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What is the range of the 5 numbers x, y, 10, 15, and 20?

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What is the range of the 5 numbers x, y, 10, 15, and 20?

by Max@Math Revolution » Fri May 11, 2018 12:18 am
[GMAT math practice question]

What is the range of the 5 numbers x, y, 10, 15, and 20?

1) x and y lie between 10 and 20, inclusive.
2) The average (arithmetic mean) of the five numbers is 15
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by Terry@ThePrincetonReview » Fri May 11, 2018 3:51 am
Range is defined as difference between the least and greatest values in a set. So, we need to know the values of both x and y relative to 10 and 20, the least and greatest known values in the set.

Statement 1 makes it clear that neither of the variables x or y is less than 10 or greater than 20. The range is thus 20 - 10 = 10. Statement is sufficient. Eliminate B, C, E.

Statement 2: If the average is 15, then the sum is 15 * 5 = 75. (Average = Sum/Count.) Therefore, x + y + 10 + 15 + 20 = 75. Because 10 + 15 + 20 = 45, x + y = 30. Now, both x and y could equal 15 (range of 20-10=10), or x = 10 and y = 20 (range of 20-10=10), or x = 0 and y = 30 (range of 30-0=30), or x = 1 and y = 29 (range of 29-1=28). Different possibilities yield different ranges, so this statement is not sufficient. Eliminate D.

Answer is A.
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by Max@Math Revolution » Sun May 13, 2018 5:34 pm
=>

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 (x and y) 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):
Since we have 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10.
The range is the difference between the maximum and the minimum, which is 20 - 10 = 10.
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)
Since 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10.
The range is the difference between the maximum and the minimum, which is 20 - 10 = 10.
Thus, condition 1) is sufficient.

Condition 2)
If x = 10 and y = 20, the range is 10.
If x = 9 and y = 21, the range is 12.
Since we don't have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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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by Scott@TargetTestPrep » Mon May 14, 2018 4:06 pm
Max@Math Revolution wrote:
What is the range of the 5 numbers x, y, 10, 15, and 20?

1) x and y lie between 10 and 20, inclusive.
2) The average (arithmetic mean) of the five numbers is 15
We need to determine the range of x, y, 10, 15, and 20. Recall that range of a set = the greatest value in the set - the least value in the set.

Statement One Alone:

x and y lie between 10 and 20, inclusive.

Since the smallest value of x and y can be are 10, and the largest they can be are 20, and since we already see that the least number in the list is 10 and the greatest is 20, the range is 10. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The average (arithmetic mean) of the five numbers is 15

Although we know that the average of the numbers is 15, its possible to have a number less than 10 or greater than 20. Thus, we cannot determine the range.

Answer: A

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