DS Question - 28

Is the three-digit number n less than 550?

1) The product of the digits in n is 30
2) The sum of the digits in n is 10

Answer: C

From statement (1) : the factors of 30 are 1,2,3,5,6,10,15,30
Now because the number must be digits (single number) we do not need to consider 10,15 and 50

Now if the hundreds digit of the 3-digit number = any digit among the 1,2,3 digits ---> answer to the question is clearly Yes.

But if the hundreds digit = 5 or 6 ---> answer to the question is No.

Hence (1) alone is insufficient.

From statement (2) : There are different combinations where the sum of digits can be equal to 10. e.g 541 and 145.

Hence (2) alone is insufficient.

Combining statements (1) and (2) we get :

If the hundreds digit= 5 , the second digit can only be 1,2,3 because if the digit is equal to 6 it violates statement (2) Hence in this case answer to the question is Yes.

If hundreds digit = 6 then the number n must contain 5 so as to satisfy the first statement but then it will violate statement (2) as the total of digits of n will exceed 10

Thus no 3-digit number exists with the hundreds digit equal to 6 satisfying both the statements together.

Hence the number n will always be less than 550 as it will be the combination of 1, 2, 3 and 5

Hence ans is C