SAT Math Multiple Choice Practice Question 124: Answer and Explanation

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Question: 124

14. A bag of candy was divided among four children. The first child got exactly one-fourth of the candy. Then, the second child got one-third of the candy that was left. Next, the third child got one-half of the candy remaining. Finally, the fourth child got everything left over. Which child now has the least candy?

A. The first child got the least.
B. The second child got the least.
C. The third child got the least.
D. The third and fourth children are tied for the least.
E. All four children got the same amount of candy.

Correct Answer: E

Explanation:

E. Yes, this one is a trick question. If (like me) you think fractions are cool, you solved this question this way: 1/4 goes to the first child, which leaves 3/4. One-third of that equals 1/3 × 3/4 = 1/4, so 1/4 goes to the second child, too, with 1/2 of the candy still left. Because the third child takes half of the half that's left, that's another 1/4, and the fourth child gets the 1/4 that remains. Of course, you can also do this problem by picking a nice number (say, 100) and working it out that way, a method you might like better.

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