What is the least amount that a person can have , such that when he…
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What is the least amount that a person can have , such that when he distributed it into groups of rs. 16 or rs. 18 or rs. 20 or rs. 25 he is always left with rs. 4?
Answer: C. Rs. 3,604 — Key idea: The required amount must leave remainder 4 when divided by 16, 18, 20 and 25, so subtracting 4 gives a number divisible by all four divisors. Let M…
- A.
Rs. 2,245
- B.
Rs. 2,615
- C.
Rs. 3,604
- D.
Rs. 2,475
Attempted by 238 students.
Show answer & explanation
Correct answer: C
Key idea: The required amount must leave remainder 4 when divided by 16, 18, 20 and 25, so subtracting 4 gives a number divisible by all four divisors.
Let M = amount − 4. Then M must be a common multiple of 16, 18, 20 and 25.
Compute the least common multiple (LCM) by prime factorization:
16 = 2^4
18 = 2 × 3^2
20 = 2^2 × 5
25 = 5^2
Take the highest powers of each prime: 2^4, 3^2, 5^2. So LCM = 2^4 × 3^2 × 5^2 = 16 × 9 × 25 = 3600.
Thus the smallest positive common multiple M is 3600, so the least amount is M + 4 = 3604.
Answer: Rs. 3,604