Problem Solving

Hi Sana.noor,

Mitch & Matt have both properly explained the high-concept idea behind this question, so I won't rehash that idea. Instead, I'll offer an alternative. On of the toughest things that you have to face on Test Day is the Countdown Clock. You have just 75 minutes to get the Quant section done, and while 75 minutes is enough time to do what you need to do, if you're staring at the screen (and doing nothing), then you're in trouble.

Certain high-concept questions on the GMAT can be beaten rather easily, by children, who have no knowledge of advanced math. Essentially, the children just "brute force" the question. You can do what I'm about to show you and have the solution relatively quickly.

First, how many ways are there for x, y and z to be positive integers and add up to 9?

117
126
135
144
225
234
333

So, there are 7 sets of numbers.

Now, how many ways are there to match each variable (x, y and z) to a number in each set?

When the 3 numbers are different, such as 234, you'd have:
234
243
324
342
423
432
6 ways

When the 3 numbers include a duplicate, such as 225, you'd have:
225
252
522
3 ways

When the 3 numbers are the same, such as 333, you'd have
333
1 way

With this info and the master list of possibilities, you'd have:
117 3 ways
126 6 ways
135 6 ways
144 3 ways
225 3 ways
234 6 ways
333 1 way

Total: 28 ways

Now, I absolutely love knowing all of the shortcuts, but if you're "stuck" or "unsure" of how a concept works, then you have to be ready to shift tactics. When a question asks for the number of possibilities and the options are obvious limited, sometimes you just have to map out all the options.

GMAT assassins aren't born, they're made,
Rich