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

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1785
WE: General Management (Education)
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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92% (01:36) correct 8% (02:09) wrong based on 29 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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Joined: 22 May 2016
Posts: 3847
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)

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If the list of integers from 1 to 10 is multiplied by 3, the median of   [#permalink] 10 Aug 2018, 08:09