Let $\dfrac{m}{n} = \dfrac{90^2+5 \times 90+4}{90^2+5\times 90+6} \times \dfrac{91^2+5\times 91+4}{91^2+5\times 91+6} \times .......\times \dfrac{98^2+5\times 98+4}{98^2+5\times 98+6}$ where m and n are co-primes.

What is the value of $|m - n|$ ?

Question

Let

\dfrac{m}{n} = \dfrac{90^2+5 \times 90+4}{90^2+5\times 90+6} \times \dfrac{91^2+5\times 91+4}{91^2+5\times 91+6} \times .......\times \dfrac{98^2+5\times 98+4}{98^2+5\times 98+6}

where m and n are co-primes.

What is the value of

|m - n|

?

Accepted Answer

A - 3. n^2+5n+4=(n+1)(n+4), n^2+5n+6=(n+2)(n+3). Product for n=90..98 telescopes: [91/100] x [102/93] = 9282/9300 = 1547/1550. |m-n| = 3.

Answer

B - 4

Answer

C - 6

Answer

D - 8

Let \(\dfrac{m}{n} = \dfrac{90^2+5 \times 90+4}{90^2+5\times 90+6} \times \dfrac{91^2+5\times 91+4}{91^2+5\times 91+6} \times .......\times \dfrac{98^2+5\times 98+4}{98^2+5\times 98+6}\) where m and…