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The average of 7 distinct integers is 12, and the least of these integ
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06 Apr 2022, 08:27
06 Apr 2022, 08:27
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The average of 7 distinct integers is 12, and the least of these integers is -15. What is the maximum possible value of the largest integer in the set?
A. 84
B. 158
C. 159
D. 160
E. 161
A. 84
B. 158
C. 159
D. 160
E. 161
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Joined: 10 Apr 2015
Posts: 6218
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Re: The average of 7 distinct integers is 12, and the least of these integ
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06 Apr 2022, 08:32
06 Apr 2022, 08:32
2
Carcass wrote:
The average of 7 distinct integers is 12, and the least of these integers is -15. What is the maximum possible value of the largest integer in the set?
A. 84
B. 158
C. 159
D. 160
E. 161
A. 84
B. 158
C. 159
D. 160
E. 161
The average of 7 distinct integers is 12, and the least of these integers is -15
If we let a, b,... to g represent the seven integers in ascending order, we can write: \(\frac{a+b+c+d+e+f+g}{7}=12\)
Multiply both sides of the equation by \(7\) to get: \(a+b+c+d+e+f+g = 84\)
Since the smallest number is -15, we can write: \((-15)+b+c+d+e+f+g = 84\)
What is the maximum possible value of the largest integer in the set?
In order to maximize the largest integer (aka g), we must MINIMIZE the other values in the sum.
Since each integer must be distinct, the second smallest integer must be -14, and then -13, and so on.
We get: \((-15)+(-14)+(-13)+(-12)+(-11)+(-10)+g = 84\)
Simplify: \((-75)+g = 84\)
Add \(75\) to both sides: \(g = 159\)
Answer: C
Re: The average of 7 distinct integers is 12, and the least of these integ
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06 Apr 2022, 09:31
06 Apr 2022, 09:31
In such questions we often have the trap of distinct or not distinct once that is clear the question becomes easy
x1 x2 x3 x4 x5 x6 x7 , 7 distinct intergers avg = 12 so sum = 84
x1 = -15 since given all are intergers and -15 is thw lowest x2 onwards will be -14 -13 -12 -11 -10 sum = -75
so x7 = x1 to x6 + 84
x7 = 75+84 = 159
x1 x2 x3 x4 x5 x6 x7 , 7 distinct intergers avg = 12 so sum = 84
x1 = -15 since given all are intergers and -15 is thw lowest x2 onwards will be -14 -13 -12 -11 -10 sum = -75
so x7 = x1 to x6 + 84
x7 = 75+84 = 159
