Question

If HCF of 210 and 55 is expressed in the form of \[210 \times 5 - 55y,\] find the value of \[{y^2}\].
A) 381
B) 368
C) 361
D) 19

Answer 1

Hint: First find the HCF of 210 and 55 then equate it with \[210 \times 5 - 55y\] this will help you to find the value of y, which is ultimately lead you to find the value of \[{y^2}\].

Complete Step by Step Solution:
Let us try to find the HCF of 210 and 55 first for that we can rewrite both of them as
\[\begin{array}{l}
210 = 2 \times 3 \times 5 \times 7\\
55 = 5 \times 11
\end{array}\]
Comparing these two it can be easily seen that there’s only one factor common in these 2 and that is 5.
Therefore the HCF of 210 and 55 is 5 only.
Therefore for getting the value of y we can generate the equation as
\[\begin{array}{l}
\therefore 210 \times 5 - 55y = 5\\
 \Rightarrow - 55y = 5 - 1050\\
 \Rightarrow - 55y = - 1045\\
 \Rightarrow 55y = 1045\\
 \Rightarrow y = \dfrac{{1045}}{{55}}\\
 \Rightarrow y = 19
\end{array}\]
So now as we have the value of y as 19
\[{y^2} = 19 \times 19 = 361\]
Hence option C is the correct option.

Note: In this question, after finding the GCD when it comes to the equation solving part that's where many students make mistakes while dealing with signs and also it is often being ignored that we are told to find the value of \[{y^2}\] .