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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 a, b, c, d, e, f, and g are seven integers in arithmetic progression with four of them being odd, which of the following is/are true about the seven integers?
I. The average is not an integer.
II. The median is an even integer.
III. The difference between the average and the median is an even integer.
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. The average is not an integer.
II. The median is an even integer.
III. The difference between the average and the median is an even integer.
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
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31 Dec 2021, 16:59
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Bunuel
Conditions:
a is even and r is even, In this case all numbers will be even but we know 4 numbers are odd. So out.
a is even and r is odd, In this case there will be only 3 odd numbers, we know they are 4. So out.
a is odd and r is even, In this case all numbers will be odd. So out.
a is odd and r is odd, In this case there will be exactly 4 odds.
I. The average is not an integer.
Since its an AP So, average = sum of first and last term/2
a+g/2
odd+odd/2
even/2 It's definitely an integer.
II. The median is an even integer.
Median will be 4th term which is d = even. So true.
Starting from a alternate numbers are odd.
III. The difference between the average and the median is an even integer.
avg = even
median = even
even-even = even True.
So II and III are correct.
