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06 Dec 2021, 07:47
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\(x\) and \(y\) are integers from 0 to 170, both inclusive. For how many ordered pairs \((x,y)\) is the average (arithmetic mean) of \(x\) and \(y\) equal to 60 ?
A. \(60\)
B. \(118\)
C. \(119\)
D. \(120\)
E. \(121\)
A. \(60\)
B. \(118\)
C. \(119\)
D. \(120\)
E. \(121\)
06 Dec 2021, 07:47
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Official Solution:
\(x\) and \(y\) are integers from 0 to 170, both inclusive. For how many ordered pairs \((x,y)\) is the average (arithmetic mean) of \(x\) and \(y\) equal to 60 ?
A. \(60\)
B. \(118\)
C. \(119\)
D. \(120\)
E. \(121\)
The average (arithmetic mean) of \(x\) and \(y\) is 60 means that the sum of \(x\) and \(y\) is 120.
\(x+y=120\).
\(x\) and \(y\) are integers from 0 to 170, both inclusive, so \((x,y)\) can be:
\((0,120)\);
\((1,119)\);
\((2,118)\);
\((3,117)\);
\(...\)
\((120,0)\).
So, there are total of 121 such pairs.
Answer: E
\(x\) and \(y\) are integers from 0 to 170, both inclusive. For how many ordered pairs \((x,y)\) is the average (arithmetic mean) of \(x\) and \(y\) equal to 60 ?
A. \(60\)
B. \(118\)
C. \(119\)
D. \(120\)
E. \(121\)
The average (arithmetic mean) of \(x\) and \(y\) is 60 means that the sum of \(x\) and \(y\) is 120.
\(x+y=120\).
\(x\) and \(y\) are integers from 0 to 170, both inclusive, so \((x,y)\) can be:
\((0,120)\);
\((1,119)\);
\((2,118)\);
\((3,117)\);
\(...\)
\((120,0)\).
So, there are total of 121 such pairs.
Answer: E
Engineer1
Joined: 01 Jan 2014
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07 Jan 2024, 09:18
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Bunuel
Hi Bunuel, what is ordered pair? I have considered for instance, (1,119) the same as (119,1). Hence, my answer is not correct.
MartyMurray
Thanks!
