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04 Oct 2020, 05:11
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
58% (01:57) correct
42%
(01:59)
wrong
based on 184
sessions
History
Date
Time
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Not Attempted Yet
If the average of three numbers of 2, 5, and x is equal to the median, what is the value of x?
1) x < 3
2) x > -2
1) x < 3
2) x > -2
04 Oct 2020, 05:53
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Quote:
Step 1: Understanding the question
Average of the numbers = (2+5+x)/3 = Median
As the value of x is unknown, there are three possible cases:
Case 1: x ≤ 2, set is {x, 2, 5}, Median = 2
Hence (2+5+x)/3 = 2
Simplifying, x = -1
Case 2: 2 < x < 5, set is {2, x, 5}, Median = x
Hence (2+5+x)/3 = x
Simplifying, x = 3.5
Case 3: x ≥ 5, set is {2, 5, x}, Median = 5
Hence (2+5+x)/3 = 5
Simplifying, x = 8
Step 2: Analysing statement 1 alone
1) x < 3
Only x = -1 is possible
Sufficient
Step 3: Analysing statement 2 alone
2) x > -2
x = -1, 3.5 or 8 are possible.
Insufficient
A is correct
04 Oct 2020, 12:23
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Forget the conventional way to solve DS questions.
We will solve this DS question using the variable approach.
DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.
We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.
To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.
If you have a set of consecutive integers, the median is equal to the average (arithmetic mean): Conversely, when the median and the average (arithmetic mean) of a set are equal, it is very likely that the set consists of consecutive integers.
1st Property of medians: Assumption of median
When we are looking for the median of a set, it is assumed that the set is in ascending order, from least to greatest. So, if you see the elements are not in order, rearrange the elements in increasing order. The question will normally state ‘in that order’ if the elements are in order.
Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question. We have to find the value of 'x'.
=> Given that average of (2 , 5 and x) = median
=> Possible cases :{x,2,5},{2,x,5}, and {2,5,x}
Second and the third step of Variable Approach: From the original condition, we have 1 variable (x).To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Let’s take look at each condition.
Condition(1) tells us that the x < 3.
=> Only possible case is {x,2,5} for mean = median.
=> For x = -1, Average = 2 and Median = 2
Since the answer is unique, condition(1) alone is sufficient by CMT 2.
Condition(2) tells us that x > -2 .
=> For x = -1 , mean = median
=> For x = 8 , mean = median
Since the answer is not unique, condition (2) alone is not sufficient by CMT 2.
Condition(1) alone is sufficient.
So, A is the correct answer.
Answer: A
We will solve this DS question using the variable approach.
DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.
We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.
To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.
If you have a set of consecutive integers, the median is equal to the average (arithmetic mean): Conversely, when the median and the average (arithmetic mean) of a set are equal, it is very likely that the set consists of consecutive integers.
1st Property of medians: Assumption of median
When we are looking for the median of a set, it is assumed that the set is in ascending order, from least to greatest. So, if you see the elements are not in order, rearrange the elements in increasing order. The question will normally state ‘in that order’ if the elements are in order.
Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question. We have to find the value of 'x'.
=> Given that average of (2 , 5 and x) = median
=> Possible cases :{x,2,5},{2,x,5}, and {2,5,x}
Second and the third step of Variable Approach: From the original condition, we have 1 variable (x).To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Let’s take look at each condition.
Condition(1) tells us that the x < 3.
=> Only possible case is {x,2,5} for mean = median.
=> For x = -1, Average = 2 and Median = 2
Since the answer is unique, condition(1) alone is sufficient by CMT 2.
Condition(2) tells us that x > -2 .
=> For x = -1 , mean = median
=> For x = 8 , mean = median
Since the answer is not unique, condition (2) alone is not sufficient by CMT 2.
Condition(1) alone is sufficient.
So, A is the correct answer.
Answer: A
