Aptitude - Problems on H.C.F and L.C.M - Discussion

Here we have two conditions:

Conclusion 1:

The correct answer choice must be divisible by the given numbers 5, 6, 7 and 8 and leaves a remainder 3 or we can say the "correct answer choice - 3" completely divided by 5, 6, 7 and 8.

Let we look at con 1 first:

(1677 - 3)/5 1674 is not divisible by 5 it give some remainder. So simply eliminate this choice.

(1683 - 3)/5 remainder is "0",
(1683 - 3)/6 remainder is "0",
(1683 - 3)/7 remainder is "0",
(1683 - 3)/8 remainder is "0", all 4 values are satisfied the condition so it may be a correct choice.

Lets continue with next choice.

(2523 - 3)/5 remainder is "0",
(2523 - 3)/6 remainder is "0",
(2523 - 3)/7 remainder is "0",
(2523 - 3)/8 remainder is "0", all 4 values are satisfied the condition so it also may be a correct choice.

Lets continue with next choice.

(3363 - 3)/5 remainder is "0",
(3363 - 3)/6 remainder is "0",
(3363 - 3)/7 remainder is "0",
(3363 - 3)/8 remainder is "0", all 4 values are satisfied the condition so it may be a correct choice.

When we finish with the first condition we eliminate one choice and remaining we have 3 choices, to find the correct answer choice from these 3 choice we need to go for condition 2;

Conclusion 2:

The correct answer choice must be divide by 9 without any remainder.

Before go for the calculation please remind one thing, if we need to know whether the give number is completely divisible by 9 or not, simply add the digits, if it is the multiples of 9 then the given number is divisible by 9. Let we check it now.

1683 = 1 + 6 + 8 + 3 = 18 = 1 + 8 = 9 (9 is a multiple of 9 (1 x 9 = 9).

2523 = 2 + 5 + 2 + 3 = 12 = 1 + 2 = 3 (3 is not a multiple of 9). Condition false so we can eliminate this choice also.

3363 = 3 + 3 + 6 + 3 = 15 = 1 + 5 = 6 (6 is not a multiple of 9). Condition is false so we can also eliminate this option.

Finally we have only one option left that satisfies both the conditions so, that's our answer. "Choice B - 1683".

It may be look like a lengthy one but if you understand whats actually happened behind the calculations, it's simple.

We can stop our calculation Once we find choice B is correct, no need to go and option C and D, but in case we have any option like 'can not be determined' or 'insufficient data', we need to check all the options.

Hope you enjoy, got struck with any step ask me.

Good Luck. !

If they don't give options how can I get 'k' value? Please explain.

Oh, its simple one. You have to check only options. As question said when divided by 9 leaves no remainder. Means you have to check the divisibility of 9.

Simply divide the options with 9 and which option whose remainder is 0 it is the answer.

@Kranthi you can check from the options by dividing the number by 5, 6, 7, 8 and find if the required remainder is coming or not.

If all the options divided by 9 then what we have to choose?

In question when number is divided by 9 no reminder. If reminder is 2 then how can solve this question. Please reply anyone.