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07 Oct 2022, 04:00
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N is a positive integer and N=XYZ , where X,Y and Z are unique prime numbers. Which of the following CANNOT be true?
A. N is a multiple of 14
B. N is a multiple of 15
C. N is a multiple of 21
D. N is a multiple of 27
E. N is a multiple of 35
A. N is a multiple of 14
B. N is a multiple of 15
C. N is a multiple of 21
D. N is a multiple of 27
E. N is a multiple of 35
07 Oct 2022, 04:23
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Bunuel
N=XYZ , where X,Y and Z are unique prime numbers
i.e. N may be any anagram of {235} or any anagram of {357} or any anagram of {257} or any anagram of {237}
CONCEPT: For a number to be divisible by 9, sum of the digits of the number must be divisible by 9
2+3+5 = 10 i.e. any anagram formed by these digits will Never be divisible by 3 (hence not divisible by 27 either)
3+5+7 = 15 i.e. any anagram formed by these digits will be divisible by 3 but will Never be divisible by 9 (hence not divisible by 27 either)
2+5+7 = 14 i.e. any anagram formed by these digits will Never be divisible by 3 (hence not divisible by 27 either)
2+3+7 = 15 i.e. any anagram formed by these digits will be divisible by 3 but will Never be divisible by 9 (hence not divisible by 27 either)
i.e. The number formed N=xyz will Never be divisible by 27
Answer: Option D
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11 Oct 2022, 12:06
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N can not have more than 1 prime number because of clause :"where X,Y and Z are unique prime numbers" . if N is a multiple of 27 that means N=3^3 i.e. N will have three 3s that violates our condition.
