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DisciplinedPrep
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Set A contains all multiples of 4 less than 500, Set B 21 Dec 2020, 10:38
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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:

95% (hard)

Question Stats:

51% (02:42) correct 49% (03:21) wrong based on 97 sessions

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Set A contains all multiples of 4 less than 500, Set B contains all odd multiples of 7 less than 500, and Set C comprises all multiples of 6 less than 500. How many elements are present in A ∪ B ∪ C?

A. 186
B. 202
C. 220
D. 228
E. 243
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B
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Set A contains all multiples of 4 less than 500, Set B 21 Dec 2020, 11:37
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Set A contains all multiples of 4 less than 500, Set B contains all odd multiples of 7 less than 500, and Set C comprises all multiples of 6 less than 500. How many elements are present in A ∪ B ∪ C?

A. 186
B. 202
C. 220
D. 228
E. 243

if you consider 0 as multiple of 4 and 6 then answer comes out to be 203 , hope the question asks only positive multiples
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Set A contains all multiples of 4 less than 500, Set B 21 Dec 2020, 21:28
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B. 202


Multiples of 4 (4x125=500)............ 124
Multiples of 7 (7x70=490)...70/2+1...36
Multiples of 6 (6x82=492)...82/2+1...42 (note that even multiples of 6 are also multiples of 4)

Add 124+36+42=202
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Set A contains all multiples of 4 less than 500, Set B 21 Dec 2020, 21:33
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Zero is universal multiple of any number , so until and unless positive multiples is told zero is considered so basically this question is faulty and just for practice can’t be official one

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Set A contains all multiples of 4 less than 500, Set B 22 Dec 2020, 02:52
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DisciplinedPrep
Set A contains all multiples of 4 less than 500, Set B contains all odd multiples of 7 less than 500, and Set C comprises all multiples of 6 less than 500. How many elements are present in A ∪ B ∪ C?

A. 186
B. 202
C. 220
D. 228
E. 243
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Assuming we are talking about positive multiples:

1 to 500

All multiples of 4 -> 500/4 = 125
The last multiple is 500 which we should not include since we need multiples less than 500.
Hence 124 multiples.

All odd multiples of 7
First, let's find all multiples of 7.
500/7 = 71
First multiple is odd, then even, then odd and so on till 71st multiple which is odd.
Hence 36 odd multiples. Since they are odd, they will have 0 overlap with multiples of 4 and/or 6.

All multiples of 6 -> 500/6 = 83
First multiple is odd, then even, then odd and so on till 83rd multiple which is odd. (e.g. 6, 12, 18, 24, 30, 36 ...)
Every odd multiple will be divisible by 2 and every even multiple will be divisible by 4. The even multiples are already counted above while counting all multiples of 4. So ignore them.
We have 42 odd multiples of 6.

A ∪ B ∪ C = 124 + 36 + 42 = 202

Answer (B)
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Set A contains all multiples of 4 less than 500, Set B 28 Jul 2025, 08:25
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Should the question read all odd multiples of 6 less than 500?
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