## Quant Question Of The Day: 47

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# Numbers

How many of the ordered pairs of positive integers (T, G) satisfy the equation: T + G + TG = 2018 ?

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How many of the ordered pairs of positive integers (T, G) satisfy the equation: T + G + TG = 2018 ?

T + G + TG = 2018

i.e. 1 + T + G + TG = (T + 1)(G + 1) = 2019 = 3×673.

As T, G are positive integers, both the terms (T + 1) and (G + 1) are greater than or equal to 2. Also they are factors of 2019.

So required number of ordered pairs of positive integers (T, G) = (number of positive integral divisors of 2019) – 2 = 4-2 = 2 .

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No. Of factors of 2018

1,2,109,2018

But no ordered pair that makes 2018

According to me-0

Shouldn’t there be 2?

(2 , 672) and (672 , 2).

2 ordered pairs according to me. (2,672) and (672,2).