ShmoopTube

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And here's your shmoop du jour.

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Kyle's father, a general in the army, has promised to buy his son a tank for his 16th birthday...

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but only if he steps up his academic performance.

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On his first math test of the school year, Kyle had a score of 80 out of 100.

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On his second test, after spending some time on Shmoop, he received a score of 45 out of 50.

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By what percent did his percentage grade increase from one test to the other?

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And will it be enough to get him into a shiny new tank that will be the envy of all his friends?

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Here are our potential answers...

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First of all... decreased? After taking Shmoop?

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Get real. Just cross out answer D angrily and let's get serious.

00:51

OK, this question is really a 2-parter.

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First, we have to convert his second score to a percentage...

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...and then we have to figure out the % INCREASE from the first test to the second.

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In the first test, Kyle got an 80%.

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The question gives us the percentage, more or less, because it's just out of 100.

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So now we have to convert the second test to a percentage score...

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and we get that a familiar-looking percentage equation.

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That is, 45 is to 50 as whatever-percent is to 100.

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And a quick way to solve this one is to just multiply top and bottom by 2...

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...50 times 2 is 100 and 45 times 2 is 90

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so the answer is 90 percent. But now comes the tricky part.

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It's asking for the percent IMPROVEMENT.

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And there's a total curveball here that they give us in answer A, which is totally wrong.

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Yes, Kyle improved from 80 to 90 percent on the 2 exams.

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But his PERCENTAGE improvement was meaningfully bigger.

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If he'd gone from 100 to 110 percent ...if that were even possible...

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then he'd have improved 10 percent.

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But here he is growing from a smaller base in 80 percent.

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So hopefully it makes sense that if his percentage goes up the same amount -- 10 percent here...

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...then the RATE of growth will be higher.

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And here is one of the golden formulas of our math we should tattoo onto our leg:

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NEW MINUS OLD OVER OLD. Or NMOOO, if we ever get stuck.

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The formula gives us the RATE OF GROWTH for these kinds of problems and here the "new"

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score is 90; the old score is 80. So new minus old is 90 minus 80... or 10 in

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the numerator... and we put it over old, or 80, which goes in the denominator.

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So we have 10 over 80, or 1 over 8 or, converting to a percentage...

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...we divide 8 into 1... ...and we get 12.5%.

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And it's answer B.

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Looks like Kyle is going to be Big Man on Campus... ...tooling around town in his fancy new tank.

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Just check out those guns.

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