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The average (arithmetic mean) of 5 distinct, single digit integers is

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Re: The average (arithmetic mean) of 5 distinct, single digit integers is [#permalink]

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New post 04 Jan 2017, 02:48
AnitaBhatt wrote:
I don't understand why the answer is D. I think the answer should be B.

I evaluated it as follows:
avg of 5 distinct integers = 5 => sum of 5 distinct integers = 25
avg of 3 distinct integers = 4 => sum of 3 distinct integers = 12, when 2 of the above integers are discarded.

(1) Exactly 3 of the integers are consecutive primes.
I got 3 solutions for this case: 2,3,5,7,8 or 2,3,4,7,8 or 3,4,5,6,7
therefore the largest integer can be either 8 or 9 => insufficient.

Unless, because (1) says exactly 3 integers are consecutive primes, meaning that only 3 of the nos. are prime, that eliminates 2 scenarios I mentioned and the solution can only be 2,3,4,7,8. In this case the largest integer can only be 8 => sufficient!

(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!

Sorry, I guess I answered my own question, the answer is D.


For more you can check the following posts:
the-average-of-5-distinct-single-digit-integers-is-5-if-138274.html#p1118237
the-average-of-5-distinct-single-digit-integers-is-5-if-138274.html#p1290690

They address the doubt you had.
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Re: The average (arithmetic mean) of 5 distinct, single digit integers is [#permalink]

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New post 10 Aug 2017, 01:01
What is tested is whether you are able to figure out the solution by considering all the conditions given.

Statement 1:

The three consecutive primes could be, 2, 3,5. The remaining numbers can only be 6 and 9. But we need three numbers that add up to 13 which we do not have in this case. Condition not satisfied.

The other possibility is the three consecutive primes could be 3,5 and 7. Then the other two numbers are 4 and 6. This satisfies all the conditions. So sufficient

Statement 2:

The least of all is 3. The remaining 4 numbers should add up to 22 and satisfy the other conditions. The numbers can only be 4,5,6,7. So sufficient.

Answer D.
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Re: The average (arithmetic mean) of 5 distinct, single digit integers is [#permalink]

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New post 11 Aug 2017, 09:08
Bunuel wrote:
Correct answer must be D, not A.

The average of 5 distinct single digit integers is 5. If two of the integers are discarded, the new average is 4. What is the largest of the 5 integers?

From the stem:
The sum of 5 distinct single digit integers is 5*5=25;
The sum of 3 of the integers is 3*4=12;
The sum of the other 2 of the integers is 25-12=13.

(1) Exactly 3 of the integers are consecutive primes. We can have two cases:

Case 1
The three consecutive primes are: 2, 3 and 5 --> 2+3+5=10.
The remaining 2 integers could be: 0, 1, 4, 6, 8 or 9 (notice that neither of the remaining 2 integer can be 7, since in this case we would have 4 consecutive primes, not 3). The sum of these two integers must be 25-10=15. From the list, only two integers whose sum is 15 are 6 and 9 (6+9=15).
Now, in this case the 5 integers would be {2, 3, 5, 6, 9}, but no 2 integers from the list give the sum of 13, thus the case when 3 consecutive primes are 2, 3 and 5 is not possible.

Case 2
The three consecutive primes are: 3, 5, and 7 --> 3+5+7=15.
The remaining 2 integers could be: 0, 1, 4, 6, 8 or 9 (notice that neither of the remaining 2 integer can be 2, since in this case we would have 4 consecutive primes, not 3). The sum of these two integers must be 25-15=10. From the list, there are two pairs of integers whose sum is 10: (1, 9) and (4, 6).
Now, in this case the 5 integers would be {1, 3, 5, 7, 9} or {3, 4, 5, 6, 7}. From the first list there are no 2 integers whose sum is 13. In the second list, such two integers are 6 and 7.

Hence, the 5 integers are {3, 4, 5, 6, 7}. Sufficient.

(2) The smallest integer is 3. The sum of the other 4 integers, each of which must be greater than 3, must be 25-3=22. Only 4+5+6+7=22 is possible (the sum of any other 4 integers will be more than 22), so the 5 integers are {3, 4, 5, 6, 7}. Sufficient.

Answer: D.

Hope it's clear.


Hey Bunuel ,
This is a trial and error based approach and is very time consuming. Is there a more logical and crisp approach to this? Something algebraic, maybe? :)
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Re: The average (arithmetic mean) of 5 distinct, single digit integers is [#permalink]

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New post 13 Sep 2017, 00:18
For the 2nd statement
The case 3,5,8,2,7 is also valid
Total 25 avg 5
Remove 8,5 avg 4

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Re: The average (arithmetic mean) of 5 distinct, single digit integers is   [#permalink] 13 Sep 2017, 00:18

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The average (arithmetic mean) of 5 distinct, single digit integers is

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