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form 34a5b

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by sanju09 » Mon Oct 11, 2010 10:01 pm
How many 5-digit numbers of the form 34a5b are divisible by 36?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 9


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by Rahul@gurome » Mon Oct 11, 2010 10:20 pm
Any number which is divisible by 4 and 9, both, is divisible by 36.
A number is divisible by 4 if the last 2 digits are divisible by 4 and a number is divisible 9 if the the sum of all digits is divisible by 9.
b can be 2 and 6 for 34a5b to be divisible by 4.
If b = 2, then 3 + 4 + a + 5 + 2 = 14 + a, which can be divisible by 9 if a = 4.
If b = 6, then 3 + 4 + a + 5 + 6 = 18 + a, which is divisible by 9 if a = 0 or 9.

Therefore, possible 5-digit numbers are 34452, 34056 and 34956

[spoiler]The correct answer is (B).[/spoiler]
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by sanju09 » Mon Oct 11, 2010 10:23 pm
Rahul@gurome wrote:Any number which is divisible by 4 and 9, both, is divisible by 36.
A number is divisible by 4 if the last 2 digits are divisible by 4 and a number is divisible 9 if the the sum of all digits is divisible by 9.
b can be 2 and 6 for 34a5b to be divisible by 4.
If b = 2, then 3 + 4 + a + 5 + 2 = 14 + a, which can be divisible by 9 if a = 4.
If b = 6, then 3 + 4 + a + 5 + 6 = 18 + a, which is divisible by 9 if a = 0 or 9.

Therefore, possible 5-digit numbers are 34452, 34056 and 34956

[spoiler]The correct answer is (B).[/spoiler]
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