Four rods of length 91 cm, 104 cm, 117 cm and 169 cm are to be cut into parts…
2025
Four rods of length 91 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
- A.
21
- B.
19
- C.
37
- D.
27
Attempted by 8 students.
Show answer & explanation
Correct answer: C
Concept: When several rods must be cut into pieces of one common size such that each piece is as large as possible and every rod is used up exactly (no leftover), that common piece length must be the Highest Common Factor (H.C.F.) of all the given lengths — the H.C.F. is the largest number that divides every length exactly, so it maximizes the piece size while leaving no wastage.
Write each rod length as a product involving 13: 91 = 7 x 13, 104 = 8 x 13, 117 = 9 x 13, 169 = 13 x 13.
The common factor across all four rods is 13, and no larger number divides all four exactly, so H.C.F. = 13 cm — this is the length of each piece.
Divide each rod length by 13 to get the number of pieces cut from that rod: 91 / 13 = 7, 104 / 13 = 8, 117 / 13 = 9, 169 / 13 = 13.
Add the piece counts from all four rods together to get the total number of pieces cut.
Cross-check: 13 x 7 = 91, 13 x 8 = 104, 13 x 9 = 117, 13 x 13 = 169 — each product matches the original rod length exactly, confirming 13 cm is genuinely a common divisor of all four lengths and the piece count computed this way is correct.
