This page organizes my video explanations to all of the 22 quantitative ability questions that are part of the 2022 CAT exam Slot 1. The entire exam in pdf format can be downloaded from this link: 2022 CAT Quant Slot 1: Quantitative Ability.
Question 1: Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A$, $B$, $C$ are $(1,1),(3,4)$ and $(-2, 8)$, respectively. Then, the coordinates of the vertex $D$ are
- $\quad (-4, 5)$
- $\quad (4,5)$
- $\quad (-3,4)$
- $\quad (0,11)$
Question 2: The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is
Question 3: A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio $1:3$, then the ratio of lemon juice and sugar syrup in the new mixture is
- $\quad 1:6$
- $\quad 1:4$
- $\quad 1:5$
- $\quad 1:7$
Question 4: For natural numbers $x$, $y$, and $z$, if $xy+yz=19$ and $yz+xz=51$, then the minimum possible value of $xyz$ is
Question 5: Let $a, b, c$ be non-zero real numbers such that $b^2 \lt 4ac$, and $f(x)=ax^2+bx+c$. If the set $S$ consists of all integers $m$ such that $f(m) \lt 0$, then the set $S$ must necessarily be
- $\quad \textrm{the set of all integers}$
- $\quad \textrm{either the empty set or the set of all integers}$
- $\quad \textrm{the empty set}$
- $\quad \textrm{the set of all positive integers}$
Question 6: Trains $A$ and $B$ start traveling at the same time towards each other with constant speeds from stations $X$ and $Y$, respectively. Train $A$ reaches station $Y$ in 10 minutes while train $B$ takes $9$ minutes to reach station $X$ after meeting train $A$. Then the total time taken, in minutes, by train $B$ to travel from station $Y$ to station $X$ is
- $\quad 15$
- $\quad 12$
- $\quad 6$
- $\quad 10$
Question 7: The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$ is
- $\quad 3$
- $\quad 4$
- $\quad 5$
- $\quad 1$
Question 8: Pinky is standing in queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is $3:5$. If the total number of persons in the queue is less than $300$, then the maximum possible number of persons standing ahead of Pinky is
Question 9: Ankita buys $4$ kg cashews, $14$ kg peanuts and $6$ kg almonds when the cost of $7$ kg cashews is the same as that of $30$ kg peanuts or $9$ kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹$1752$. She sells $4$ kg of the mixture at this marked price and the remaining at a $20\%$ discount on the marked price, thus making a total profit of ₹$744$. Then the amount, in rupees, that she had spent in buying almonds is
- $\quad 1440$
- $\quad 1176$
- $\quad 1680$
- $\quad 2520$
Question 10: The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite number of solutions for $x$ is
- $\quad -1$
- $\quad 0$
- $\quad 1$
- $\quad 2$
Question 11: A trapezium $ABCD$ has side $AD$ parallel to $BC$, $\angle BAD=90^{\circ}$, $BC=3$ cm and $AD=8$ cm. If the perimeter of this trapezium is $36$ cm, then its area, in sq. cm, is
Question 12: For any real number $x$, let $[x]$ be the largest integer less than or equal to $x$. If $\sum_{n=1}^{N} \left[\displaystyle \frac{1}{5} + \frac{n}{25}\right] = 25$, then $N$ is
Question 13: In a village, the ratio of number of males to females is $5:4$. The ratio of number of literate males to literate females is $2:3$. The ratio of the number of illiterate males to illiterate females is $4:3$. If $3600$ males in the village are literate, then the total number of females in the village is
Question 14: Amal buys $110$ kg of syrup and $120$ kg of juice, syrup being $20\%$ less costly than juice, per kg. He sells $10$ kg of syrup at $10\%$ profit and $20$ kg of juice at $20\%$ profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹$308.32$ per kg and makes an overall profit of $64\%$. Then, Amal’s cost price for syrup, in rupees per kg, is
Question 15: Let $a$ and $b$ be natural numbers. If $a^2+ab+a=14$ and $b^2+ab+b=28$, then $(2a+b)$ equals
- $\quad 7$
- $\quad 10$
- $\quad 9$
- $\quad 8$
Question 16: Alex invested his savings in two parts. The simple interest earned on the first part at $15\%$ per annum for $4$ years is the same as the simple interest earned on the second part at $12\%$ per annum for $3$ years. Then, the percentage of his savings invested in the first part is
- $\quad 62.5\%$
- $\quad 37.5\%$
- $\quad 60\%$
- $\quad 40\%$
Question 17: In a class of $100$ students, $73$ like coffee, $80$ like tea and $52$ like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
- $\quad 48$
- $\quad 53$
- $\quad 47$
- $\quad 52$
Question 18: For any natural number $n$, suppose the sum of the first $n$ terms of an arithmetic progression is $(n+2n^2)$. If the $n^{th}$ term of the progression is divisible by $9$, then the smallest possible value of $n$ is
- $\quad 4$
- $\quad 8$
- $\quad 7$
- $\quad 9$
Question 19: All the vertices of a rectangle lie on a circle of radius $R$. If the perimeter of the rectangle is $P$, then the area of the rectangle is
- $\quad \displaystyle \frac{P^2}{2} – 2PR$
- $\quad \displaystyle \frac{P^2}{8} – 2R^2$
- $\quad \displaystyle \frac{P^2}{16} – R^2$
- $\quad \displaystyle \frac{P^2}{8} – \frac{R^2}{2}$
Question 20: The average weight of students in a class increases by $600$ gm when some new students join the class. If the average weight of the new students is $3$ kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
- $\quad 1:2$
- $\quad 3:1$
- $\quad 1:4$
- $\quad 4:1$
Question 21: Let $A$ be the largest positive integer that divides all the numbers of the form $3^k+4^k+5^k$, and $B$ be the largest positive integer that divides all the numbers of the form $4^k+3(4^k)+4^{k+2}$, where $k$ is any positive integer. Then $(A+B)$ equals
Question 22: Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to
- $\quad 100$
- $\quad 25$
- $\quad 0$
- $\quad 50$
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