If a, b, c and n are positive integers and m = a^4*b^3*c^n, how many

Question

If a, b, c and n are positive integers and  m=a^4*b^3*c^n , how many factors does m have?

(1) a, b, and c are prime numbers

(2) n = 2

Archit3110 · Answer

given that 
a, b, c and n are positive integers and  m=a^4*b^3*c^n , how many factors does m have
#1
 a, b, and c are prime numbers
factors will vary because its not clear whether a,b,c are all different or same prime numbers
insufficient
#2
n=2
a,b,c are not known
from 1 &2
we cannot determine factors of m because a,b,c values are not known , though prime they are but value is not known
option E

krish0709 · Answer

Bunuel  Don't you think the answer should be C?

Statement 1 : a,b & c are prime numbers  (NOT SUFFICIENT)

Statement 2: n=2  (NOT SUFFICIENT)

Combing 1 & 2,
The number of factors of a number when it is in the above form (question), then the number of factors are (4+1)*(3*1)*(n+1)
Since we know n is 2 and a,b,c are prime we can get the number of factors.

Bunuel · Answer

The point is, unless explicitly stated otherwise, different variables can represent the same number. So, a, b, and c could all be different, two of them could be the same while the third is different, or all three could be the same. These scenarios would result in different answers to the question. That’s why the correct answer is E.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:
 
 Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this and similar questions.

Hope it helps.

djangobackend · Answer

I understood that B isn't sufficient since we don't know if A,B,C are prime factorised forms or not. 
together then I thought that yes A,B,C, are prime numbers and hence we have N as well so sufficient, BUT answer will be different depending if A,B,C are same or different 
SAY if a=b=c=3 then 3^4 * 3^3 * 3^2 = 3^9 so factors = 10 
whereas if a=2, b=3, c=5 then 2^4 * 3^3 * 5^2 = 5*4*3 = 60 
 
LEARNING - we can only apply the factors formula only on prime factorised forms. and all prime factors in the factorised form should be different, if they are same then first club them together before using the formula. Also, always make sure to check the constraints, here for example we were not given that all numbers are different and that's what was exactly tested.

bumpbot · Answer

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If a, b, c and n are positive integers and m = a^4b^3c^n, how many

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