two hard ps questions

[yakiraz]

A) In a certain restaurant there are 4 different dressing. a customer can choose 0,1,2 or 3 different dressing. How many different dressing can a customer choose?

B) A, B, C, and X are prime consecutive positive numbers. what is A+B+C in terms of X.
1)4X+6
2)3X+12
3)3X+5
4)X^2
5)X

please expalin how you got to the answer

[atlantic]

Hi Yakiraz,

A) You can chose 0, 1, 2 or 3 diferent dressings.

If you choose 0, you have only 1 way to dress the meal

If you choose 1, you have 4 ways (or 4C1).

If you choose 2, you have (4C2)

If you choose 3, you have (4C3)

So 1+4+6+4 = 15

OA?

[beeparoo]

A, B, C, and X are prime consecutive positive numbers. what is A+B+C in terms of X.
1)4X+6
2)3X+12
3)3X+5
4)X^2
5)X

please expalin how you got to the answer

Just by looking at the answer choices, I can't help but feel there is some vital information missing from the question stem.
Where did you get this question?

[atlantic]

Sure beeparoo, in B setence is incomplete. Waiting for more information

[Ian Stewart]

A) In a certain restaurant there are 4 different dressing. a customer can choose 0,1,2 or 3 different dressing. How many different dressing can a customer choose?

atlantic definitely has this right, above, and it's worthwhile understanding that method. You can also look at it this way: for each dressing, the customer has 2 choices: use it, or don't. So with no restrictions, the customer has 2^4 = 16 choices of dressing combinations. If he chooses 0, 1, 2 or 3 different dressings, he did not choose 4 different dressings, and there's only one way to choose all four dressings: say yes to everything. Thus there are 16 - 1 = 15 ways to choose 0, 1, 2 or 3.

B) A, B, C, and X are prime consecutive positive numbers. what is A+B+C in terms of X.
1)4X+6
2)3X+12
3)3X+5
4)X^2
5)X

There are no equation-based formulas whatsoever in mathematics that relate any string of primes by addition. Indeed, there are many famous unsolved problems in math about the addition of primes: Goldbach's conjecture, for example. There is no way this question can contain the word 'prime'. My best guess is that the question means to talk about 'odd' numbers, not 'prime' numbers, and that the second answer choice is supposed to have a minus sign, not a plus sign. But that's just a guess. What's the source?

[llewellyn27]

atlantic

Im really confised with this 4C2 etc.

can you please explain further