cost of p pens is d dollars

sanju09 wrote:The unit cost of pens is the same regardless of how many pens are purchased. If the cost of p pens is d dollars, what is the cost, in dollars, of x pens?
(A) xd
(B) xpd
(C) xd/p
(D) xp/d
(E) pd/x

With these "Variables in the Answer Choices" questions, we typically have 2 options.
1) Use algebra
2) Plug in numbers

I'll demonstrate the plugging-in-numbers approach.

If the cost of p pens is d dollars, what is the cost, in dollars, of x pens?
First plug in some nice numbers that work. Say...
If the cost of 5 pens is 10 dollars, what is the cost, in dollars, of 20 pens?
We can see that the cost of 20 pens will be 40 dollars.
In other words, when p=5, d=10 and x=20, then the output(answer to the question) will be 40

Now we check then answer choices to see which one yields an output of 40
(A) xd --> (20)(10) = 200 NO - eliminate
(B) xpd --> (20)(5)(10) = 1000 NO - eliminate
(C) xd/p --> (20)(10)/(5) = 40 YES - keep
(D) xp/d --> (20)(5)/(10) = 10 NO - eliminate
(E) pd/x --> (5)(10)/(20) = 2.5 NO - eliminate

So, the answer must be C

Cheers,
Brent

sanju09 wrote:The unit cost of pens is the same regardless of how many pens are purchased. If the cost of p pens is d dollars, what is the cost, in dollars, of x pens?

There is another tricky way to solve this problem which is not very much efficient for a simple problem like this but this may help to solve some tough problems very easily.

The method utilizes the concept of units and dimensions.
Note that the problem is asking for cost of x pens in dollars. Hence, whatever our correct answer is, its unit must be dollars.

Now note that only options C and E are in dollars.
As in both cases, the unit is (Np. of pens)*(dollars)/(No. of pens) = dollars

In other cases the unit is different.
For example, the unit of option A is (No. of pens)*(dollars).

Now pick some number as Brent did and eliminate either of C or E.