If D={x:x is a positive multiple of 7 less than 50}, how many elements does D have?
Answer and explanation
Correct answer: 7
The governing idea is counting positive multiples of a fixed number subject to an upper bound. The positive multiples of 7 are 7×1, 7×2, 7×3, and so on. We need 7k<50 with k a positive integer. Dividing by 7 gives k<50/7≈7.14, so k can be 1,2,3,4,5,6, or 7. The corresponding elements are 7, 14, 21, 28, 35, 42, and 49, which makes seven distinct elements. The next multiple, 7×8=56, is already greater than 50 and is excluded. Therefore option B, 7, is correct. Zero is not positive, and the strict phrase “less than 50” would exclude 50 even if it were a multiple.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The governing idea is counting positive multiples of a fixed number subject to an upper bound. The positive multiples of 7 are 7×1, 7×2, 7×3, and so on. We need 7k<50 with k a positive integer. Dividing by 7 gives k<50/7≈7.14, so k can be 1,2,3,4,5,6, or 7. The corresponding elements are 7, 14, 21, 28, 35, 42, and 49, which makes seven distinct elements. The next multiple, 7×8=56, is already greater than 50 and is excluded. Therefore option B, 7, is correct. Zero is not positive, and the strict phrase “less than 50” would exclude 50 even if it were a multiple.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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