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Four values from a data set of 5 elements are 10, 10, 11, an

by Max@Math Revolution » Tue May 01, 2018 4:58 am

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[GMAT math practice 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
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue May 01, 2018 8:15 am

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Max@Math Revolution wrote:[GMAT math practice 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
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

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by Max@Math Revolution » Thu May 03, 2018 1:00 am

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=>

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):
( 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.
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by deloitte247 » Mon May 07, 2018 12:39 pm

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Values = 10,10,11,11 (4 values)
let the fifth element = x
Target question = what is the value of x?
Statement 1 : the range of the data set = 2
Range = highest value - lowest value
2 = highest value - lowest value
This means that x= biggest value OR x= smallest value
first case (smallest value) :
x= 9 : the set = {9,10,10,11,11}
second case(biggest value)=
x = 12: the set = {10,10,11,11,12}
the answer to the target question is either 9 or 12 (it is not definite)
we cannot answer statement 1 with certainty. So it is NOT SUFFICIENT
STATEMENT 2 : The average of data values together than 10
There are so many values that satisfy statement 2
using two random values
x = 500 (case a)
x = 600 (case b)
1st case = average > 10
average = $$average=\ \frac{fx}{f}
average\ =\ \frac{\left(10+10+11+11+600\right)}{5}\ =\ \frac{642}{5}=128.4\ <greater\ than\ 10>$$ $$average=\ \frac{fx}{f}average\ =\ \frac{\left(10+10+11+11+600\right)}{5}\ =\ \frac{642}{5}
=128.4\ <greater\ than\ 10>$$
statement 2 cannot be answered with certainty so it is NOT SUFFICIENT
Statement 1 and 2 together are NOT SUFFICIENT
Answer is option E
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