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# If the list of integers from 1 to 10 is multiplied by 3, the median of

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Senior DS Moderator
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If the list of integers from 1 to 10 is multiplied by 3, the median of  [#permalink]

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10 Aug 2018, 07:27
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Difficulty:

15% (low)

Question Stats:

90% (01:13) correct 10% (02:37) wrong based on 21 sessions

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If the list of integers from 1 to 10 is multiplied by 3, the median of the new list will be how many times the average of that new list?
A. $$\frac{1}{3}$$
B. 1
C. 3
D. 9
E. 27

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If the list of integers from 1 to 10 is multiplied by 3, the median of  [#permalink]

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10 Aug 2018, 08:09
gmatbusters wrote:
If the list of integers from 1 to 10 is multiplied by 3, the median of the new list will be how many times the average of that new list?
A. $$\frac{1}{3}$$
B. 1
C. 3
D. 9
E. 27

In an evenly spaced sequence,
Median = mean

Multiplying each term of an evenly spaced sequence (integers from 1 to 10) by the same number (3) produces another evenly spaced sequence.

The integers from 1 to 10 are evenly spaced consecutive integers.

The integers from 3 to 30 are evenly spaced consecutive multiples of 3.

In an evenly spaced sequence, the median equals the mean.

The median of the new list is how many times the average of that list?

Med = mean
$$\frac{Med}{mean}=1$$

No need to do these calculations, but if unsure:
MEDIAN of new sequence = average of two middle terms
3, 6, 9, 12, 15, 16.5 18, 21, 24, 27, 30
MEAN of new sequence = $$\frac{First+ Last}{2}=\frac{3+30}{2}=16.5$$
You could also use the integers from 1 to 10, because "median = mean" applies to all evenly spaced sequences
Median: $$6.5$$
MEAN: $$\frac{(1 + 10)}{2} = \frac{11}{2} = 6.5$$
Median = (MEAN * 1)
If the list of integers from 1 to 10 is multiplied by 3, the median of &nbs [#permalink] 10 Aug 2018, 08:09
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