1995 AMC 8 Problem 5

Attempt Problem 5 of the 1995 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

Find the smallest whole number that is larger than the sum
212+313+414+515.2\tfrac12 + 3\tfrac13 + 4\tfrac14 + 5\tfrac15.
1414
1515
1616
1717
1818
Answer: C
Concepts:fractionestimation
Small hint:
Add the whole-number parts and the fraction parts separately
Big hint:
The fractions 12+13+14+15\dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 add to a little more than 11
Solution:
The whole-number parts sum to 2+3+4+5=142 + 3 + 4 + 5 = 14.
The fractions 12+13+14+15\dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 add to about 1.28,1.28, which is between 11 and 2.2. So the total is between 1515 and 16,16, and the smallest whole number larger than it is 1616.
Thus, the correct answer is C .
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