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# If a, b, c and d are distinct numbers, can b be the average of a, b, c

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If a, b, c and d are distinct numbers, can b be the average of a, b, c  [#permalink]

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03 Jul 2017, 04:59
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If a, b, c and d are distinct numbers, can b be the average of a, b, c and d?

(1) a + c = 2d
(2) b + d = 2c

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If a, b, c and d are distinct numbers, can b be the average of a, b, c  [#permalink]

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03 Jul 2017, 08:05
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If a, b, c and d are distinct numbers, can b be the average of a, b, c and d?

(1) a + c = 2d
If a+c =2d, the average of a,b,c,d is $$\frac{a+b+c+d}{4} = \frac{3d+b}{4}$$(Because a+c = 2d)
If b has to be average of these numbers, it is possible if and only if d=b.
We can never have distinct numbers. Hence, sufficient.

(2) b + d = 2c
Since b+d=2c, the average of a,b,c,d is $$\frac{a+b+c+d}{4} = \frac{a+3c}{4}$$(Because b+d = 2c)
If b has to be average of these numbers, it is possible a+3c = 4b.
The combination a=7, c=3, b=4 can give us a solution
Similarly, if a=c=b=2, this also gives us a favorable solution.
We can/cannot have distinct numbers. Hence, insufficient.(Option A)
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If a, b, c and d are distinct numbers, can b be the average of a, b, c   [#permalink] 03 Jul 2017, 08:05
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