gmat1393 wrote:

A certain electronics store purchased 500 tablets for $150 each. If it sold some tablets at a profit of 20% and the rest at a profit of 40%, then how many tablets were sold at 40% profit?

(1) Had the store sold all the tablets at a profit of 30%, then its gross profit would have been 6.25% lower than the current gross profit.

(2) The gross profit from the 40% lot were three times the gross profit from the 20% lot.

Fun problem! I'm going to give the interesting / easy solution first, and the boring / long one second.

First solution:

This is actually sort of like a weighted averages problem. Notice that we're combining two groups: a group of tablets (group A) with a 20% profit, and a group of tablets (group B) with a 40% profit. We want to know the profit of the groups combined.

It's like a weighted average, because if group A and group B had exactly the same number of tablets, then the profit would be exactly in the middle of the two groups, at 30%.

If group A had more tablets, the profit would be closer to 20%.

If group B had more tablets, the profit would be closer to 40%.

And, if you knew the overall % profit, you'd be able to work out the ratio of group A to group B. (For example, if the profit was 25% overall, that's 3 times closer to 20% than to 40%. So, group A would be 3 times as big as group B.) Since we already know the total number of tablets, that would tell us the number of tablets in each group.

Statement 1: You could use this to figure out the actual overall percent profit. So, you can use it to figure out the ratio of A to B. Since you know the overall number of tablets, that's enough to figure out the size of group B. Sufficient.

Statement 2: Each tablet from group B brings in twice as much profit as each tablet from group A. However, the tablets from group B actually brought in

three times as much profit overall. Therefore, there must have been more tablets in group B than in group A. Using the actual numbers, you'd be able to figure out how many exactly - so, this is sufficient.

The answer is D.

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Here's the boring/mathematical answer. I really encourage you to try to use the thinking from the answer above, instead!

a of the 500 tablets were sold for a profit of 20%,

b were sold for a profit of 40%. That means some earned a profit of (.2)(150) and others earned a profit of (.4)(150).

Statement 1: 30%(150*500) is 6.25% lower than the actual profit. So, .3(150*500) = .9375(actual profit). Therefore, the actual profit can be calculated.

Knowing the actual profit, and given the info from the question stem, you have two equations:

actual profit = .2(150)(a) + .4(150)(b)

a + b = 500

Since 'actual profit' is now a known value, these two equations only have two variables. So, you can solve for b and the statement is sufficient.

Statement 2: here are two equations:

(.4)(150)(b) = 3(.2)(150)(a) (from the statement)

a + b = 500

Again, two equations and two variables, so you can solve for b and the statement is sufficient. The answer is D.

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