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24 May 2022, 08:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
74% (03:13) correct
26%
(03:08)
wrong
based on 139
sessions
History
Date
Time
Result
Not Attempted Yet
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?
A) 18
B) 27
C) 36
D) 45
E) 54
A) 18
B) 27
C) 36
D) 45
E) 54
24 May 2022, 11:09
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Bunuel
Breaking Down the Info:
Let the number of cards be N. We may denote Merry as E and Michelle as I but it is not necessary. We can create a table to help organize the information. Another hint is that the total amount of cards is always 2N, so we don't have to add or subtract the amount they give each other, it will just be a total of 2N cards regardless.
After Turn X | Merry | Michelle
1 | \(\frac{4}{3}N\) | \(\frac{2}{3}N\)
2 | \(\frac{8}{9}N\) | \(\frac{10}{9}N\)
3 | \(\frac{34}{27}N\) | \(\frac{20}{27}N\).
Then Merry has 14 more cards than Michelle. \(\frac{34}{27}N - \frac{20}{27}N = 14\).
\(N = 27\)
Answer: B
24 May 2022, 18:30
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Bunuel
Algebra? Nah, I think PITA (Plugging In The Answers) sounds tastier!
Let's try B. They both start with 27. Merry gives 9 to Michelle, so Merry has 18 and Michelle has 36. Michelle gives 12 to Merry, so Merry has 30 and Michelle has 24. Merry gives 10 to Michelle, so Merry has 20 and Michelle has 34. Did Merry end up with 14 more than Michelle? Yep. Done.
Answer choice B.
ThatDudeKnowsPITA
