Final answer:
Jerry initially had 360 marbles, giving 1/6 of his collection, which is 60 marbles, to Otto. So, Otto received 60 marbles, not 15 as the options suggest.
Step-by-step explanation:
To determine how many marbles Otto received from Jerry's collection, we first need to find out the total number of marbles Jerry started with. Since Jerry gave away 1/2, 1/4, and 1/6 of his collection and then had 30 marbles left, we can use these fractions along with the remaining marbles to calculate the original number of marbles.
To find a common denominator for the fractions, we can use 12 (since it's the least common multiple of 2, 4, and 6). So Jerry gave away 6/12 (1/2), 3/12 (1/4), 2/12 (1/6) of his collection. Adding the fractions together gives us 6/12 + 3/12 + 2/12 = 11/12 of his collection. The remaining 1/12 is what he gave to Pete, which is 30 marbles. Therefore, Jerry's original number of marbles is 12 * 30 = 360 marbles.
Now, to find out how many marbles Otto received, we take 1/6 of the original total which is 360/6 = 60 marbles. Thus, Otto received 60 marbles, making Option C) 15 marbles incorrect.