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08 Nov 2021, 08:42
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B
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53%
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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.
(1) The sum of two of the numbers chosen is 16.
(2) The sum of two of the numbers chosen is 14.
08 Nov 2021, 08:42
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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
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
