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12 Mar 2014, 07:37
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How to use divisibility rule to find out 2 unknown digits in an amount?
a45b2 is divisible by 72 then what is a and b?
a45b2 is divisible by 72 then what is a and b?
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12 Mar 2014, 08:18
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zeeshan798
For a45b2 to be divisible by 72=8*9, it must be divisible by both 8 and 9:
A number is divisible by 9 if the sum of its digits is divisible by 9. Thus a45b2 to be divisible by 9, a+4+5+b+2=11+a+b must be divisible by 9 --> a+b can be 7 or 16.
A number is divisible by 8 if its last three digits are divisible by 8. Thus 5b2 can be 512, 552, or 592 --> b can be 1, 5, or 9.
If b=1 and a+b=7, then a=6 --> a45b2 = 64512;
If b=1 and a+b=16, then a=15, which is not possible since a must be a single digit integer.
If b=5 and a+b=7, then a=2 --> a45b2 = 24552;
If b=5 and a+b=16, then a=11, which is not possible since a must be a single digit integer.
If b=9 and a+b=7, then a=-2, which is not possible since a must be a single digit positive integer.
If b=9 and a+b=16, then a=7 --> a45b2 = 74592.
So, (a,b) can be (6,1), (2, 5) or (7,9).
For more on divisiblity rules check Number Theory chapter of our math book: https://gmatclub.com/forum/math-number-theory-88376.html
Hope it helps.
P.S. Also, please read carefully and follow: https://gmatclub.com/forum/rules-for-pos ... 33935.html Thank you.
18 Nov 2020, 04:13
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