kiennguyen-
The question and prompts should be a type of red flag to you. If they aren't yet, they will be after you review additional problems.
The stem sets up a basic problem (that the GMAT will expect any test taker to recognize) in:
x=#pencils, y=#pens, C=total cost; .23x + .21y = C
You see that you have three variables (x, y, C).
Prompt 1 tells you x + y.
Prompt 2 tells you C.
You should instantly be cautious when the question is very easy to interpret, and you are given exactly what you need (3 equations with 3 variables). The instinct is the say "C".
However, you haven't accurately validated Prompt 2 by itself.
A red flag should be that 21 and 23 are not "easy" numbers (like 3 and 4, 2 and 5, etc.) that could have multiple combinations to form a total (in this case 130). There may be only 1 value for each x and y that works for our stem equation (.23x + .21y = C).
So, let's test it:
.23x + .21y = C
Let's quickly find the highest possible value for x or y. Since the price of y < price of x, y has the potential to be greater that x.
So, let's divide 21 into 130. At most, this will be 6R4. So, y must be <=5.
If y=5, x=(130-(5*21))/23 = 25/23 Fail (must divide evenly)
If y=4, x=(130-(4*21))/23 = 46/23 = 2 This is possible
If y=3, x=(130-(3*21))/23 = 67/23 Fail
If y=2, x=(130-(2*21))/23 = 88/23 Fail
If y=1, x=(130-(1*21))/23 = 109/23 Fail
So, y=4 is the only solution. And in that solution, x=2.
So, the answer is B.
You don't need all the algebra to solve this. You just need to recognize the initial "tricky" premise of the question. And, you need to do a bit of validation.
Hope that helps clear it up.
