Do it without plugging values

Algebra Level 2

Compare the two quantities if $f$ is a positive integer:

$\textbf{Quantity A}$

$\text{The remainder when}$ $2f$ is divided by $9$

$\textbf{Quantity B}$

$\text{The remainder when}$ $2f+27$ is divided by $9$

The two quantities are equal Quantity A is greater The relationship cannot be determined Quantity B is greater

1 solution

Aaryan Maheshwari
Dec 23, 2017

Suppose $2f$ leaves remainder $y$ on being divided by 9. Then, $2f=9x+y\text{(for some}\space x, x\text{ is a natural number)}$ Now, $2f+27=9x+y+27=9(x+3)+y$ Hence, both $2f$ and $2f+27$ leave the same remainder on being divided by 9.

Do it without plugging values

1 solution

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