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28 Oct 2021, 04:45
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Difficulty:
95%
(hard)
Question Stats:
33% (02:22) correct
67%
(02:37)
wrong
based on 293
sessions
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Not Attempted Yet
List A consists of at least two different values and contains only positive multiples of 30. Which of the following CANNOT be true?
I. The range of list A is twice as big as the median of list A.
II. The variance of list A is less than the standard deviation of list A.
III. The median of list A is the square of an integer but not an element in list A.
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only
I. The range of list A is twice as big as the median of list A.
II. The variance of list A is less than the standard deviation of list A.
III. The median of list A is the square of an integer but not an element in list A.
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only
28 Oct 2021, 05:13
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The GMAT doesn't test some of these things.
Item I can clearly be true, because our list can be 30, 60, 150, say, and then the range, 120, is twice the median, 60.
Item III can be true, because the list can be 210, 240, and then the median, 225, is equal to 15^2 and is not in the list.
Item II is the item you'd never see tested on the GMAT. Standard deviation is the square root of variance. This list has at least two different values, so its variance is positive. When we take the square root of a positive number, usually we get something smaller, but not always -- not if we take the square root of something between 0 and 1. And the variance of this list can be between 0 and 1, because we can have repeated values. For example, if our list contains one million values equal to 30, and one value equal to 60, then the variance of the list will be extremely small (very close to zero), because almost every value in the list will be negligibly different from the mean. In that case, the standard deviation will exceed the variance.
So all three items can be true, and the answer is "none".
Item I can clearly be true, because our list can be 30, 60, 150, say, and then the range, 120, is twice the median, 60.
Item III can be true, because the list can be 210, 240, and then the median, 225, is equal to 15^2 and is not in the list.
Item II is the item you'd never see tested on the GMAT. Standard deviation is the square root of variance. This list has at least two different values, so its variance is positive. When we take the square root of a positive number, usually we get something smaller, but not always -- not if we take the square root of something between 0 and 1. And the variance of this list can be between 0 and 1, because we can have repeated values. For example, if our list contains one million values equal to 30, and one value equal to 60, then the variance of the list will be extremely small (very close to zero), because almost every value in the list will be negligibly different from the mean. In that case, the standard deviation will exceed the variance.
So all three items can be true, and the answer is "none".
General Discussion
26 Jul 2023, 07:05
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IanStewart
I agree with you. I do not give information about the formula of the SD or the variance. The GMAT doesn't ask for that, only for the concept of dispersion. So most students would not know or remember the formulas.
