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The average (arithmetic mean) of 5 distinct, single digit integers is 5. If two of the integers are discarded, the new

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by BTGmoderatorDC » Tue Feb 16, 2021 7:20 pm

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The average (arithmetic mean) of 5 distinct, single digit integers is 5. If two of the integers are discarded, the new average is 4. What is the greatest of these integers?

(1) Exactly 3 of the integers are consecutive primes.

(2) The least integer is 3.


OA D

Source: Princeton Review
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Re: The average (arithmetic mean) of 5 distinct, single digit integers is 5. If two of the integers are discarded, the n

by swerve » Wed Feb 17, 2021 4:11 pm
BTGmoderatorDC wrote: ↑
Tue Feb 16, 2021 7:20 pm
 The average (arithmetic mean) of 5 distinct, single digit integers is 5. If two of the integers are discarded, the new average is 4. What is the greatest of these integers?

(1) Exactly 3 of the integers are consecutive primes.

(2) The least integer is 3.


OA D

Source: Princeton Review
average of \(5\) distinct integers \(= 5 \Rightarrow\) sum of \(5\) distinct integers \(= 25\)
average of \(3\) distinct integers \(= 4 \Rightarrow\) sum of \(3\) distinct integers \(= 12,\) when \(2\) of the above integers are discarded.

1) Says exactly \(3\) integers are consecutive primes, meaning that only \(3\) of the numbers are prime, so the solution is \(2,3,4,7,8.\) In this case the largest integer can only be \(8.\) Sufficient \(\Large{\color{green}\checkmark}\)

2) The smallest integer is \(3.\)
The solution is \(3,4,5,6,7\) to give \(25,\) and then drop \(6,7\) to give \(12.\) Largest integer is \(7.\) Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, D
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