Set A comprises all three digit numbers that are multiples of 5 Set B comprises all three ndash digi...........

Quantitative Aptitude ( CCS) Set theory

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 A ∪ B ∪ C?

420

405

555

480

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Explanation:

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.

A ∩ B = {120, 150, 180, …..990} ? All 3-digit multiples of 30 ? 30 elements.
B ∩ C = {108, 120, 132, …..996} ? All 3-digit multiples of 12 ? 75 elements.
C ∩ A = {120, 140, 160, …..980} ? All 3-digit multiples of 20 ? 45 elements.

A ∩ B ∩ C = {120, 180, …..960} ? All 3-digit multiples of 60 ? 15 elements.
A ∪ B ∪ C = A + B + C – A ∩ B – B ∩ C – C ∩ A + A ∩ B ∩ C
= 180 + 150 + 225 – 30 – 75 – 45 + 15 = 420