Please solve and illustrate the GRE® Quant problem

[Pondergre]

I would appreciate if anyone would solve and illustrate the solution for me!

What is the total number of three-digit numbers where both the first digit and second digit represent prime numbers?

(A) 80
(B) 160
(C) 200
(D) 240
(E) 320

Thank you and Happy Holiday!

[Shalini_Chabra]

240

[Pondergre]

Thank yu Shalini for the answer.
Could you also show me the process to how to get to the answer. That will be really helpful

[Pondergre]

When I computed the problem, I came up with the answer (B) 160.
Please suggest if the answer is right or not.

Here is how I did it:

There are 4 prime nos. that are single digit. We can not take more than single unit prime number as it will not get three digit numbers. They are 2,3,5,7
Taking 2,3 were first two digits there would be 230-239 and 320-329 desired nos. so hence 20 such numbers.
Taking 2,5 then 20 more numbers, taking 2,7 then 20 more numbers, taking 3,5 then 20 more, taking 3,7 then 20 more, taking 5,7 then 20 more. so, total of 120 such numbers till now.
Last but not least, taking 2,2 then 10 more, 3,3 then 10 more, 5,5 then 10 more, and 7,7 then 10 more.
So, all total of 160 three digit numbers.

[Pomergranatefan]

Actually, this is a permutation/combination problem, which you can solve in a few seconds if you memorize the formulas.

http://en.wikipedia.org/wiki/Permutations_and_combinations

So it says that the first two numbers must be a prime, which means that it is a permutation with repetition (because order matters, and the number can repeat).

So the formula for permutation with repetition is n^r, where n is the number of items to choose from, and r is the number of items we want.

So in this case, we can choose from 2, 3, 5, 7, so n = 4, and we want 2 number so r = 2. So the possible permutations are 4^2 = 16. Then the third number can be any of 10 numbers, so 16 * 10 = 160.

I strongly advise learning the 3 formulas for permutations and combinations outlined in the wikipedia article: permutation with repetitition, permutation w/out repetition, and combination without repetition. They will most likely show up on the test, and you can solve these types of problems in about 15 seconds if you know the formulas.