If the area of a number is defined...

[BTGmoderatorLU]

If the area of a number is defined as the difference between that number's greatest and least prime factors, what is the area of 100 ?

A. 0
B. 2
C. 3
D. 5
E. 9

The OA is C.

Can any expert explain this PS question please? Thanks.

[[email protected]]

Hi LUANDATO,

This question is an example of a 'symbolism' question (although the prompt doesn't include a physical symbol, we are told the 'definition' of a term and then asked to use that knowledge to perform a calculation).

We're told that the "area" of a number is defined as the DIFFERENCE between that number's greatest and least PRIME factors. We're asked to find the "area" of 100.

100 = (4)(25) = (2)(2)(5)(5)
Largest prime factor = 5
smallest prime factor = 2
"area" of 100 = 5 - 2 = 3

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[EconomistGMATTutor]

If the area of a number is defined as the difference between that number's greatest and least prime factors, what is the area of 100 ?

A. 0
B. 2
C. 3
D. 5
E. 9

The OA is C.

Can any expert explain this PS question please? Thanks.

Hi LUANDATO,
Let's take a look at your question.

It is stated in the question that area of the number is defined as the difference between the number's greatest and least prime factors, hence, we will first find write 100 as a product of its prime factors to find out its prime factors.

100 = 2 * 2 * 5 * 5
Therefore, the prime factors of 100 are 2 and 5.
Area of Number = Greatest prime factor - Least prime factor
Area of 100 = 5 - 2 = 3

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.