BTGModeratorVI wrote: ↑Mon Sep 07, 2020 6:58 am
If x, y and z are non-negative integers such that x < y < z, then the equation x + y + z = 11 has how many distinct solutions?
A) 5
B) 10
C) 11
D) 22
E) 78
Answer:
B
Source: GMAT Prep Now
I created this question to show that there can be times when the best (i.e., fastest) way to solve a counting question is by
listing and counting
How do we know when it's not a bad idea to use listing and counting?
The answer choices will tell us (ALWAYS scan the answer choices before beginning any answer choices)
Here, the answer choices are reasonably small, so listing and counting shouldn't take long.
ASIDE: Yes, 78 (answer choice E) is pretty big. However, if you start listing possible outcomes and you eventually list
more than 22 outcomes (answer choice D), you can stop because the answer must be E.
Okay, let's list possible outcomes in a systematic way.
We'll list outcomes as follows:
x, y, z
Since x is the smallest value.
Let's list the outcomes in which
x = 0. We get:
0, 1, 10
0, 2, 9
0, 3, 8
0, 4, 7
0, 5, 6
Now, the outcomes in which
x = 1. We get:
1, 2, 8
1, 3, 7
1, 4, 6
Now, the outcomes in which
x = 2. We get:
2, 3, 6
2, 4, 5
Now, the outcomes in which
x = 3. We get:
3, 4...hmmm, this won't work.
So, we're done listing!
Count the
outcomes to get a total of 10
Answer: B
Cheers,
Brent
