 0
Quotient = q ; q > 2
The Sequence is
\(d(q-2) \quad d(q-1) \quad dq \quad d(q+1) \quad d(q+2)\)
Question: What is the remainder when the largest term of the sequence is divided by 2
Inference - The remainder can be either 0 or 1. We want to find whether the largest term is even.
Statement 1
The median of the sequence is even.
Median of the sequence is dq
Case 1: d is even
If d is even, the largest term is also even.
Remainder when d(q+2) is divided by 2 = 0
Case 2: d is odd & q is even
If q is even, q+2 is even. Hence the largest term, d(q+2), is even.
Remainder when d(q+2) is divided by 2 = 0
This statement is sufficient. We can eliminate B, C and E.
Statement 2
The second term of the sequence is odd.
The second term in the sequence is d(q-1) and its given that this term is odd.
Therefore, d = odd & (q-1) = odd
(q-1) = odd
q = odd + 1 = even ; q = even
q + 2 = even + 2 = even
Hence the largest term, d(q+2), is even.
Remainder when d(q+2) is divided by 2 = 0
The statement is also sufficient.
Option D
14 Dec 2022, 08:10
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PriyamRathor
Solution:
Pre Analysis:
- P consists of 5 consecutive positive multiples of a positive integer
- Let us assume the positive integer be n
- And the 5 consecutive positive multiple be \(kn, (k+1)n, (k+2)n, (k+3)n\) and \((k+4)n\)
- We are asked the remainder when \((k+4)n\) is divided by 2 or in other words, we are asked if \((k+4)n\) is even or odd
Statement 1: The median of the sequence is even
- According to this statement, \((k+2)n=even\) which means either \(n=even\) or \(k=even\)
- In both cases, we can be sure that \((k+4)n\) is even
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: The second term of the sequence is odd
- According to this statement, \((k+1)n=odd\) which means \(n=odd\) and \(k=even\)
- In the above case, we can be sure that \((k+4)n\) is even
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
