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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.
(1) Exactly 3 of the integers are consecutive primes.
(2) The least integer is 3.
03 Sep 2012, 03:45
Kudos
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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.
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.
General Discussion
raghupro
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WE:Business Development (Computer Software)
02 Oct 2012, 00:55
Kudos
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Bunuel
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.
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.
The question does not mention that the integers are positive. What about the case where integers are negative?
