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28 Dec 2017, 00:28
Kudos
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B
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:
84% (01:14) correct
16%
(01:21)
wrong
based on 61
sessions
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If the average (arithmetic mean) of five positive numbers is 30, how many of the numbers are greater than 30?
(1) None of the five numbers is equal to 10.
(2) The average (arithmetic mean) of the four smallest numbers is 4.
(1) None of the five numbers is equal to 10.
(2) The average (arithmetic mean) of the four smallest numbers is 4.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
28 Dec 2017, 04:26
Kudos
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Bunuel
We'll try a few numbers to help us understand the logic.
This is an Alternative approach.
(1) We can choose all our numbers to be 30 or have all 30 except for one 29 and one 31
Insufficient.
(2) Let's try making the 4 smallest numbers exactly 4. Then the last number is definitely larger than 30.
We've seen that we can make 1 number greater than 30; next we'll try to make 2 numbers greater than 30.
Say our two largest numbers are 31 and 31. Then the 4 smallest numbers are 31, x, y, z.
These must have an average of 4 so (31+x+y+z)/4 = 4 --> 31+x+y+z = 16 --> x+y+z=16-31<0
But all our numbers are positive! This is impossible, and therefore (2) is sufficient to answer the question.
(B) is our answer.
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