The Math Mark Mystery
The students in Ms. Lewis's class that got lower than 60 on their math exam were Mary, Ann, Caleb, Ben, and Julia. Each of them did not solve problems well on one of the five particular topics: logarithms, trigonometry, radicals, geometry, and exponential functions. If we know that the lowest marks in the class were 45, 48, 50, 52 and 53, use the clues below to find out what mark Mary got and the topic she made mistakes on.
Clues:
- Mary's mark was higher than Caleb's but two points lower than the mark of the boy who made mistakes in geometry.
- Ann knows trigonometry better than logarithms.
- A girl that made mistakes in trigonometry received one point more on the exam than the girl who made mistakes in logarithms.
- The mark of the boy who made mistakes in exponential functions is lower than the mark received by the girl who made mistakes in radicals.
Note: Caleb and Ben are boys. Mary, Ann, and Julia are girls.
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1 solution
To solve this problem its best to make a chart to organize all the information:
CLUE 1: Mary's mark was higher than Caleb's but two points lower than the mark of the boy who made mistakes in geometry.
-From this, we can see that Mary's mark can only be 48 or 50 because those are the two marks that have a 2 point difference with a higher mark. We also know that Caleb has a mark of 45 or 48 because his mark is lower than Mary's. Finally, we realize that Ben, the only other boy, made a mistake in geometry and his mark is 50 or 52.
CLUE 2: Ann knows trigonometry better than logarithms.
-We know that Ann did not mess up on trigonometry.
CLUE 3: A girl that made mistakes in trigonometry received one point more on the exam than the girl who made mistakes in logarithms.
-The only marks with a one point difference are 52 and 53. That means Mary couldn't have been mentioned in this clue since she could have only received 48 or 50. So, the only two other girls left are Ann and Julia. Since Ann did not mess up on trigonometry, Ann messed up on logarithms and Julia messed up on trigonometry. This also means that Ann got 52 and Julia got 53.
-However, after putting this into our chart we realize that Ben could have only gotten a 50. So, Mary must have a 48 and Caleb must have a 45.
CLUE 4: The mark of the boy who made mistakes in exponential functions is lower than the mark received by the girl who made mistakes in radicals.
-Lastly, from this clue we know straight up that the last boy left, Caleb, made mistakes in exponential functions and Mary made mistakes in radicals.
Therefore, Mary got a 48 and needs to work on her radical skills.