GRE Sample Test 1 Quantitative Reasoning 1

Start by finding the mean for Set A—this can be done by calculating the sum of the set divided by 4, or by observing that the numbers are evenly spaced, so the sum must be the average of the two middle numbers. The total variance of the set (the total distance of the members from the mean) is 8. Therefore, the possible values of x must create a total variance for Set B of equal to or greater than 8. Since the values of Set A are evenly spaced with a difference of 2 between each value, look for the answer choice that creates the same condition for Set B. The value 18 creates the set {12, 14, 16, 18}, which has a mean of 15 and a total variance from the mean of 8. This set would thus have the same standard deviation as that of Set A. Since the question asks for the values of x that would create a Set B with a higher standard deviation than that of Set A, x must be greater than 18. The correct answers are (E) and (F).