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16 Sep 2014, 01:06
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What is the sum of four consecutive odd integers?
(1) The product of the four integers is 105
(2) The median of the four integers is 4
(1) The product of the four integers is 105
(2) The median of the four integers is 4
16 Sep 2014, 01:06
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Official Solution:
What is the sum of four consecutive odd integers?
(1) The product of the four integers is 105
Factoring 105 gives: \(105 = 3*5*7\). Consequently, the four consecutive odd integers could be 1, 3, 5, and 7. However, be careful not to fall into the trap: the product of four negative integers would also result in a positive number, hence the four consecutive odd integers can also be -1, -3, -5, and -7. Not sufficient.
(2) The median of the four integers is 4
The median of a set with an even number of terms is the average of the two middle terms. Thus, 4 is the average of two consecutive odd integers, which are 3 and 5. Therefore, the four consecutive odd integers are 1, 3, 5, and 7. Sufficient.
Answer: B
What is the sum of four consecutive odd integers?
(1) The product of the four integers is 105
Factoring 105 gives: \(105 = 3*5*7\). Consequently, the four consecutive odd integers could be 1, 3, 5, and 7. However, be careful not to fall into the trap: the product of four negative integers would also result in a positive number, hence the four consecutive odd integers can also be -1, -3, -5, and -7. Not sufficient.
(2) The median of the four integers is 4
The median of a set with an even number of terms is the average of the two middle terms. Thus, 4 is the average of two consecutive odd integers, which are 3 and 5. Therefore, the four consecutive odd integers are 1, 3, 5, and 7. Sufficient.
Answer: B
16 Jul 2020, 09:55
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I think this is a high-quality question and I agree with explanation.
