Is the median monthly salary of 15 randomly selected employees of

Question

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.

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Dereno · Answer

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

sujoykrdatta · Answer

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

ExpertsGlobal5 · Answer

Explanation: Let the number of employees be n. Since there are 15 randomly selected employees: n = 15. Let the median monthly salary be M. Let the average monthly salary be A. We need to find whether M > 1.05A. Statement (1) M = 250 + A (Equation I) Possibility 1: If M = 1.1A, then from Equation I, M = 2,750 and A = 2,500. It is possible to construct multiple sets with this condition and in this scenario M > 1.05A. Possibility 2: If M = 1.01A, then from Equation I, M = 25,250 and A = 25,000. It is possible to construct multiple sets with this condition and in this scenario M < 1.05A. It is NOT possible to determine with certainty whether M > 1.05A. Hence, Statement (1) is insufficient . Statement (2) The sum of the monthly salaries of the 15 employees < 70,000 An < 70,000 A(15) < 70,000 A < 4,666.67 (Equation II) This condition does not impose any restrictions on the median. It is NOT possible to determine with certainty whether M > 1.05A. Hence, Statement (2) is insufficient . Statement (1) and Statement (2) combined From Equation II we know that A < 4666.67 and from Equation I we know that M = 250 + A. If A = 4666.67, then 1.05A = 4900 and M = 4916.67, and thus M > 1.05A. For any value of A less than 4666.67, the difference between 1.05A and M will further increase and M will still be greater than 1.05A. It is possible to determine with certainty that M > 1.05A. Hence, Statement (1) and Statement (2) combined are insufficient . C is the correct answer choice.

Is the median monthly salary of 15 randomly selected employees of

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GMAT Data Sufficiency (DS) Questions

Is the median monthly salary of 15 randomly selected employees of

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