# Lesson: Variables in the Answer Choices

## Comment on Variables in the Answer Choices

### For the second question, with

For the second question, with the rectangle, couldn't we use x=3 and the adjacent side =2? That would mean that the area is 6, as you have in your example, but answer choice A would work because it would be 10-(2 squared).

### I think you mean that, if we

I think you mean that, if we make x = 2, (and the other side = 3), then the area is still 6. In this case answer choice A also works (as does answer choice E). We get:

A) 10 - x² = 10 - 2² = 6 (works)
E) x(5 - x) = 2(5 - 2) = 6 (works)

If that's what you meant, you're absolutely right. That's the downside of the INPUT-OUTPUT approach. Sometime more than one answer choice yields the correct output.

In such cases, we must go back and input another x-value so that we can eliminate either A or E.

Cheers,
Brent

### For the below question

For the below question
http://greprepclub.com/forum/qotd-18-if-j-and-k-are-even-integers-and-j-k-which-of-the-2651.html

i used j = 2 and k = 8

for that option A yield 2
and option d yield 6

since they asked for even integer greater than j and less than k, i choose d as answer.

in your case when j = 0 and k = 2

option A = 0, and option D = 2.

you had picked option A. may i please know how did you choose
A as answer. 0 equal to j not greater than j.

### When I used j = 0 and k = 2,

When I used j = 0 and k = 2, the answer to the question (What is the number of even integers that are greater than j and less than k ?) is 0. So, when I plugged j = 0 and k = 2 into each answer choice, I was looking for the one that yielded 0 as the OUTPUT.

Only answer choice A met that condition.

On the other hand, you are using j = 2 and k = 8 (which is totally find). In your case, the answer to the question (What is the number of even integers that are greater than j and less than k ?) is 2 (since there are 2 even integers between 2 and 8). So, when you plug j = 2 and k = 8 into each answer choice, you are looking for the one that yielded 2 as the OUTPUT.

Only answer choice A meets that condition.

I'm not sure where you got the 6 from.

Thanks for your patient response, Brent!

I am not reading question properly, being anxious to run out of short time, it will be a big problem. Silly mistakes will pay great cost. I have to give more importance to understand questions correctly.

### I used a slightly different

I used a slightly different approach, using all sides of the perimeter, two sides of (x) and two sides of (y); so, 10 = 2x +2y, or 10-2x = 2y which divided by two yields the value of y=(5-x). Given that the area of a rectangle is bh or (x)(y), we arrive at the fact that A = x (5-x).

### Perfect reasoning! Nice work,

Perfect reasoning! Nice work, Omar!

### https://greprepclub.com/forum

Can this be solved using double matrix

Yes, we can definitely use the Double Matrix to solve this.
Give it a try!

Cheers,
Brent

No solution

### https://greprepclub.com/forum

https://greprepclub.com/forum/if-p-pencils-cost-c-cents-at-the-same-rate-how-many-3599.html

### https://greprepclub.com/forum

https://greprepclub.com/forum/if-p-pencils-cost-c-cents-at-the-same-rate-how-many-3599.html
When I try to use the input output method
Using P=2
C=2
D=3
So I get 3 and apply the method for each answer I don’t get the right amount.
I don’t know what I am missing.

### GIVEN: If p pencils cost c

GIVEN: If p pencils cost c CENTS, at the same rate, how many pencils can be bought for d DOLLARS?
If p = 2 and c = 2, then each pencil costs 1 CENT
If d = 3, then we are spending 3 DOLLARS
So, at 1 CENT per pencil, we can buy 300 pencils (not 3 pencils) with 3 DOLLARS.

Cheers,
Brent

### Regarding: https:/

Regarding: https://greprepclub.com/forum/if-p-pencils-cost-c-cents-at-the-same-rate-how-many-3599.html

"If p pencils cost c cents at the same rate"

What do they mean by "at the same rate". I've never seen this use of "at the same rate" before, and it's not clear to me what they are trying to convey.

In real life, I've never heard anyone say, for example, "These tickets cost \$20 dollars at the same rate", or "These tacos cost \$5 at the same rate." Same rate as what?

Good catch, Kevin. I never noticed the awkward writing the first time around.
You're absolutely right; the question is poorly worded.
The intent was to express the idea that the PRICE PER PENCIL (i.e., the RATE) is constant throughout.

Here's one way we might rewrite the question:
p pencils cost c cents. At that rate (cost per pencil), how many pencils can be bought for d dollars?

Cheers,
Brent