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# a, b, c, d, e and f are integers. Is their median greater than their a

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Math Revolution GMAT Instructor
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a, b, c, d, e and f are integers. Is their median greater than their a  [#permalink]

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06 Aug 2018, 00:34
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Difficulty:

85% (hard)

Question Stats:

51% (02:09) correct 49% (01:39) wrong based on 103 sessions

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[Math Revolution GMAT math practice question]

a, b, c, d, e and f are integers. Is their median greater than their average (arithmetic mean)?

1) a<b<c<d<e<f
2) b-a=d-c=f-e

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Re: a, b, c, d, e and f are integers. Is their median greater than their a  [#permalink]

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06 Aug 2018, 04:28
a, b, c, d, e and f are integers. Is their median greater than their average (arithmetic mean)?

1) a<b<c<d<e<f
if a,b,c,d,e are in AP, the median will be the mean and hence ans will be NO
if a is 1, b is 2, c is 9, d is 10, e is 11 and f is 13.. avg = 46/6 = 23/3....median = (9+10)/2=9.5.. yes
insuff
2) b-a=d-c=f-e
again if its AP, NO
b-a=d-c=f-e=1
if a is 1, b is 2, c is 9, d is 10, e is 11 and f is 12.. avg = 45/6 = 15/2....median = (9+10)/2=9.5.. yes
insuff

combined
same example in two statements still hold
insuff

E
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Re: a, b, c, d, e and f are integers. Is their median greater than their a  [#permalink]

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08 Aug 2018, 02:09
=>

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 6 variables (x, y and z) and 0 equations, E 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.

If a = 1, b = 2, c =5, d = 6, e = 7, f = 8, we have a median of 5.5 and an average of 29/6. The median is greater than the average, and the answer is “yes”.

If a = 1, b = 2, c =3, d = 4, e = 5, f = 6, we have a median of 3.5 and an average of 3.5. The median is not greater than the average, and the answer is “no”.

Since we don’t have a unique solution, both conditions are not sufficient, when considered together.
.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: a, b, c, d, e and f are integers. Is their median greater than their a   [#permalink] 08 Aug 2018, 02:09
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