JIPMAT 2025 (QA) - The value of 9991/7 + 9992/7 + 9993/7 + 9994/7 + 9995/7 + 9996/7 is equal to : | PYQs + Solutions

JIPMAT 2025

Algebra

Linear Equations

Easy

The value of $999\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + 999\frac{4}{7} + 999\frac{5}{7} + 999\frac{6}{7}$ is equal to :

5997

5979

5994

2997

✅ Correct Option: 1

Basic learning:

1 + 0.5 = 1.5

This can be written as a fraction:

1.5 = 1 \frac{1}{2}

This can also be written as:

1 \frac{1}{2} = 1 + \frac{1}{2}

Hence, question states:

999\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + 999\frac{4}{7} + 999\frac{5}{7} + 999\frac{6}{7}

This can be written as:

999 + \frac{1}{7} + 999 + \frac{2}{7} + 999 + \frac{3}{7} + 999 + \frac{4}{7} + 999 + \frac{5}{7} + 999 + \frac{6}{7}

We can add the fractions separately. Also,

999

appears six times:

\Rightarrow 6 \times 999 + \left( \frac{1}{7} + \frac{2}{7} + \frac{3}{7} + \frac{4}{7} + \frac{5}{7} + \frac{6}{7} \right)

\Rightarrow 5994 + \left( \frac{1}{7} + \frac{2}{7} + \frac{3}{7} + \frac{4}{7} + \frac{5}{7} + \frac{6}{7} \right)

\Rightarrow 5994 + \frac{21}{7}

\Rightarrow 5994 + 3 = \boxed{5997}