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If the average of four numbers is 35, how many of the numbers are less than 35?
1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.
OA E
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If the average of four numbers is 35, how many of the
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Sum of the 4 numbers = (quantity)(average) = 4*35 = 140.AAPL wrote:Veritas Prep
If the average of four numbers is 35, how many of the numbers are less than 35?
1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.
Statement 1: None of the numbers are exactly 3
To save time, check whether it's possible to get different answers to the question stem while also satisfying Statement 2.
Case 1: 0, 33, 33, 74 --> sum = 0+33+33+74 = 140
In this case, three numbers are less than 35.
Case 2: 33, 33, 36, 38 --> sum = 33+33+36+38 = 140
In this case, two numbers are less than 35.
Since Cases 1 and 2 satisfy both statements but yield different answers to the question stem, the two statements combined are INSUFFICIENT.
The correct answer is E.
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AAPL wrote:Veritas Prep
If the average of four numbers is 35, how many of the numbers are less than 35?
1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.
OA E
Target question: How many of the numbers are less than 35?Bunuel wrote:If the average of four numbers is 35, how many of the numbers are less than 35?
(1) None of the numbers are exactly 35
(2) Two of the numbers are exactly 33
Given: The average of four numbers is 35
All this tells us is that the SUM of the 4 numbers is 140 (since 140/4 = 35)
Given the limited amount of information, it's likely that the correct answer is C or E
Statement 1: None of the numbers are exactly 35
There are many sets of 4 numbers y that satisfy statement 1. Here are two:
Case a: The numbers are {34, 34, 36, 36}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 0, 0, 140}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Two of the numbers are exactly 33
There are many sets of 4 numbers y that satisfy statement 1. Here are two:
Case a: The numbers are {33, 33, 37, 37}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 33, 33, 74}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that the cases I created for statement 2 ALSO satisfy statement 1.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: The numbers are {33, 33, 37, 37}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 33, 33, 74}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
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