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If the average of four numbers is 35, how many of the number

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If the average of four numbers is 35, how many of the number

by fskilnik@GMATH » Tue Jan 22, 2019 6:17 am

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BTGmoderatorDC 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
Source: Veritas Prep
$$\mu \left( {x,y,z,w} \right) = 35$$
$$?\,\,:\,\,\,\,\# \,\,{\rm{less}}\,\,{\rm{than}}\,\,35$$
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y,z,w} \right) = \left( {35 - 2,35 - 2,35 + 2,35 + 2} \right)\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y,z,w} \right) = \left( {35 - 2,35 - 2,35 - 1,35 + 5} \right)\,\,\,\, \Rightarrow \,\,\,? = 3 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( {\rm{E}} \right)$$

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

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by Brent@GMATPrepNow » Wed Jan 23, 2019 5:40 am

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BTGmoderatorDC 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

Target question: How many of the numbers are less than 35?
If we're able to see that the statements FEEL insufficient, and we're able to come up with some counter-examples in our head, then we can head straight to...
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Statements 1 and 2 combined
There are several sets of 4 values that satisfy BOTH statements. Here are two:
Case a: The numbers are {33, 33, 37, 37}. In this case, the answer to the target question is there are TWO numbers less than 35
Case b: The numbers are {33, 33, 34, 40}. In this case, the answer to the target question is there are THREE numbers less than 35
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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by swerve » Thu Jan 24, 2019 10:22 am

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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

No unique answer, hence the correct option is E
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