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

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If the average of four numbers is 35, how many of the numbers are less  [#permalink]

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28 Feb 2016, 11:47
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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

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If the average of four numbers is 35, how many of the numbers are less  [#permalink]

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28 Feb 2016, 12:01
1
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

Average is 35
Sum should be 35*4 =140

Statement 1 -
Numbers can be 1,2,3,134 (3 less than 35)
Number can be 34,36,36,34 (2 less than 35)
etc

Statement 2-
Numbers can be 33,33,37,37 (2 less than 35)
Number can be 33,33,1,73 (3 less than 35)
etc

Combining both
Numbers can be 33,33,37,37 (2 less than 35)
Number can be 33,33,1,73 (3 less than 35)
etc

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If the average of four numbers is 35, how many of the numbers are less  [#permalink]

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03 Jan 2019, 09:32
Top Contributor
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

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

Cheers,
Brent

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Re: If the average of four numbers is 35, how many of the numbers are less  [#permalink]

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22 Jan 2019, 07:31
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

$$\mu \left( {x,y,z,w} \right) = 35$$

$$?\,\,:\,\,\,\,\# \,\,{\rm{less}}\,\,{\rm{than}}\,\,35$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y,z,w} \right) = \left( {35 - 2,35 - 2,35 + 2,35 + 2} \right)\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr \,{\rm{Take}}\,\,\left( {x,y,z,w} \right) = \left( {35 - 2,35 - 2,35 - 1,35 + 5} \right)\,\,\,\, \Rightarrow \,\,\,? = 3 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( {\rm{E}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If the average of four numbers is 35, how many of the numbers are less   [#permalink] 22 Jan 2019, 07:31
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