The sum of all 2 digit divisors of the number obtained by the difference of a 3 digit number of succ

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05 Feb 2014 Solve

The sum of all 2 digit divisors of the number obtained by the difference of a 3 digit number of successive digits in decreasing order and a 3 digit number having same digits in reciprocal order. Only 1, 2, 3, 4, 5, 6, 7, 8, 9 can be used as digits

OPtion

1) 250
2) 31
3) 448
4) 29
5) 19
6) 16
7) 249
8) 198
9) 150
10)None of these

Solution

321-123=198

2 digit divisors of 198 are 11, 18, 22, 33, 66, 99.

Correct Option: 7 Best Solution (12)

Venkatesh KK   10 years AGO

The three digit numbers having successive digits in decreasing order are,
987
876
765
...
...

Then difference between three digit number and reciprocal order of the same number is,

987-789=198
876-678=198
765-567=198
...
...

The difference is 198. The divisors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.

Now the sum of two digit divisors of 198 is,

11+18+22+33+66+99 = 249 (Option 7)

Like? Yes (11) | No (2)  

Praneeth   10 years AGO

321-123=198
432-234=198
543-345=198
so all 2digit factors of 198 are
11+18+22+33+66+99=249

Like? Yes (4) | No   

Srinath   10 years AGO

Take any 3 successive digits in giver series.
I take 456, the reciprocal for this num is 654
The difference is 654-456=198
The 2 digit divisors for the number 198 are: 11,18,22,33,66,99
Now finally the sum is 11+18+22+33+66+99=249

Like? Yes (4) | No   

nitesh   10 years AGO

always diff=198, 11,18,22,33,66,99 are divisor ,,sum=249

Like? Yes (3) | No   

madanpal vishwakarma    10 years AGO

the 3 digit numbers in

decreasingorder -reciprocal order
123 - 321=198
234-432=198
345-543=198
456-654=198
567-765=198
678-876=198
789-987=198

so two digit divisors of 198
99+66+33+22+18+11 =249
so option 7 is correct

Like? Yes (3) | No   

KUMAR ASHUTOSH   10 years AGO

ans:249
diff=198
divisors:99+66+33+22+11+18=249

Like? Yes (3) | No   

SADINENI RAGHAVENDRA BABU   10 years AGO

the difference of a any 3 digit number of successive digits in decreasing order and a 3 digit number having same digits in reciprocal order is 198.
and its 2 digit numbers sum is 11+18+22+33+66+99=249

Like? Yes (3) | No   

S.SHAFI   10 years AGO

The digits are 1,2,3,4,5,6,7,8,9
3 digit number of successive digits in decreasing order = 987, 876, 765, 654, 543, 432, 321
3 digit number having same digits in reciprocal order = 789, 678, 567, 456, 345, 234, 123

So, the difference is 198 for all the values..
and the 2 digit divisors of 198 are 11,18,22,33,66,99 and the sum is 249

Like? Yes (3) | No (1)  

Niraj   10 years AGO

Difference of a 3 digit number of successive digits in decreasing order and a 3 digit number having same digits in reciprocal order will be 198

These are 2 digits divisors of 198 11, 18, 22, 33, 66, 99 and sum of these will be 249.

Like? Yes (2) | No   

Anantharaman   10 years AGO

Number formed by three digit consecutive numbers in decreasing order = 321, 432, 543, 654, 765, 876, 987

Number formed by reversing the above numbers = 123, 234, 345, 456, 567, 678, 789 respectively

Difference between any of the above pairs is 198

2 digit divisors of 198 = 11, 18, 22, 33, 66, 99

Sum of all 2 digit divisors = 249

Option 7

Like? Yes (2) | No   

D.HARINATH REDDY   10 years AGO

987-789=198
876-678=198
similarly for all numbers.
2 digit divisors of 198 =11,18,22,33,66,99
sum= 11+18+22+33+66+99 = 249

Like? Yes (1) | No   

Manikumar R   10 years AGO

432-234=198
543-345=198
654-456=198
.
.
.
.
198 two digit divisors is 11, 18, 22, 33, 66, 99
sum of divisors is 249

Like? Yes (2) | No (1)