Question

Observe the given multiples of 37
37 x 3 = 111
 37 x 6 = 222
37 x 9 = 333
37 x 12 = 444
Find the product of 37 x 27?
 A. 999
 B. Greatest 3 digit number
C. Either A or B
D. Smallest 3-digit number

Answer 1

Hint: By observing the given question it is evident that four multiples of 37 are given and the fourth multiple which is \[37\times 27\] should be found. If observed carefully it can be noticed that a series is being formed at the right hand side of every equation, henceforth it can be anticipated that our answer will also be present in the same series.

Complete step-by-step answer:
Now let’s split the given equations to find the trend
Which implies that \[37\times 3=111\] can be written as \[37\times 3\times 1=111\]
Similarly,
\[37\times 6=222\] Can be written as \[37\times 3\times 2=222\]
\[37\times 9=333\] Can be written as \[37\times 3\times 3=333\]
\[37\times 12=444\] Can be written as \[37\times 3\times 4=444\]

 Coming back to our question we need to find \[37\times 27\]
We know that 27 can be written as a product of multiples of 3
Which implies
\[27=3\times 3\times 3\]
Therefore \[37\times 27\] can be modified to
\[37\times 3\times 3\times 3\]
Looking at our above equations we already have
\[37\times 3\times 3=333\]
Which implies
\[\begin{align}
  & 37\times 27=\left( 37\times 3\times 3 \right)\times 3 \\
 & 37\times 27=\left( 333 \right)\times 3 \\
 & 37\times 27=999 \\
\end{align}\]
We have now calculated the value of \[37\times 27\] which is \[999\]
Let’s tally our answer with the given options
The first option A is 999 which matches with our answer
Hence option A is correct
The second option B says the largest three digit number which is 999 and the answer we obtained is 999 too
Hence option B is correct too
Option C that states both option A and option B are correct id true as the question requires a single option to be the correct answer

So, the correct answers are “Option A and B”.

Note: While solving questions like these the student should not always first jump into the solution by calculating the whole value like multiplying it. The student should always try for a logical approach to the question by clearly looking at all the options and finding a trend in the given question. All the four options should be checked thoroughly.