# CAT 2020 Set-3 | Question: 74

468 views

A batsman played $n + 2$ innings and got out on all occasions. His average score in these $n + 2$ innings was $29$ runs and he scored $38$ and $15$ runs in the last two innings. The batsman scored less than $38$ runs in each of the first $n$ innings. In these $n$ innings, his average score was $30$ runs and lowest score was $x$ runs. The smallest possible value of $x$ is

1. $2$
2. $3$
3. $4$
4. $1$

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average age of all three, then Harry’s age, in years, is
$\text{A}$ and $\text{B}$ are two railway stations $90 \; \text{km}$ apart. A train leaves $\text{A}$ at $9:00 \; \text{am},$ heading towards $\text{B}$ at a speed of $40... 1 votes 1 answer 3 638 views Let$k$be a constant. The equations$kx + y= 3$and$4x + ky= 4$have a unique solution if and only if$|k| \neq 2$$|k| = 2$$k \neq 2$$k= 2 1 votes 1 answer 4 594 views If x_{1} = \;– 1 and x_{m} = x_{m+1} + (m + 1) for every positive integer m,  then x_{100} equals  – 5151$$ – 5150 $$– 5051$$ – 5050 $1 votes 0 answers 5 366 views Vimla starts for office every day at$9 \; \text{am}$and reaches exactly on time if she drives at her usual speed of$40 \; \text{km/hr}.$She is late by$6 \; \text{min...