Question

A number is between 30 and 50. It is also a common multiple of 6 and 8. When this number is added to 45, the result will be:
(a) 77
(b) 87
(c) 90
(d) 93

Answer 1

Hint: First of all find the number which lies between 30 and 50 and is also a common multiple of 6 and 8. Find the L.C.M of 6 and 8 to find the factor of the required number which is 24. Now, the number should lie between 30 and 50 so multiply 24 by such a number so that it lies between 30 and 50. After getting the required number add 45 to it to get the required result.

Complete step-by-step answer:
We are going to find the number which lies between 30 and 50 and is also a common multiple of 6 and 8.
Now, there are about 19 numbers between 30 and 50. We start to find the number by using the other information which says that number is a common multiple of 6 and 8. To find one of the factors of the required number we are going to find the L.C.M of 6 and 8.
L.C.M of 6 and 8 is calculated by writing the prime factorization of 6 and 8.
 $ \begin{align}
  & 6=2\times 3 \\
 & 8=2\times 2\times 2 \\
\end{align} $
The L.C.M of 6 and 8 is equal to:
 $ \begin{align}
  & 2\times 3\times 2\times 2 \\
 & =24 \\
\end{align} $
Now, we have got one of the factors of required number i.e. 24 and we also know the number is lying between 30 and 50 so if we multiply 24 by 2 we get 48 and that will lie between 30 and 50.
Hence, the required number is 48.
Now, we have to add 45 in the required number i.e. 48 we get,
 $ \begin{align}
  & 45+48 \\
 & =93 \\
\end{align} $
From the above, after adding 45 to 48 the result is 93.
Hence, the correct option is (d).


Note: A very plausible mistake is that you will write the common multiple of 6 and 8 as 48 and that will not harm you because the multiplication is giving you the number which lies between 30 and 50. It's very easy to get carried away and make this mistake. But it won’t cost you marks in competitive exam but will cost you marks in the subjective exam because common multiple (i.e. L.C.M) of 6 and 8 is 24 not 48.