# Recent questions tagged cat2018-1

1
Fuel contamination levels at each of $20$ petrol pumps $P1, P2, \dots , P20$ were recorded as either high, medium, or low. Contamination levels at three pumps among $P1 - P5$ were recorded as high. $P6$ was the only pump among $P1 - P10$ where the ... the same. Contamination levels at $P13$ and $P17$ were recorded as the same. Contamination levels at P11 and P16 were recorded as the same.
2
A company administers a written test comprising of three sections of $20$ marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of $80$) is calculated by doubling her marks in DI and adding it to the sum ... Chetna in DI. Jatin scored more than Indu in GA. Only $2$ Only $1$ Both $1$ and $2$ Both $2$ and $3$
3
Fuel contamination levels at each of $20$ petrol pumps $P1, P2, \dots , P20$ were recorded as either high, medium, or low. Contamination levels at three pumps among $P1 - P5$ were recorded as high. $P6$ was the only pump among $P1 - P10$ where the ... $P14$ was recorded as medium. The contamination level at $P15$ was recorded as medium. The contamination level at $P18$ was recorded as low.
4
A company administers a written test comprising of three sections of $20$ marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of $80$) is calculated by doubling her marks ... s composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI? ________
5
A company administers a written test comprising of three sections of $20$ marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of $80$) is calculated by doubling her marks in DI ... score was less than that of Falak. Bala's composite score was less than that of Ester. Bala scored same as Jatin in DI.
6
Fuel contamination levels at each of $20$ petrol pumps $P1, P2, \dots , P20$ were recorded as either high, medium, or low. Contamination levels at three pumps among $P1 - P5$ were recorded as high. $P6$ was the only pump among $P1 - P10$ where the contamination level was ... of pumps at which the contamination levels were recorded as medium? Exactly $8$. More than $4$. At least $8$. At most $9$.
7
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, ... administration committee, and $20\%$ are in the teaching committee. What is the number of educationalists in the research committee?
8
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, ... . The total number of bureaucrats in the three committees. The size of the research committee. The size of the teaching committee.
9
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats ... administration committee, and $20\%$ are in the teaching committee. What is the number of bureaucrats in the administration committee?
10
Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ratio of the geometric progression is $3/6$ $3/2$ $5/2$ $1/6$
11
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, ... is equal to the number of educationalists. The size of the research committee is less than the size of the teaching committee.
12
A company administers a written test comprising of three sections of $20$ marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of $80$) is calculated by doubling her marks in ... 's. If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE? _____
13
A trader sells $10$ litres of a mixture of paints $A$ and $B$, where the amount of $B$ in the mixture does not exceed that of $A$. The cost of paint $A$ per litre is Rs. $8$ more than that of paint $B$. If the trader sells the entire mixture for Rs. $264$ and makes a profit of $10\%$, then the highest possible cost of paint $B$, in Rs. per litre, is $26$ $16$ $20$ $22$
14
Point $P$ lies between points $A$ and $B$ such that the length of $BP$ is thrice that of $AP$. Car $1$ starts from $A$ and moves towards $B$. Simultaneously, car $2$ starts from $B$ and moves towards $A$. Car $2$ reaches $P$ one hour after car $1$ reaches $P$. If the speed of car $2$ is half that of car $1$, then the time, in minutes, taken by car $1$ in reaching $P$ from $A$ is _________.
15
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is $35/4$ $37/4$ $31/4$ $33/4$
16
In a circle, two parallel chords on the same side of a diameter have lengths $4$ cm and $6$ cm. If the distance between these chords is $1$ cm, then the radius of the circle, in cm, is $\sqrt{12}$ $\sqrt{14}$ $\sqrt{13}$ $\sqrt{11}$
17
A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in $6$ hours when $6$ filling and $5$ draining pipes are on, ... $6$ draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?
18
If $\log_2(5+\log_3a)=3$ and $\log_5(4a+12+\log_2b)=3$, then $a+b$ is equal to $67$ $40$ $32$ $59$
19
If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be $93$ $26$ $23$ $96$
20
In an apartment complex, the number of people aged $51$ years and above is $30$ and there are at most $39$ people whose ages are below $51$ years. The average age of all the people in the apartment complex is $38$ years. What is the largest possible average age, in years, of the people whose ages are below $51$ years? $27$ $28$ $26$ $25$
21
Given an equilateral triangle $T1$ with side $24$ cm, a second triangle $T2$ is formed by joining the midpoints of the sides of $T1$. Then a third triangle T3 is formed by joining the midpoints of the sides of $T2$. If this process of forming triangles is continued, the sum of the ... of infinitely many such triangles $T1, T2, T3, \dots$ will be $164\sqrt 3$ $188\sqrt 3$ $248\sqrt 3$ $192\sqrt 3$
22
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$
23
If $x$ is a positive quantity such that $2^x=3^{\log_52}$, then $x$ is equal to $1+\log_3\dfrac{5}{3}$ $\log_58$ $1+\log_5\dfrac{3}{5}$ $\log_59$
24
While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of the sum of squares of the other two numbers is _________
25
Points $E, F, G, H$ lie on the sides $AB, BC, CD$, and $DA$, respectively, of a square $ABCD$. If $EFGH$ is also a square whose area is $62.5\%$ of that of $ABCD$ and $CG$ is longer than $EB$, then the ratio of length of $EB$ to that of $CG$ is $2:5$ $4:9$ $3:8$ $1:3$
26
Each of $74$ students in a class studies at least one of the three subjects $H, E$ and $P$. Ten students study all three subjects, while twenty study $H$ and $E$, but not $P$. Every student who studies $P$ also studies $H$ or $E$ or both. If the number of students studying $H$ equals that studying $E$, then the number of students studying $H$ is _________
27
Train $T$ leaves station $X$ for station $Y$ at $3$ pm. Train $S$, traveling at three quarters of the speed of $T$, leaves $Y$ for $X$ at $4$ pm. The two trains pass each other at a station $Z$, where the distance between $X$ and $Z$ is three-fifths of that between $X$ and $Y$. How many hours does train $T$ take for its journey from $X$ to $Y$?
28
$\log_{12}81=p$, then $3\bigg (\frac{4-p}{4+p}\bigg)$ is equal to $\log_416$ $\log_68$ $\log_616$ $\log_28$
29
A right circular cone, of height $12$ ft, stands on its base which has diameter $8$ ft. The tip of the cone is cut off with a plane which is parallel to the base and $9$ ft from the base. With $\pi = 22/7$, the volume, in cubic ft, of the remaining part of the cone is ________
30
In a parallelogram $ABCD$ of area $72$ sq cm, the sides $CD$ and $AD$ have lengths $9$ cm and $16$ cm, respectively. Let $P$ be a point on $CD$ such that $AP$ is perpendicular to $CD$. Then the area, in sq cm, of triangle $APD$ is $18\sqrt 3$ $24\sqrt 3$ $32\sqrt 3$ $12\sqrt 3$
31
A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold $8$ kg of peanuts at a profit of $10\%$ and $16$ kg of walnuts at a profit of $20\%$ to a shopkeeper. However, the shopkeeper lost $5$ kg of walnuts and $3$ ... making an overall profit of $25\%$. At what price, in Rs. per kg, did the wholesaler buy the walnuts? $98$ $96$ $84$ $86$
32
A CAT aspirant appears for a certain number of tests. His average score increases by $1$ if the first $10$ tests are not considered, and decreases by $1$ if the last $10$ tests are not considered. If his average scores for the first $10$ and the last $10$ tests are $20$ and $30$, respectively, then the total number of tests taken by him is ________
33
Raju and Lalitha originally had marbles in the ratio $4:9$. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became $5:6$. What fraction of her original number of marbles was given by Lalitha to Raju? $1/4$ $7/33$ $1/5$ $6/19$
34
Let $ABCD$ be a rectangle inscribed in a circle of radius $13$ cm. Which one of the following pairs can represent, in cm, the possible length and breadth of $ABCD$? $24,10$ $25,9$ $24,12$ $25,10$
35
In a circle with center $O$ and radius $1$ cm, an arc $AB$ makes an angle $60$ degrees at $O$. Let $R$ be the region bounded by the radii $OA$, $OB$ and the arc $AB$. If $C$ and $D$ are two points on $OA$ and $OB$, respectively, such that $OC = OD$ and the area of triangle $OCD$ is ... $\bigg(\dfrac{\pi}{6} \bigg)^\frac{1}{2} \\$ $\bigg(\dfrac{\pi}{4\sqrt 3} \bigg)^\frac{1}{2}$
36
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
37
The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x +2$ is perfectly divisible by either $3$ or $4$, is _______
If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________
In an examination, the maximum possible score is $N$ while the pass mark is $45\%$ of $N$. A candidate obtains $36$ marks, but falls short of the pass mark by $68\%$. Which one of the following is then correct? $N\leq 200$ $243\leq N\leq 252$ $N\geq 253$ $201\leq N\leq 242$
Two types of tea, $A$ and $B$, are mixed and then sold at Rs. $40$ per kg. The profit is $10\%$ if $A$ and $B$ are mixed in the ratio $3 : 2$, and $5\%$ if this ratio is $2 : 3$. The cost prices, per kg, of $A$ and $B$ are in the ratio $18:25$ $19:24$ $21:25$ $17:25$