If the average of four numbers is 35, how many of the numbers are less than 35?

[BTGModeratorVI]

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

Answer: E
Source: Veritas Prep

[Jay@ManhattanReview]

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

Answer: E
Source: Veritas Prep

Let's take each statement one by one.

(1) None of the numbers are exactly 35.

We cannot conclude only on this information. At least one or at most three numbers can be less than 35. Insufficient.

(2) Two of the numbers are exactly 33.

Cace 1: Say the numbers are 33, 33, 34 and 40, making the average equal to 35. The answer is: there are three numbers that are less than 35.

Cace 2: Say the numbers are 33, 33, 37 and 37, making the average equal to 35. The answer is: there are two numbers that are less than 35.

No unique answer. Insufficient.

(1) and (2) together

Both cases discussed above are applicable for Statement 1, too. No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

Answer: E
Source: Veritas Prep

Target question: How many of the numbers are less than 35?

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

Cheers,
Brent