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What is the largest 4-digit number that can be added to 7,700 for the sum to be divisible by 22, 25, and 32?
A. 1,100
B. 2,200
C. 7,700
D. 8,800
E. 9,900
A. 1,100
B. 2,200
C. 7,700
D. 8,800
E. 9,900
29 Jul 2024, 02:59
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Official Solution:
What is the largest 4-digit number that can be added to 7,700 for the sum to be divisible by 22, 25, and 32?
A. 1,100
B. 2,200
C. 7,700
D. 8,800
E. 9,900
For a number to be divisible by 22, 25, and 32, it should be divisible by the least common multiple of these numbers. The LCM of 22 (\(2 * 11\)), 25 (\(5^2\)), and 32 (\(2^5\)) is \(2^5 * 5^2 * 11 = 8,800\).
Thus, we need the largest 4-digit number \(n\) such that \(7,700 + n\) is a multiple of 8,800. The smallest positive number we could add to 7,700 to make the result divisible by 8,800 is \(8,800 - 7,700 = 1,100\). On the other hand, the largest 4-digit number that can be added to 7,700 to achieve this is \(1,100 + 8,800 = 9,900\). So, we get \(7,700 + n = 7,700 + (1,100 + 8,800) = 7,700 + 9,900=17,600\).
Answer: E
What is the largest 4-digit number that can be added to 7,700 for the sum to be divisible by 22, 25, and 32?
A. 1,100
B. 2,200
C. 7,700
D. 8,800
E. 9,900
For a number to be divisible by 22, 25, and 32, it should be divisible by the least common multiple of these numbers. The LCM of 22 (\(2 * 11\)), 25 (\(5^2\)), and 32 (\(2^5\)) is \(2^5 * 5^2 * 11 = 8,800\).
Thus, we need the largest 4-digit number \(n\) such that \(7,700 + n\) is a multiple of 8,800. The smallest positive number we could add to 7,700 to make the result divisible by 8,800 is \(8,800 - 7,700 = 1,100\). On the other hand, the largest 4-digit number that can be added to 7,700 to achieve this is \(1,100 + 8,800 = 9,900\). So, we get \(7,700 + n = 7,700 + (1,100 + 8,800) = 7,700 + 9,900=17,600\).
Answer: E
08 Jul 2025, 18:20
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The number 8800 is in itself divisible by 22, 25, 32.
A number being divisible by another number can be proved by expressing in this below format.
8800 = 22 * K (or) 25 * Q (or) 32* A.
The number is "divisible" by all 3 numbers.
I believe it is best if the language of the question is changed. pls let me know your thoughts
A number being divisible by another number can be proved by expressing in this below format.
8800 = 22 * K (or) 25 * Q (or) 32* A.
The number is "divisible" by all 3 numbers.
I believe it is best if the language of the question is changed. pls let me know your thoughts
