Four values from a data set of 5 elements are 10, 10, 11, and 11. What

Question

Four values from a data set of 5 elements are 10, 10, 11, and 11. What is the fifth data value?

1) The range of the data set is 2
2) The average of the data values is greater than 10

amanvermagmat · Answer

10, 10, 11, 11, __

(1) Range is 2, so the difference between highest and smallest value is '2'. Then the fifth data value could be '12' (12-10=2) but it could also be '9' (11-9=2). Not sufficient.

(2) If average of 5 values is > 10, then their sum is > 10*5 = 50. Sum of given four values = 10+10+11+11= 42, so the fifth value is > 8. Not sufficient.

Combining the statements, fifth value should be > 8, but both '9' and '12' from first statement are > 8. Not sufficient.

Hence  E answer

BrentGMATPrepNow · Answer

Let's say that x = the missing data value

Target question :    What is the value of x?

Given : The other 4 values are 10, 10, 11 and 11

Statement 1 : The range of the data set is 2  
So, (the biggest value) - (the smallest value) = 2
The problem here is that x COULD be the smallest value, or x COULD be the biggest value
Consider these two possible cases: 
 Case a : x = 9. In this case, the numbers are {9, 10, 10, 11, 11}, so the range is 2. Here, the answer to the target question is  x = 9 
 Case b : x = 12. In this case, the numbers are {10, 10, 11, 11, 12}, so the range is 2. Here, the answer to the target question is  x = 12 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The average of the data values is greater than 10 
There are infinitely many values of x that satisfy statement 2. Here are two: 
 Case a : x = 1000. In this case, the average is definitely greater than 10. Here, the answer to the target question is  x = 1000 
 Case b : x = 2000. In this case, the average is definitely greater than 10. Here, the answer to the target question is  x = 2000 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that EITHER x = 9 OR x = 12
Statement 2 tells us that the average of the data values is greater than 10
Let's examine the averages for each case (i.e., x = 9 and x = 12)
If  x = 9 , then the average of the 5 values = (9 + 10 + 10 + 11 + 11)/5 = 51/5 = 10.2
If  x = 12 , then the average of the 5 values = (10 + 10 + 11 + 11 + 12)/5 = 54/5 = 10.8
In BOTH cases, the average is greater than 10
So, the answer to the target question is  EITHER x = 9 OR x = 12 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

MathRevolution · Answer

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable, x which is the fifth data value and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
The fifth data value could be  x = 9  or  x = 12 .
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2):
 \frac{( x + 10 + 10 + 11 + 11 )}{5} > 10 
 => x + 10 + 10 + 11 + 11 > 50 
 => x + 42 > 50 
 => x > 8 
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2) :
Condition 1) tells us that  x = 9  or  x = 12 , and condition 2) tells us that  x > 8 . 
So,  x = 9  or  x = 12 . 
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

Answer: E

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

BelalHossain046 · Answer

Statement 1:
If the fifth number is 9, range = 11-9=2.
If the fifth number is 12 range = 12-10=2.
So, fifth number can be 9 or 12.
INSUFFICIENT.

Posted from my mobile device

BelalHossain046 · Answer

Statement 2:
Average of five numbers is GREATER than 10. That means, TOTAL of the five numbers is greater than 50.
Sum of know four numbers is 42. 
So, the fifth number will be GREATER than 8. That is, the fifth number can be anything such as 9,10,11,12, etc.
INSUFFICIENT.

Combining both statements,
9 &12 Are common in both statements (9&12 suffice both statements).
So, the fifth number can be 9 or 12.
INSUFFICIENT.

E answer

Posted from my mobile device

Four values from a data set of 5 elements are 10, 10, 11, and 11. What

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Four values from a data set of 5 elements are 10, 10, 11, and 11. What

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards