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12 Aug 2025, 08:53
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:48) correct
0% (00:00) wrong based on 1 sessions
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S is the set of all integer multiples of 999. T is the set of all integer multiples of 9,999.
Quantity A
The number of elements in the intersection sets S and T
Quantity B
9
Quantity A
The number of elements in the intersection sets S and T
Quantity B
9
24 Aug 2025, 06:38
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Official Explanation
It may be easier to think about this problem with smaller numbers. For example, if set S contained the multiples of 3—3, 6, 9, 12, 15, 18 ...—and set T contained the multiples of 5—5, 10, 15, 20, 25 ...—then the intersection, or overlap, of the two sets would be the set of all multiples of 15. This set—15, 30, 45, 60 ...—continues indefinitely and is infinite. In general, if one set consists of all multiples of m and another set consists of all multiples of n, then the intersection of the two sets will contain all multiples of the integer, mn, which is an infinite set, as long as neither number is 0. Infinity is greater than 9, so (A) is correct.
Answer: A
It may be easier to think about this problem with smaller numbers. For example, if set S contained the multiples of 3—3, 6, 9, 12, 15, 18 ...—and set T contained the multiples of 5—5, 10, 15, 20, 25 ...—then the intersection, or overlap, of the two sets would be the set of all multiples of 15. This set—15, 30, 45, 60 ...—continues indefinitely and is infinite. In general, if one set consists of all multiples of m and another set consists of all multiples of n, then the intersection of the two sets will contain all multiples of the integer, mn, which is an infinite set, as long as neither number is 0. Infinity is greater than 9, so (A) is correct.
Answer: A
