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05 Feb 2025, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (01:20) correct
13%
(01:43)
wrong
based on 98
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The average (arithmetic mean) of 6 numbers is 8.4. When one number is discarded, the average of the remaining numbers becomes exactly 1 less than the original average. What is the discarded number?
(A) 6.0
(B) 9.4
(C) 11.4
(D) 12.0
(E) 13.4
(A) 6.0
(B) 9.4
(C) 11.4
(D) 12.0
(E) 13.4
05 Feb 2025, 01:49
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Mean = 8.4 & n = 6
8.4 * 6 = 50.4
1 number removed
New n = 5 and New Mean = 7.4
5*7.4 = 37.0
50.4 - 37.0 = 13.4
IMO Ans = 13.4
8.4 * 6 = 50.4
1 number removed
New n = 5 and New Mean = 7.4
5*7.4 = 37.0
50.4 - 37.0 = 13.4
IMO Ans = 13.4
05 Feb 2025, 01:55
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We know
Average of 6 numbers = (sum of 6 numbers / 6 )
Average of 5 numbers = (sum of 5 numbers /5 )
=> sum of 6 numbers = average of 6 numbers * 6
=> sum of 5 numbers = average of 5 numbers * 5
According to question,
Average of 6 numbers = 8.4
=> sum of 6 numbers = 8.4 * 6 ----------->(a)
similarly " the average of the remaining numbers becomes exactly 1 less than the original average" states
average of 5 numbers + 1 = 8.4
=> sum of 5 numbers /5 + 1 = 8.4
=> sum of 5 numbers + 5 = 8.4*5
=> sum of 5 numbers = 8.4*5 - 5 --------------> (b)
Now discarded number = sum of 6 numbers - sum of 5 numbers
=> 8.4*6 - (8.4*5 - 5) [using (a) and (b)]
=> 8.4*6 -8.4*5+5
=>8.4+5
=> 13.4
The correct answer should be (E)
Average of 6 numbers = (sum of 6 numbers / 6 )
Average of 5 numbers = (sum of 5 numbers /5 )
=> sum of 6 numbers = average of 6 numbers * 6
=> sum of 5 numbers = average of 5 numbers * 5
According to question,
Average of 6 numbers = 8.4
=> sum of 6 numbers = 8.4 * 6 ----------->(a)
similarly " the average of the remaining numbers becomes exactly 1 less than the original average" states
average of 5 numbers + 1 = 8.4
=> sum of 5 numbers /5 + 1 = 8.4
=> sum of 5 numbers + 5 = 8.4*5
=> sum of 5 numbers = 8.4*5 - 5 --------------> (b)
Now discarded number = sum of 6 numbers - sum of 5 numbers
=> 8.4*6 - (8.4*5 - 5) [using (a) and (b)]
=> 8.4*6 -8.4*5+5
=>8.4+5
=> 13.4
The correct answer should be (E)
