Set Theory, Calendars, Clocks and Binomial Theorem

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Set Theory: Number of Elements

    Set A comprises all three digit numbers that are multiples of 5, Set B comprises all three–digit even numbers that are multiples of 3 and Set C comprises all three–digit numbers that are multiples of 4. How many elements are present in ?
    1. 420
    2. 405
    3. 555
    4. 480

 

  • Correct Answer
    Choice A. 420

Explanatory Answer

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Detailed Solution

This question is more of a Number Systems question than a Set Theory one!!

Set A = {100, 105, 110, ….995} {5 × 20, 5 × 21, ….. 5 × 199} 180 elements.

Set B = {102, 108, 114, ……996} {6 × 17, 6 × 18, 6 × 19, ….. 6 × 166} 150 elements.

Set C = {100, 104, 108, …..996} {4 × 25, 4 × 26, ….. 4 × 249} 225 elements.

= {120, 150, 180, …..990} All 3-digit multiples of 30 30 elements.

= {108, 120, 132, …..996} All 3-digit multiples of 12 75 elements.

= {120, 140, 160, …..980} All 3-digit multiples of 20 45 elements.

= {120, 180, …..960} All 3-digit multiples of 60 15 elements.

= A + B + C – +

= 180 + 150 + 225 – 30 – 75 – 45 + 15 = 420 Answer choice (a)

Correct Answer: 420.



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