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12 Mar 2023, 09:54
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E
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Difficulty:
55%
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56% (01:46) correct
44%
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wrong
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An arithmetic progression is one in which each subsequent term is the sum of the preceding number and a constant. If the elements in a set S are integers in arithmetic progression, is the median of S a part of S?
(1) The constant in S is an even integer.
(2) The range of S is even.
(1) The constant in S is an even integer.
(2) The range of S is even.
12 Mar 2023, 14:27
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TBT
If the elements in a set S are in arithmetic progression, the median is a part of the set if the number of terms is odd.
Statement 1
(1) The constant in S is an even integer.
As discussed above, the number of terms is what matters. Hence we can eliminate this statement as the information is not sufficient.
Example:
Case 1:
S = {\(2, \quad 4, \quad 6, \quad 8\)}
Median = 5; is the median of S a part of S ⇒ No
Case 2:
What matters to us is the number of terms.
S = {\(2, \quad 4, \quad 6\)}
Median = 4; is the median of S a part of S ⇒ Yes
Eliminate A and D.
Statement 2
(2) The range of S is even
As discussed above, the number of terms is what matters. Hence we can eliminate this statement as the information is not sufficient.
Example:
Case 1:
S = {\(2, \quad 4, \quad 6, \quad 8\)}
Range = 6; Median = 5; is the median of S a part of S ⇒ No
Case 2:
S = {\(2, \quad 4, \quad 6\)}
Range= 4; Median = 4; is the median of S a part of S ⇒ Yes
Eliminate B.
Statement 2
The statements combined wouldn't help either as the cases for both Statement 1 and Statement 2 are the same. Eliminate C.
Option E
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