[GMAT math practice question]
What is the median of m, n and 5?
1) m+n=10
2) m=5
What is the median of m, n and 5?
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- Max@Math Revolution
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Target question: What is the median of m, n and 5?Max@Math Revolution wrote: What is the median of m, n and 5?
1) m + n = 10
2) m = 5
Statement 1: m + n = 10
Let's examine the ONLY TWO possible cases: m and n are equal and m and n are NOT equal
Case a: m and n are equal. That is m = 5 and n = 5. In this case, the set = {5, 5, 5 }, in which case the answer to the target question is the median is 5
Case b: m and n are NOT equal. This means one value is greater than 5, and one value is less than 5. In this case, the set = {a number less than 5, 5, a number greater than 5 }, in which case the answer to the target question is the median is 5
Since there are only 2 possible cases, and since the answer to the target question is the SAME in each case, we can conclude that there's only ONE possible answer to the target question: the median is 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: m = 5
So, the set = {n, 5, 5}
Since two of the three values are 5, the median MUST be 5. Here's why:
If n is less than 5, then set set = {a number less than 5, 5, 5}, in which case the median is 5
If n = 5, then set set = {5, 5, 5}, in which case the median is 5
If n is greater than 5, then set = {5, 5, a number greater than 5 }, in which case the median is 5
So, the median MUST BE 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
- Max@Math Revolution
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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 2 variables and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2) together:
Since m + n = 10 and m = 5, we have m = n = 5.
Thus, the median of m, n and 5 is 5.
Both conditions together are sufficient.
Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1): m + n = 10
If one of m and n is less than 5, the other one must be greater than 5. For example, if m < 5, then n > 5.
If one of m and n is 5, the other must also equal 5. For example, if m = 5, then n = 5.
In both cases, the median is 5.
Condition 1) is sufficient.
Condition 2) : m = 5.
If n > 5, the numbers are 5, 5, n in ascending order.
If n < 5, the numbers are n, 5, 5 in descending order.
If n = 5, the numbers are 5, 5, 5.
In each of the possible cases, the median is 5.
Condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can't figure out condition 2), you should choose D as the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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 2 variables and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2) together:
Since m + n = 10 and m = 5, we have m = n = 5.
Thus, the median of m, n and 5 is 5.
Both conditions together are sufficient.
Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1): m + n = 10
If one of m and n is less than 5, the other one must be greater than 5. For example, if m < 5, then n > 5.
If one of m and n is 5, the other must also equal 5. For example, if m = 5, then n = 5.
In both cases, the median is 5.
Condition 1) is sufficient.
Condition 2) : m = 5.
If n > 5, the numbers are 5, 5, n in ascending order.
If n < 5, the numbers are n, 5, 5 in descending order.
If n = 5, the numbers are 5, 5, 5.
In each of the possible cases, the median is 5.
Condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can't figure out condition 2), you should choose D as the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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