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Kaushik786
Joined: 20 May 2018
Last visit: 13 Dec 2023
Posts: 71
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Location: India
Schools: Booth '22 Anderson '22 CBS '22 Johnson '22
GMAT 1: 740 Q50 V41
07 Mar 2020, 21:51
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B
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Set Fn gives all factors of n. Set Mn gives all multiples of n less than 1000. Which of the following statements is/are true?
i. F108 ∩ F84 = F12
ii. M12 ∪ M18 = M36
iii.M12 ∩ M18 = M36
iv.M12 ⊂ M6 ∩ M4
A. i, ii and iii only
B. i, iii and iv only
C. i and iii only
D. All statements are true
i. F108 ∩ F84 = F12
ii. M12 ∪ M18 = M36
iii.M12 ∩ M18 = M36
iv.M12 ⊂ M6 ∩ M4
A. i, ii and iii only
B. i, iii and iv only
C. i and iii only
D. All statements are true
07 Mar 2020, 22:07
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This is more a question on Number Systems than on Set Theory.
i) F108 ∩ F84 = Set of all numbers that are factors of both 108 and 84 => this is set of all common factors of 84 and 108 => this is set of numbers that are factors of the Highest Common Factor of 84 and 108. HCF (84, 108) = 12. F108 ∩ F84 = F12. Statement A is true.
ii) M12 will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in M36. So, Statement ii cannot be true.
iii) M12 ∩ M18= Set of all numbers that are multiples of both 12 and 18. => this is set of all common multiples of 12 and 18 => this is set of numbers that are multiples of the least Common Multiple of 12 and 18. LCM (12, 18) = 36. M12 ∩ M18= M36. Statement iii is true.
iv) M6 ⊂ M4 is identical to M12 {Explanation is exactly as we have seen in statement iii}. So, Statement iv is also true. Bear in mind that M12 is a subset of itself. Statement iv is true.
Imo. Ans. B
i) F108 ∩ F84 = Set of all numbers that are factors of both 108 and 84 => this is set of all common factors of 84 and 108 => this is set of numbers that are factors of the Highest Common Factor of 84 and 108. HCF (84, 108) = 12. F108 ∩ F84 = F12. Statement A is true.
ii) M12 will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in M36. So, Statement ii cannot be true.
iii) M12 ∩ M18= Set of all numbers that are multiples of both 12 and 18. => this is set of all common multiples of 12 and 18 => this is set of numbers that are multiples of the least Common Multiple of 12 and 18. LCM (12, 18) = 36. M12 ∩ M18= M36. Statement iii is true.
iv) M6 ⊂ M4 is identical to M12 {Explanation is exactly as we have seen in statement iii}. So, Statement iv is also true. Bear in mind that M12 is a subset of itself. Statement iv is true.
Imo. Ans. B
02 Aug 2022, 14:54
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Looks like a CAT question - moving it to the CAT Forum.
Thx.
Thx.
