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Four consecutive odd integers add up to 72. What is the average of the
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16 May 2022, 04:14
16 May 2022, 04:14
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Four consecutive odd integers add up to 72. What is the average of the smaller three?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 22
(A) 15
(B) 16
(C) 17
(D) 18
(E) 22
Part of the project: Skill Builder Project for a Q170
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: Four consecutive odd integers add up to 72. What is the average of the
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16 May 2022, 08:17
16 May 2022, 08:17
1
The first step in this problem is ensuring you understand the terminology.
Four consecutive odd numbers is a sequence of odd numbers in the order they would appear on a number line, skipping the positive numbers. Some examples of numbers that would fit this criterion would be 1, 3, 5, 7 and -7, -5, -3, -1.
Since the sum is 72, we know that the numbers are positive.
Using the guess and check method, we might start with a number that, roughly, could be 72:
13 + 15 + 17 + 19 = 64.
That's close, but let's go up a little higher. We were off by 8.
15 + 17 + 19 + 21 = 72
Great! The last step is to take the average of the smaller three.
The average is 17 since it's in the middle and they are equidistant from each other. You could check this by doing (15 + 17 + 19)/3.
Therefore, the answer is (C) 17.
Four consecutive odd numbers is a sequence of odd numbers in the order they would appear on a number line, skipping the positive numbers. Some examples of numbers that would fit this criterion would be 1, 3, 5, 7 and -7, -5, -3, -1.
Since the sum is 72, we know that the numbers are positive.
Using the guess and check method, we might start with a number that, roughly, could be 72:
13 + 15 + 17 + 19 = 64.
That's close, but let's go up a little higher. We were off by 8.
15 + 17 + 19 + 21 = 72
Great! The last step is to take the average of the smaller three.
The average is 17 since it's in the middle and they are equidistant from each other. You could check this by doing (15 + 17 + 19)/3.
Therefore, the answer is (C) 17.
Re: Four consecutive odd integers add up to 72. What is the average of the
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16 May 2022, 13:51
16 May 2022, 13:51
It can be done this way:
x= first odd positive integer, therefore the next positive consective odd integer is (x+2) and so on ...
So, the four consecutive odd integers are:
x, (x+2), (x+4), (x+6)
Summing the above to 72:
x + (x+2) + (x+4) + (x+6)=72
x=15
The average of the smaller three is:
(15+17+19)/3 = 17 (C)
x= first odd positive integer, therefore the next positive consective odd integer is (x+2) and so on ...
So, the four consecutive odd integers are:
x, (x+2), (x+4), (x+6)
Summing the above to 72:
x + (x+2) + (x+4) + (x+6)=72
x=15
The average of the smaller three is:
(15+17+19)/3 = 17 (C)
