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19 Dec 2015, 03:08
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n = a^3 * b^4
if a number is written in the form of the powers of its prime factors then total factors for that number are calculated by increasing powers of each prime number by 1 and multiplying all of them.
(1) a and b are prime numbers - SUFFICIENT
n will have (3+1)*(4+1) = 4*5 = 20 factors.
(2) n has only prime factors 5 and 7 - SUFFICIENT
here it wont matter if a = 5 or 7 or b = 5 or 7. we only need powers of prime numbers. hence n will have 20 factors.
Option D is the correct answer.
if a number is written in the form of the powers of its prime factors then total factors for that number are calculated by increasing powers of each prime number by 1 and multiplying all of them.
(1) a and b are prime numbers - SUFFICIENT
n will have (3+1)*(4+1) = 4*5 = 20 factors.
(2) n has only prime factors 5 and 7 - SUFFICIENT
here it wont matter if a = 5 or 7 or b = 5 or 7. we only need powers of prime numbers. hence n will have 20 factors.
Option D is the correct answer.
19 Dec 2015, 03:39
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n=a^3∗b^4, To find the number of factors of n.
Lets take choice 1.
(1) a and b are prime numbers
Since both a and b are prime numbers, then number of factors of n will be (3+1)(4+1)=4*5=20 factors.
This choice is sufficient.
(2) n has only prime factors 5 and 7.
Again, since both a and b are prime numbers, then number of factors of n will be (3+1)(4+1)=4*5=20 factors.
This choice is sufficient.
Each statement Alone is sufficient to answer the question and therefore choice D.
Lets take choice 1.
(1) a and b are prime numbers
Since both a and b are prime numbers, then number of factors of n will be (3+1)(4+1)=4*5=20 factors.
This choice is sufficient.
(2) n has only prime factors 5 and 7.
Again, since both a and b are prime numbers, then number of factors of n will be (3+1)(4+1)=4*5=20 factors.
This choice is sufficient.
Each statement Alone is sufficient to answer the question and therefore choice D.
19 Dec 2015, 05:44
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N=a^3*b^4
1) Sufficient, (3+1)*(4+1) = 20 factors
2) n has only 5, 7 as prime factors.. again we have 20 factors.. so D ans
1) Sufficient, (3+1)*(4+1) = 20 factors
2) n has only 5, 7 as prime factors.. again we have 20 factors.. so D ans
