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Number sytem

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Number sytem

by gmat_jan » Fri Jan 15, 2010 8:01 am
Is a number divisible by 88.
(1) The number formed by the last three digits (unit's, ten's, hundred's) of the number is divisible by 8.
(2) The number added to its inverse (on reversing the digits) is divisible by 11.

1. statement (1) alone is sufficient but statement (2) alone is not
2. statement (2) alone is sufficient but statement (1) alone is not
3. both (1) and (2) together are sufficient but none of them alone is sufficient
4. both independently are sufficient
5. both statements (1) and (2) together are not sufficient
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by sreak1089 » Fri Jan 15, 2010 8:52 am
For a number to be divisible by 88, it must be divisible by both 8 and 11.

stmt 1) says that last three digits are divisible by 8. If the last 3 digits of a number are divisible by 8, then the number is divisible by 8, by the divisibility property of number 8. However, we do not know if the number is divisible by 11. Hence NOT SUFFICIENT.

stmt 2) says that number added to inverse is divisible by 11. I tried to take few examples like 132, 1089, 198, etc. and the sum of these numbers & their inverses seem to be divisible by 11. Hence, possibily, this is a property of number 11. thus we know this number is divisible by 11. However, we do not know if it is divisible by 8. Hence NOT SUFFICIENT.

Combining 1) and 2), we know that number is divisible by both 8 & 11. Hence SUFFICIENT. Thus, IMO C
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