Question

Check what the result would have been if Sundaram had chosen the numbers
shown below.
4. 937
1. 417
2. 632
3. 117​

Answer 1

Given : Minakshi: Think of any 3-digit number.

Sundaram: Alright, I have done so.

Minakshi: Now use this number to form two more 3-digit numbers, like this: if the

number you chose is abc, then

• ‘the first number is cab (i.e., with the ones digit shifted to the “left end” of

the number);

• the other number is bca (i.e., with the hundreds digit shifted to the “right

end” of the number).

Now add them up. Divide the resulting number by 37. I claim that there will

be no remainder.

To find :      what the result would have been if Sundaram had chosen the numbers  shown below.

1. 417

2. 632

3. 117​

4. 937

Solution :

Generalized

Numbers  abc  , cab   , bca

Sum = 100a + 10b + c  + 100c + 10a + b + 100B + 10c  + a

= 111a + 111b + 111c

= 111(a + b + c)

= 37 * 3 (a + b + c)

Hence any  three number in this way will be divisible by 37

937  + 793 +  379  =     2109  =  37 * 57

417 + 741 + 174  =     1332 =  37 * 36

632 + 263 + 326  =      1221  = 37 * 33

117 + 711  + 171   = 999   = 37 * 27

in all cases remainder would have been zero

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