CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like **Speed-time-distance**, **Mixture and Alligations**. This year, there was a surprise. The questions from **Geometry** were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 8 : Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

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Let Rahul, Rakshita and Gurmeet take A, B and C days respectively to finish the job on their own, this means, in one day, the fraction of work done by Rahul, Rakshita and Gurmeet is \( \frac { 1 } { A } , \frac { 1 } { B } , \frac { 1 } { C } \).

*Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job.*

This means, the fraction of work done by all three of them, together, in one day, is less than \( \frac { 1 } { 7 } \).

\( \frac { 1 } { A } + \frac { 1 } { B } + \frac { 1 } { C } < \frac { 1 } { 7 } \)

*However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job.*

6 × (the fraction of work done by them together in one day) + 3 × (the fraction of work done by Rakshita in one day) = (one full job)

\( 6 \left( \frac { 1 } { A } + \frac { 1 } { B } + \frac { 1 } { C } \right) + \frac { 3 } { B } = 1 \)

\( \frac { 3 } { B } = 1 - 6 \left( \frac { 1 } { A } + \frac { 1 } { B } + \frac { 1 } { C } \right) \)

But, we know that, \( \frac { 1 } { A } + \frac { 1 } { B } + \frac { 1 } { C } < \frac { 1 } { 7 } \)

\( \frac { 3 } { B } > 1 - \frac { 6 } { 7 } \)

\( \frac { 1 } { B } > \frac { 1 } { 21 } \)

\( B < 21 \)

So, Rakshita should take less than 21 days to finish the job.

The extra information can be used to find the lower bound of B.

*On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job.*

\( \frac { 1 } { A } + \frac { 1 } { c } > \frac { 1 } { 15 } \)

But, we know that, \( \frac { 1 } { A } + \frac { 1 } { B } + \frac { 1 } { C } < \frac { 1 } { 7 } \)

So, the maximum value of \( \frac { 1 } { B } = \frac { 1 } { 7 } - \frac { 1 } { 15 } = \frac { 8 } { 7 ( 15 ) } \).

The minimum value of B = 13.125

The question is **" Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be " **

Choice B is the correct answer.

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