# Lesson: Testing Possible Cases

## Comment on Testing Possible Cases

### Hi Brent,

Hi Brent,

I tried solving it by input-output method and I don't think that's the best approach for it. I chose the following values: m = 3; p = 5; s = 7; v = 2 Yeah, the input-output method MAY help you eliminate some answer choices, but it won't take you all the way to the correct answer.

Here's my full solution: https://gmatclub.com/forum/if-m-p-s-and-v-are-positive-and-m-p-s-v-which...

Cheers,
Brent

### Hey Brent :) Can you give me

Hey Brent :) Can you give me your solution to exercise 390 and 176 in the official 2019 guide? ### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-x-and-y-are-positive-integers-is-the-product-xy-even-75229.html

Hi Brent. I just wanted to say thank you for all these videos and resources. If I had looked at the above linked questions before taking your course, I would have been in shock. But now I am having much much greater success. Good to hear!!

### Hi Brent,

Hi Brent,

statement 1: xy+y=ODD ; y(x+1)=Odd . This implies y= odd and x+1 = odd. If x+1=odd then x= even.(sufficient)

statement 2: 6x-3y=ODD; 3(2x-y)=odd. We know 3 is odd.(2x-y)=Odd ; x can be even or x can be odd. (Not sufficient)

So, opt A is the correct ans. ### That's a perfectly-reasoned

That's a perfectly-reasoned solution. In fact, it's exactly how I'd solve such a question.

That said, if students aren't sure how to proceed with similar questions, they can always just test all possible cases as we have done above.

### If r and s are integers and

If r and s are integers and rs + r is odd, which of the following must be even ?

A. r
B. s
C. r + s
D. rs - r
E. r^2 + s

I drew a table.there are two scenarios
When rs+r is odd...
1/r=odd,s =even,rs+r odd
2/ r=even, S= odd, rs+r odd..
Confused what to do! ### That's a good approach. Let's

That's a good approach. Let's start it from the beginning by testing all four possible cases:

1) r is EVEN and s is EVEN: Here, rs + r is EVEN
2) r is EVEN and s is ODD: Here, rs + r is EVEN
3) r is ODD and s is EVEN: Here, rs + r is ODD
4) r is ODD and s is ODD: Here, rs + r is EVEN

Aha! In your solution, you say that, if r=even and s=odd, then rs+r is odd, but this is not the case.
For example, if r = 0 and s = 1, then rs + r = (0)(1) + 0 = 0, which is even.

As we can see above, case #3 is the only scenario that yields an ODD value of rs + r.
So, it must be the case that r is ODD and s is EVEN

Does that help?

### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-x-and-y-are-integers-is-x-even-226190.html
Basically we test four cases;but in here two cases is being tasted in your solution. Would you please explain? Let's compare this question to the question I answered in the above comments (If r and s are integers and rs + r is odd, which of the following must be even?)
For the rs+r question, we're given the expression rs + r, and our job is to determine the circumstances in which rs + r is odd.
Notice that rs + r is an algebraic EXPRESSION (not an EQUATION).
As such, we can test all 4 possible cases (e.g., r is odd and s is even) to see which case(s) yields an odd value for rs + r

In the other question (If x and y are integers, is x even?), statement 1 tells us that x + y = y⁵
Notice that x + y = y⁵ is an EQUATION.
So, while we COULD try testing all four cases, it's more convenient to rewrite x + y = y⁵ as x = y⁵ - y, and then see what happens to x when y is ODD and when y is EVEN.

That said, we could have also tested all four cases. Let's do that.

1) x is EVEN and y is EVEN:
Here, x + y = y⁵ becomes EVEN + EVEN = EVEN⁵
Simplify: EVEN + EVEN = EVEN
This works.

2) x is EVEN and y is ODD:
Here, x + y = y⁵ becomes EVEN + ODD = ODD⁵
Simplify: EVEN + ODD = ODD
This works.

3) x is ODD and y is EVEN:
Here, x + y = y⁵ becomes ODD + EVEN = EVEN⁵
Simplify: ODD + EVEN = EVEN
Does NOT work.

4) x is ODD and y is ODD:
Here, x + y = y⁵ becomes ODD + ODD = ODD⁵
Simplify: ODD + ODD = ODD
Does NOT work.

Cases 1 and 2 are the only ones that work.
In both cases, x is EVEN, so we can answer the target question with certainty.

Does that help?

Cheers,
Brent

### If n is a positive integer,

If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even

can you pls explain when it is divisible by 3 for e.g
when n is odd 3*4*5 = 60 its div by 3 ... then why ans E ... ### Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/if-n-is-a-positive-integer-then-n-n-1-n-2-is-...
Please let me know if you have any questions about my solution.