Hi RiyaR,
This DS question is a great "concept" question, meaning that if you understand the concept, then you won't have to do much math to answer the question.
The prompts tells us that there are N people standing on a line and asks us for the value of N. The information in each of the two Facts discusses the number of ways to arrange this unknown number of people, which means that we're dealing with simple Permutation math. This type of math has some limitations worth noting:
If there are....
2 people, the there are 2 ways to arrange them in line
3 people, then there are 3(2)(1) = 6 ways
4 people, then there are 4(3)(2)(1) = 24 ways
5 people, then there are 5(4)(3)(2)(1) = 120 ways
Etc.
If you know the number of people, then you can determine the number of ways that you can arrange them. ALSO, if you know the number of possible arrangements, then you can figure out how many people there are!
Fact 1: If there was 1 more person, then there would be 5040 different arrangements.
If we continued increasing the number of people and doing the calculations (in the above table), then we would eventually find the exact number of people needed to create 5040 arrangements. We could then subtract 1 to get the value of N.
Fact 1 is SUFFICIENT
Fact 2: If there were 2 fewer people, then there would be 24 different arrangements.
From the above table, we know that 4 people --> 24 arrangements. With the info in Fact 2, we know that there must be 6 people in line.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
