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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, 16:00
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Bunuel
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. I 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. I and III only
E. I, II, and III
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Experts' Global Video Official Explanation
31 Dec 2021, 16:59
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Bookmarks
Bunuel
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. I 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. I and III only
E. I, II, and III
Happy New Year Albania, Algeria, Andorra, Angola, Austria, Belgium, Benin, Bosnia and Herzegovina, Cameroon, Central African Republic, Chad, Croatia, Czech Republic, Democratic Republic of the Congo, Denmark, Equatorial Guinea, France, Gabon, Germany, Hungary, Italy, Kosovo, Liechtenstein, Luxembourg, Malta, Monaco, Montenegro, Morocco, Netherlands, Niger, Nigeria, Norway (Including Svalbard and Jan Mayen and Bouvet Island), Poland, Macedonia, Republic of the Congo, San Marino, Serbia, Slovakia, Slovenia, Spain (Including Balearic Islands, Ceuta and Melilla and excluding Canary Islands), Sweden, Switzerland, Tunisia, United Kingdom/Gibraltar, Vatican City, and Western Sahara!
Dec 31 Event: GMAT Club Around The World!
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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.
