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05 Jun 2021, 04:40
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B
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Ten slips of paper, numbered 1 through 10, are placed in a bag. If three slips are chosen at random from the bag without replacement and one of the slips chosen is numbered 7, what is the sum of numbers on the three chosen slips of paper?
(1) The sum of two of the numbers chosen is 16.
(2) The sum of two of the numbers chosen is 14.
M36-58
(1) The sum of two of the numbers chosen is 16.
(2) The sum of two of the numbers chosen is 14.
Ten slips of paper, numbered 1 through 10, are placed in a bag. If three slips are chosen at random from the bag and one of the slips chosen is numbered 7, what is the sum of numbers on the three slips of paper?
(1) The sum of two of the numbers is 16.
(2) The sum of two of the numbers is 14.
(1) The sum of two of the numbers is 16.
(2) The sum of two of the numbers is 14.
M36-58
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08 Nov 2021, 08:43
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Bunuel
Official Solution:
Ten slips of paper, numbered 1 through 10, are placed in a bag. If three slips are chosen at random from the bag without replacement and one of the slips chosen is numbered 7, what is the sum of the numbers on the three chosen slips of paper?
(1) The sum of two of the numbers chosen is 16.
If one of those two numbers is 7, then another is 9 and the third number can be any other remaining integers. So, the sum can take more than one value. Not sufficient.
(2) The sum of two of the numbers chosen is 14.
7 cannot be among those two numbers because in this case another number would also had to be 7, which cannot be the case because the three numbers chosen must be distinct (we are choosing from distinct numbers without replacement). Thus, 7 is the third number and the sum is 14 + 7 = 21. Sufficient.
Answer: B
General Discussion
05 Jun 2021, 05:55
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We have a set of three different numbers from between 1 and 10, and want their sum. Using Statement 1, two of the numbers could be 7 and 9. Then the third number could be any other integer from 1 through 10, and many sums are possible.
Using Statement 2, we know two of our numbers sum to 14. It can't be true that the '7' we know we selected is one of those two numbers, because then the other number would also need to be 7, and we know that our three numbers are all different (the selections were made without replacement). So it must be true that the two numbers not equal to 7 are the two numbers that sum to 14, and the three numbers must sum to 7 + 14 = 21. So the answer is B.
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Using Statement 2, we know two of our numbers sum to 14. It can't be true that the '7' we know we selected is one of those two numbers, because then the other number would also need to be 7, and we know that our three numbers are all different (the selections were made without replacement). So it must be true that the two numbers not equal to 7 are the two numbers that sum to 14, and the three numbers must sum to 7 + 14 = 21. So the answer is B.
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