If a is a positive integer, which of the following can must have more

Question

If a is a positive integer, which of the following must have more unique prime factors than a?

I. a^2
II. 2a
III. a^10

A. I and II
B. I and III
C. II and III
D. III only
E. None

Oppenheimer1945 · Answer

Should be 20a, 20=2^2.5=product of two primes

E is the best choice, but still I'd consider it a poor quality question

sahilsahh · Answer

sorry I made mistake on posting the question

Karmakar30 · Answer

If a is a positive integer, which of the following must have more unique prime factors than a?

I. a^2
II. 2a
III. a^10

A. I and II
B. I and III
C. II and III
D. III only
E. None

Solution: a is a positive integer however it is not mentioned whether a is prime, even or odd. 
Let us assume that a can be written as 
a = 2^x * 3^y * . . . . n^z 
Hence, a shall have prime factors (2,3,. . . n) 
This means that a^n will have the same no. of prime factors irrespective of the power of a.
a^2 and a^10 have the same unique prime factors. 
On the other hand 2a can also have the prime factors if a is a multiple of 2 
a = 2k. Thinking on this line a can be prime if k=1 or else a is even. 
In both the cases a has the same prime factors as 2a. 
Hence, actual answer is none of the above

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If a is a positive integer, which of the following can must have more

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If a is a positive integer, which of the following can must have more

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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