Ravi packs 294 marbles into packets of 7 or 10 so that no marble is left. Ravi…
2024
Ravi packs 294 marbles into packets of 7 or 10 so that no marble is left. Ravi wants to maximize the number of bags with 7 marbles. How many bags does he need if there should be atleast one bag with 10 marbles
Answer: C. 39 — Answer: 39 Let x be the number of 7‑marble bags and y the number of 10‑marble bags. Then 7x + 10y = 294 Work modulo 10: 7x ≡ 294 ≡ 4 (mod 10). The inverse of…
- A.
42
- B.
36
- C.
39
- D.
33
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Correct answer: C
Answer: 39
Let x be the number of 7‑marble bags and y the number of 10‑marble bags. Then
7x + 10y = 294
Work modulo 10: 7x ≡ 294 ≡ 4 (mod 10). The inverse of 7 modulo 10 is 3, so x ≡ 3×4 ≡ 12 ≡ 2 (mod 10).
Thus x = 2 + 10k for integer k ≥ 0. Substitute to find corresponding y:
k = 0: (x,y) = (2,28)
k = 1: (x,y) = (12,21)
k = 2: (x,y) = (22,14)
k = 3: (x,y) = (32,7)
k = 4: (x,y) = (42,0)
We need at least one 10‑marble bag, so y ≥ 1. That excludes (42,0). The remaining valid solutions give the largest possible number of 7‑marble bags as x = 32 with y = 7.
Total number of bags = 32 + 7 = 39.