When the marbles in a bag are divided evenly between
two friends, there is one marble left over. When the
same marbles are divided evenly among three friends,
there is one marble left over. When the marbles are
divided evenly among five friends, there is one marble
left over.
(i) What is the least possible number of marbles in
the bag?
(a) 31
(b) 30
(c) 32
(d) 34
What is another possible number of marbles in
the bag?
(a) 31
(b) 61
(c) 52
(d) 34
Answers
Answer:
31 and 61 ( a and b)
Step-by-step explanation:
n = the unknown number.
Dividing "N" by the 2 friends = n/2 OR 1/2n = 1 (remainder).
Dividing "N" by the 3 friends = n/3 OR 1/3n = 1 (remainder).
Dividing "N" by the 5 friends = n/5 OR 1/5n = 1 (remainder).
If the unknown amount of marbles is evenly divisible by 2, then the number of marbles NUMERICALLY should end in an even number (2, 4, 6, 8).
If the unknown amount of marbles is evenly divisible by 3, then the number of marbles NUMERICALLY should add up to a number divisible by 3.
If the unknown amount of marbles is evenly divisible by 5, then the number of marbles NUMERICALLY should end in 5 or 0.
The number should not end in 5, since the number is divisible by 2, meaning that the last digit should be even, and five is not even. Since it is divisible by 5, we must choose 0 as the last digit since 0 is divisible by 5 and 2.
To make the number divisible by 3, then 0 + x (unknown number) should make a number divisible by 3.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33....
(i) The least possible number of marbles in the bag is 31, since 30 is the amount of marbles each person can have evenly, +1 makes 1 leftover. So for the first answer, it is A.
Another possible number of marbles in the bag is 61 since 60 is divisible by 2, 3, and 5, +1 makes 1 leftover.
Given:
When marbles are divided among two friends, there is one marble left over.
When marbles are divided among three friends, there is one marble left over.
When marbles are divided among five friends, there is one marble left over.
To find:
i) The least possible number of marbles in the bag?
ii) Another possible number of marbles in the bag?
Solution:
i) The Least possible number should not be divisible by 2,3 and 5.
a) 31/2 is not divisible.
31/3 is not divisible.
31/5 is not divisible. So, there may be 31 marbles in the bag.
b) 30/2 = 15 is divisible.
c) 32/2 = 16 is divisible.
d) 34/2 = 17 is divisible.
Hence, the least possible number of marbles in the bag is a) 31.
ii) Again the Least possible number should not be divisible by 2,3 and 5.
a) 31/2 is not divisible.
31/3 is not divisible.
31/5 is not divisible. So, there may be 31 marbles in the bag.
b) 61/2 is not divisible.
61/3 is not divisible.
61/5 is not divisible. So, there may be 61 marbles in the bag.
c) 52/2 =26 is divisible.
d) 34/2 = 17 is divisible.
Hence, another possible number of marbles in the bag is b)61.