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# The average of the four integers in Set X is 5. If the greatest value

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Math Expert
Joined: 02 Sep 2009
Posts: 48051
The average of the four integers in Set X is 5. If the greatest value  [#permalink]

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12 Apr 2018, 21:32
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Difficulty:

55% (hard)

Question Stats:

41% (01:06) correct 59% (01:04) wrong based on 56 sessions

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The average of the four integers in Set X is 5. If the greatest value of any term in Set X is 7, what is the value of the least term in Set X?

A. -2
B. -1
C. 1
D. 2
E. 4

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Re: The average of the four integers in Set X is 5. If the greatest value  [#permalink]

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12 Apr 2018, 22:34
1
Bunuel wrote:
The average of the four integers in Set X is 5. If the greatest value of any term in Set X is 7, what is the value of the least term in Set X?

A. -2
B. -1
C. 1
D. 2
E. 4

Average of 4 integers = 5

i.e. Sum of those 4 integers = 5*4 = 20

Greatest of them = 7

i.e. Sum of the other 3 = 20-7 = 13

For the least value of one of the integers other 2 integers must be maximised as the sum is fixed at 13

i.e. a+b+c = 13

$$a_{min} + b_{max} + c_{max} = 13$$

i.e. $$a_{min} + 7+7 = 13$$

i.e. $$a_{min} = -1$$

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Re: The average of the four integers in Set X is 5. If the greatest value  [#permalink]

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13 Apr 2018, 00:37
Bunuel wrote:
The average of the four integers in Set X is 5. If the greatest value of any term in Set X is 7, what is the value of the least term in Set X?

A. -2
B. -1
C. 1
D. 2
E. 4

In total we have 4 terms. Sum of the 4 terms is (4*5)=20

now in this question we are asked to make a term least. if we want to make a term least other three terms must be maximized then. it is given that greatest value is 7 in the set.
so, maximum value of the 3 terms = 7*7*7=21

now, we can deduct 21 from the sum of 4 integers.

so, we are left with (20-21)=-1
so, the least vale is -1.
Option B is the correct answer.
Director
Joined: 02 Oct 2017
Posts: 616
Re: The average of the four integers in Set X is 5. If the greatest value  [#permalink]

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26 Apr 2018, 21:01
Max value of any integer is 7

To calculate least we make other three max ..ie 7
so sum now is 7*3=21
But actual sum is 20 so least value is 20-21=-1

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Re: The average of the four integers in Set X is 5. If the greatest value &nbs [#permalink] 26 Apr 2018, 21:01
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