cat 2024 Complete Paper Solution | Slot 3

In a group of 250 students, the percentage of girls was at least 44% and at most 60%.The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70%of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

For the following questions answer them individually

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: This reality is putting stress on employees who have to pay for transport, desk lunches, more childcare, clothing and that after-work socialisation - costs they haven’t incurred for nearly two years.

Paragraph: ___(1)___. Prices are rising at their fastest rate in 40 years; consequently, return-to-office-related costs have shot up - think petrol and food, for instance.___(2)___. Yet wages haven’t kept up with inflation - even despite the salary growth many workers have enjoyed during a favourable pandemic labour market. ___(3)___.This is especially jarring for workers who were able to save during remote work, when these expenditures weren’t a factor. ___(4)___. In April 2022, Umus, a London university lecturer, told BBC Worklife that they were spending nearly a quarter of what they made every day on return-to-work costs.

If $(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$, where a and b are natural numbers, then $a + b$ equals

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64.Then, the largest number in the original set of three numbers is

The author terms language “the operating system of our civilization” for all the following reasons EXCEPT that it

If $10^{68}$ is divided by 13, the remainder is

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is

For the following questions answer them individually

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: Many have had to leave their homes behind, with more than 1.3 million people being displaced due to the drought.

Passage: Somalia has been dealing with an enormous humanitarian catastrophe, driven by the longest and most severe drought the country has experienced in at least 40 years. ___(1)___. Five consecutive rainy seasons have failed, causing more than 8 million people - almost half of the country’s population - to experience acute food insecurity. ___(2)___. More than 43,000 people are believed to have lost their lives, with half of the lives lost likely being children under five. The damage the drought has caused is far-reaching. ___(3)___. Farmers have lost all their agricultural income, while pastoralists have lost more than 3 million livestock, impoverishing entire communities, and leaving them on the brink of famine. ___(4)___. Some, like the pastoralists, may never be able to go back as their livelihoods have been irreversibly wiped out.

Consider the sequence $t_1 = 1, t_2 = -1$ and $t_n = \left(\cfrac{n - 3}{n - 1}\right)t_{n - 2}$ for $n \geq 3$. Then, the value of the sum $\cfrac{1}{t_2} + \cfrac{1}{t_4} + \cfrac{1}{t_6} + ....... +\cfrac{1}{t_{2022}} + \cfrac{1}{t_{2024}}$, is