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03 Aug 2022, 10:18
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Set X consists of 11 different numbers. If the average (arithmetic mean) of the 10 smallest numbers is -1.6, and the average of the 10 largest numbers is 5.2. What is the range of set X?
A. 3.6
B. 6.8
C. 34
D. 36
E. 68
A. 3.6
B. 6.8
C. 34
D. 36
E. 68
03 Aug 2022, 11:02
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Let the terms of Set X be
[\(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a10, a11\)]
Mean of first 10 terms = -1.6 which implies
\(a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a10 = -16\) Eq1
Mean of last 10 terms = 52 which implies
\(a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a10+a11 = 52\) Eq2
Subtracting Eq1 from Eq2 we get
\(a11 - a_1 = 52-(-16) = 68\)
Which is also the range
Answer - E
Posted from my mobile device
[\(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a10, a11\)]
Mean of first 10 terms = -1.6 which implies
\(a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a10 = -16\) Eq1
Mean of last 10 terms = 52 which implies
\(a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a10+a11 = 52\) Eq2
Subtracting Eq1 from Eq2 we get
\(a11 - a_1 = 52-(-16) = 68\)
Which is also the range
Answer - E
Posted from my mobile device
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