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16 Aug 2019, 03:02
Kudos
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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:
25%
(medium)
Question Stats:
72% (00:57) correct
28%
(00:55)
wrong
based on 65
sessions
History
Date
Time
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Not Attempted Yet
If the average (arithmetic mean) of four numbers is 150, how many of the numbers are equal to 150?
(1) None of the four numbers is less than 150.
(2) None of the four numbers is greater than 150.
(1) None of the four numbers is less than 150.
(2) None of the four numbers is greater than 150.
Archit3110
Major Poster
16 Aug 2019, 07:11
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Bunuel
given sum = 600
#1
None of the four numbers is less than 150.
only valid when all are 150 sufficient
#2
None of the four numbers is greater than 150
only valid when all are 150
IMOD
18 Sep 2019, 01:10
Kudos
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Bunuel
Official Explanation
Since the average of the numbers is 150, they could all be 150, or they could be dispersed around 150. The iron law is that the differences between each of the numbers and 150 must all cancel out. On to the statements, separately first.
In Statement (1), if none of the numbers is less than 150, the only way their differences from 150 could net to zero is if all of the numbers were 150. Therefore all of the numbers are 150, we can answer definitively, and Statement (1) is sufficient.
Statement (2) is sufficient on the same grounds as Statement (1).
The correct answer is (D).
