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A 5-digits positive integer ab3cd is a multiple of 225. What

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by Max@Math Revolution » Tue Sep 17, 2019 11:06 pm
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[GMAT math practice question]

A 5-digits positive integer ab3cd is a multiple of 225. What is maximum number?

A. 98325
B. 97325
C. 96320
D. 95325
E. 95320
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by GMATGuruNY » Wed Sep 18, 2019 2:43 am
Max@Math Revolution wrote:[GMAT math practice question]

A 5-digits positive integer ab3cd is a multiple of 225. What is maximum number?

A. 98325
B. 97325
C. 96320
D. 95325
E. 95320
An integer is a multiple of 9 if its digit sum is a multiple of 9.
225 has a digit sum that is a multiple of 9:
2+2+5 = 9
Thus, 225 is a multiple of 9.
Implication:
For the correct answer to be divisible by 225, it must be divisible by 9 and thus must have a digit sum that is a multiple of 9.
Of the five answer choices, only A has a digit sum that is a multiple of 9:
9+8+3+2+5 = 27

The correct answer is A.
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by Max@Math Revolution » Thu Sep 19, 2019 11:21 pm
=>

Since 225 is a product of 9=3^2 and 25=5^2, its last two digits is a multiple of 25 and the sum of its all digits a + b + 3 + c + d is a multiple of 9.
98325 and 95325 are only two multiples of 25.
Since 9 + 8 + 3 + 2 + 5 = 27 is a multiple of 9, 98325 is a multiple of 9 and 97325 is not a multiple of 9 since 9 + 7 + 3 + 2 + 5 is 26 and 26 is not a multiple of 9.

Therefore, A is the answer.
Answer: A
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