A stamp collector arranges his stamps during his free time. What he arranges…
2024
A stamp collector arranges his stamps during his free time. What he arranges his stamps in pairs, there is one stamp left. It is the same when he arranges the stamps in groups of 3, 4, 5 and 6. Now, how many stamps will he be left with when he arranges them in groups of 8 ?
- A.
9
- B.
3
- C.
5
- D.
3.5
Attempted by 155 students.
Show answer & explanation
Correct answer: C
Answer: 5
Reasoning:
The number of stamps leaves remainder 1 when grouped into 2, 3, 4, 5, and 6.
Such numbers are 1 more than the least common multiple of 2, 3, 4, 5, and 6.
LCM(2,3,4,5,6) = 60, so the smallest positive number with the required property is 60 + 1 = 61.
Divide 61 by 8: 61 = 8 × 7 + 5, so the remainder is 5.
Therefore, when the stamps are arranged in groups of 8, there will be 5 stamps left.