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

Question

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

KarishmaParmar · Answer

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 Answer E

BrentGMATPrepNow · Answer

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

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fskilnik · Answer

\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.

Basshead · Answer

Total of the four numbers = 140

(1) We can have 1 + 2 + 3 + 134 or 34 + 34 + 34 + 38. INSUFFICIENT.

(2) We can have 1 + 33 + 33 + 73 or 33 + 33 + 37 + 37. INSUFFICIENT.

(1&2) Combined, the numbers used for statement 2 still apply. INSUFFICIENT.

Answer is E.

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards