a really good question for practice

sana.noor wrote:In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?

$3
$4
$7
$11
$51

IMPORTANT: Asking for the difference between Product Y’s sale price and cost per unit is the same as asking for the amount of profit per unit.

The average profit (over 7 days) is $5304 per day
So, the total profit for the week = ($5304)(7)
Since we know that q units were sold, we can say: (profit per unit)(q units) = ($5304)(7) profit
Rearrange to get: q = ($5304)(7)/(profit per unit)
Since q is an integer, the profit per unit must divide "nicely" into ($5304)(7)
Since (5304)(7) = (2)(2)(2)(3)(7)(13)(17), we can see that 3, 4, 7 and 51 (which equals 3x17) all divide nicely into the total profit for the week.

This leaves us with [spoiler]$11[/spoiler], so the correct answer is D

Cheers,
Brent

Hi sana.noor,

Brent provides a really nice explanation that focuses on prime factorization. In the event that you don't "see" that approach in these types of questions, then you can still do the basic arithmetic and solve. With those "brute force calculations", there are some math shortcuts that exist that can speed you up.

For example, the "rule of 3" - if the digits of a number are summed, and that sum is divisible by 3, then the big number is divisible by 3.

For example, you KNOW that 27 is divisible by 3. Using the rule of 3 though, you'll see that 2+7 = 9; since 9 is divisible by 3, then 27 is divisible by 3.

5304 per day = 5+3+0+4 = 12; 12 is divisible by 3, so 5304 is divisible by 3

By learning these Special Math Rules, you'll be able to work through many of the specific calculations that the GMAT will throw at you in a much faster way.

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

Hi sana.noor,

The easiest way to avoid silly mistakes is to write EVERYTHING down on the pad. Label and organize your work. The time you invest in note-taking is relatively minor, but has the added benefit of saving you time later on (while you're in the middle of working on a question). It's also tough to make a silly mistake when you can SEE what you're working on.

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