If two elements are dropped from set $X =\{-10, -8, 0, 6, 7\},$ what will be the percentage change in its mean?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If two elements are dropped from set $X =\{-10, -8, 0, 6, 7\},$ what will be the percentage change in its mean?

by Gmat_mission » Tue Nov 10, 2020 8:02 am

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If two elements are dropped from set $X =\{-10, -8, 0, 6, 7\},$ what will be the percentage change in its mean?

(1) The median of the set will remain the same.
(2) The range of the set will decrease by $3.$

Answer: B

Source: Manhattan GMAT

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Source: Beat The GMAT — Data Sufficiency | Tue Nov 10, 2020 8:02 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: If two elements are dropped from set $X =\{-10, -8, 0, 6, 7\},$ what will be the percentage change in its mean?

by deloitte247 » Thu Nov 12, 2020 10:13 pm

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$$X=\left\{-10,\ -8,\ 0,\ 6,\ 7\right\}$$
Mean = -1
Median = 0
Range = 17
Statement 1: The median of the set will remain the same.
x can either be {-10, 0, 6} or {-8, 0, 6} and the mean will either be -1.3 or -0.67. So, there will be a different percentage change in its mean. Statement 1 does not give a definite answer. Hence, it is NOT SUFFICIENT.

Statement 2: The range of the set will decrease by 3
New range = 17 - 3 = 14
From the given set, the range will be 14 if smallest term = -8 and the greatest term = 6
6 - (-8) = 6 + 8 = 14
So, the new set is {-8, 0, 6}; new mean = -0.67
$$\%\ change\ in\ mean=\frac{-0.67+1}{-1}\cdot\frac{100}{1}=\frac{0.33}{-1}\cdot100$$
$$\%\ change\ in\ mean=-33\%$$
Statement 2 alone is SUFFICIENT; answer = option B.