This page organizes my video explanations to all of the 22 quantitative ability questions that are part of the 2024 Official CAT mock exam. The entire exam in pdf format can be downloaded from this link: 2024 Official CAT mock exam.
Question 1: Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is $12\%$ less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to
- $\quad 144$
- $\quad 127$
- $\quad 135$
- $\quad 124$
Question 2: $f(x) = \displaystyle \frac{x^2+2x-15}{x^2-7x-18}$ is negative if and only if
- $\quad -2 \lt x \lt 3$ or $x \gt 9$
- $\quad -5 \lt x \lt -2$ or $3 \lt x \lt 9$
- $\quad x \lt -5$ or $-2 \lt x \lt 3$
- $\quad x \lt -5$ or $3 \lt x \lt 9$
Question 3: The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7$ and $8$ so that the groups always include $3$ and $5$, while $7$ and $8$ are never included together is
Question 4: Suppose the length of each side of a regular hexagon $ABCDEF$ is $2$ cm. It $T$ is the mid point of $CD$, then the length of $AT$, in cm, is
- $\quad \sqrt{12}$
- $\quad \sqrt{13}$
- $\quad \sqrt{14}$
- $\quad \sqrt{15}$
Question 5: Amal purchases some pens at Rs$\: 8$ each. To sell these, he hires an employee at a fixed wage. He sells $100$ of these pens at Rs$\: 12$ each. If the remaining pens are sold at Rs$\: 11$ each, then he makes a net profit of Rs$\: 300$, while he makes a net loss of Rs$\: 300$ if the remaining pens are sold at Rs$\:9$ each. The wage of the employee, in INR, is
Question 6: The amount Neeta and Geeta together earn in a day equals what Sita alone earns in $6$ days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in $2$ days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is
- $\quad 11:7$
- $\quad 11:3$
- $\quad 7:3$
- $\quad 3:2$
Question 7: If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12$ cm, then the length, in cm, of each side of the hexagon is
- $\quad 2\sqrt{6}$
- $\quad \sqrt{6}$
- $\quad 4\sqrt{6}$
- $\quad 6\sqrt{6}$
Question 8: Anu, Vinu and Manu can complete a work alone in $15$ days, $12$ days and $20$ days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is
- $\quad 6$
- $\quad 5$
- $\quad 7$
- $\quad 8$
Question 9: The natural numbers are divided into groups as $(1), (2, 3, 4), (5, 6, 7, 8, 9), \ldots$ and so on. Then, the sum of the numbers in the $15$th group is equal to
- $\quad 6119$
- $\quad 7471$
- $\quad 4941$
- $\quad 6090$
Question 10: Suppose hospital $A$ admitted $21$ less Covid infected patients than hospital $B$, and all eventually recovered. The sum of recovery days for patients in hospitals $A$ and $B$ were $200$ and $152$, respectively. If the average recovery days for patients admitted in hospital $A$ was $3$ more than the average in hospital $B$ then the number admitted in hospital $A$ was
Question 11: A basket of $2$ apples, $4$ oranges and $6$ mangoes costs the same as a basket of $1$ apple, $4$ oranges and $8$ mangoes, or a basket of $8$ oranges and $7$ mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is
- $\quad 10$
- $\quad 11$
- $\quad 12$
- $\quad 13$
Question 12: Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are Rs$\: 806.25$ and Rs$\: 866.72$, respectively, the interest accrued, in INR, during the fourth year is nearest to
- $\quad 931.72$
- $\quad 934.65$
- $\quad 929.48$
- $\quad 926.84$
Question 13: A circle of diameter $8$ inches is inscribed in a triangle $ABC$ where $\angle ABC = 90^{\circ}$. If $BC=10$ inches then the area of the triangle in square inches is
Question 14: If $r$ is a constant such that $|x^2-4x-13|=r$ has exactly three distinct real roots, then the value of $r$ is
- $\quad 17$
- $\quad 21$
- $\quad 18$
- $\quad 15$
Question 15: If $5 – \log_{10} {\sqrt{1+x}} + 4 \log_{10} {\sqrt{1-x}} = \log_{10} {\displaystyle \frac{1}{\sqrt{1-x^2}}}$, then $100x$ equals
Question 16: The number of integers $n$ that satisfy the inequalities $|n-60| \lt |n-100| \lt |n-20|$ is
- $\quad 18$
- $\quad 21$
- $\quad 19$
- $\quad 20$
Question 17: The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100$ cc of water. Two $800$ cc bottles are filled with indigo solutions of strengths $33\%$ and $17\%$, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to $21\%$ then the volume, in cc, of the solution left in the second bottle is
Question 18: Two trains cross each other in $14$ seconds when running in opposite directions along parallel tracks. The faster train is $160$ m long and crosses a lamp post in $12$ seconds. If the speed of the other train is $6$ km/hr less than the faster one, its length, in m, is
- $\quad 184$
- $\quad 180$
- $\quad 192$
- $\quad 190$
Question 19: Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in $1$ year, Akbar and Anthony can complete in $16$ months, Anthony and Amar can complete in $2$ years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is
Question 20: Onion is sold for $5$ consecutive months at the rate of Rs $10, 20, 25, 25$, and $50$ per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these $5$ months is closest to
- $\quad 26$
- $\quad 20$
- $\quad 18$
- $\quad 16$
Question 21: If $x_0 = 1$, $x_1 = 2$, and $x_{n+2} = \displaystyle \frac{1+x_{n+1}}{x_n}$, $n=0,1,2,3,\ldots$, then $x_{2021}$ is equal to
- $\quad 2$
- $\quad 4$
- $\quad 1$
- $\quad 3$
Question 22: How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?