Question

If the original size of an image is $540\times 680$, which of the following image sizes cannot be achieved, ensuring there is no deformation in the picture?

• A. $135\times 170$
• B. $27\times 34$
• C. $1080\times 1360$
• D. $123\times 164$

Answer 1

The correct option is D $123\times 164$

To solve this question, we need to check how $540\times 680$ can be reduced or expressed as higher fractions without changing the value of this ratio. To do this, recall that ratios are mathematically, just fractions. So, let us jump into fractions.

Dividing the numerator and denominator of the original fraction with the same number doesn't change the value of the fraction. Dividing with $4$, we get, $(540÷4)/(680÷4)=135/170$.

Similarly, dividing this fraction with $5$ (on numerator and denominator) results in $27/34$.

Our original fraction is $540/680$. Multiplying the numerator and the denominator of the fraction with the same number does not change the value of this fraction. Multiplying with $2$, we get,
$(540\times 2)/(680\times 2)=1080/1360$

Going in a similar way, we observe that the original fraction cannot be written as $123/164$ and hence this picture size cannot be achieved without compromising the picture quality.