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Difficulty:
65%
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Question Stats:
60% (02:01) correct
40%
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wrong
based on 139
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Is the median monthly salary of 15 randomly selected employees of a particular company greater than the average (arithmetic mean) monthly salary by at least 5 percent?
(1) The median monthly salary of the 15 employees is $250 greater than their average monthly salary.
(2) The sum of the monthly salaries of the 15 employees is less than $70,000.
(1) The median monthly salary of the 15 employees is $250 greater than their average monthly salary.
(2) The sum of the monthly salaries of the 15 employees is less than $70,000.
28 Jan 2026, 11:20
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ExpertsGlobal5
Is Median > 1.05 * Mean ?
Statement 1:
The median monthly salary of the 15 employees is $250 greater than their average monthly salary.
Median = 250+ Mean
substitute in the equation Median > 1.05 * Mean
250+ Mean > 1.05* Mean
Subtracting Mean from Both sides, we get
250 > 0.05 Mean
Mean < 5000.
As long as Mean remains less than 5000. The answer is Yes.
If the Mean is greater than or equal to 5000. Then, the answer is No.
Hence, Insufficient
Statement 2:
The sum of the monthly salaries of the 15 employees is less than $70,000.
Sum is less than 70000
Sum < $70,000
Mean = Sum / 15
Thus, Sum /15 < $70,000/15
Mean < $ 4666.67
Since we don’t know the value of median.
Insufficient.
Combining both Statements 1 and 2, we get
Mean < $ 4666.67
Mean < 5000.
As long as Mean remains less than 5000. The answer is Yes.
If the Mean is greater than or equal to 5000. Then, the answer is No.
We see the mean is less than 5000 , which is equal to $4666. Hence, Yes.
Sufficient.
Option C
29 Jan 2026, 00:19
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ExpertsGlobal5
If the mean is m and median is d, we need to check if d ≥ 1.05m i.e. d/m ≥ 1.05
1: d = m+250 - Insufficient since we cannot determine the ratio
2: Sum of values < 70000 => m < 70000/15 i.e. m < 14000/3 - Insufficient since we have no information on d
1 and 2: d = m+250 => d/m = 1 + 250/m ... (i)
Since m < 14000/3, we have: 250/m > 250/(14000/3)
=> 250/m > 750/14000 = 0.053
=> 1 + 250/m > 1 + 0.053
=> 1 + 250/m > 1.053
Thus, from (i): d/m > 1.053
=> d/m > 1.05 - Sufficient
Answer C
Note: If the value of 250/m had been greater than a value less than 0.05, i.e. say, 250/m > 0.045, we would NOT have been able to determine the answer, Thus, the value 250/m is the most important value in this question
