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CAT 2018 Set-2 | Question: 66
Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular ... -aged and Young visitors buying Gold tickets were equal The numbers of Gold and Platinum tickets bought by Young visitors were equal

go_editor asked in Logical Reasoning Mar 20, 2020

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CAT 2018 Set-2 | Question: 69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is

go_editor asked in Quantitative Aptitude Mar 20, 2020

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CAT 2018 Set-2 | Question: 67
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is $80707$ $80773$ $80730$ $80751$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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4

CAT 2018 Set-2 | Question: 68
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? $5$ $6$ $8$ $7$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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CAT 2018 Set-2 | Question: 75
A $20\%$ ethanol solution is mixed with another ethanol solution, say, $\text{S}$ of unknown concentration in the proportion $1:3$ by volume. This mixture is then mixed with an equal volume of $20\%$ ethanol solution. If the resultant mixture is a $31.25\%$ ethanol solution, then the unknown concentration of $\text{S}$ is $52\%$ $50\%$ $55\%$ $48\%$

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

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CAT 2018 Set-2 | Question: 73
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of the same circle is $8$ $6\sqrt2$ $5\sqrt3$ $2\pi$

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

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CAT 2018 Set-2 | Question: 72
On a triangle $\text{ABC}$, a circle with diameter $\text{BC}$ is drawn, intersecting $\text{AB}$ and $\text{AC}$ at points $\text{P}$ and $\text{Q}$, respectively. If the lengths of $\text{AB, AC}$, and $\text{CP}$ are $30$ cm, $25$ cm, and $20$ cm respectively, then the length of $\text{BQ}$, in cm, is __________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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CAT 2018 Set-2 | Question: 70
Gopal borrows Rs. $\text{X}$ from Ankit at $8\%$ annual interest. He then adds Rs. $\text{Y}$ of his own money and lends Rs. $\text{X+Y}$ to Ishan at $10\%$ annual interest. At the end of the year, after returning Ankit's dues, ... interest retained by him would have increased by Rs. $150$. If all interests are compounded annually, then find the value of $\text{X+Y}$.

go_editor asked in Quantitative Aptitude Mar 20, 2020

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9

CAT 2018 Set-2 | Question: 74
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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10

CAT 2018 Set-2 | Question: 71
On a long stretch of east-west road, $\text{A}$ and $\text{B}$ are two points such that $\text{B}$ is $350$ km west of $\text{A}$. One car starts from $\text{A}$ and another from $\text{B}$ at the same time. If they move towards ... after $1$ hour. If they both move towards east, then they meet in $7$ hrs. The difference between their speeds, in km per hour, is _______

go_editor asked in Quantitative Aptitude Mar 20, 2020

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11

CAT 2018 Set-2 | Question: 78
A water tank has inlets of two types $\text{A}$ and $\text{B}$. All inlets of type $\text{A}$ when open, bring in water at the same rate. All inlets of type $\text{B}$, when open, bring in water at the same rate. The empty tank is completely ... will the empty tank get completely filled if $7$ inlets of type $\text{A}$ and $27$ inlets of type $\text{B}$ are open?

go_editor asked in Quantitative Aptitude Mar 20, 2020

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12

CAT 2018 Set-2 | Question: 77
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 > 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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3 votes

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13

CAT 2018 Set-2 | Question: 76
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump $\text{A}$ or pump $\text{B}$ or both start working until the tank is full. On Monday, $\text{A}$ alone completed filling the tank at $8$ pm. On Tuesday, $\text{B}$ ... tank filled on Thursday if both pumps were used simultaneously all along? $4:36$ pm $4:12$ pm $4:24$ pm $4:48$ pm

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

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3 votes

2 answers

14

CAT 2018 Set-2 | Question: 83
A jar contains a mixture of $175$ ml water and $700$ ml alcohol. Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now $35.2$ $30.3$ $20.5$ $25.4$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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2 votes

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15

CAT 2018 Set-2 | Question: 84
In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior ... number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

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3 votes

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CAT 2018 Set-2 | Question: 82
Ramesh and Ganesh can together complete a work in $16$ days. After seven days of working together, Ramesh got sick and his efficiency fell by $30\%$. As a result, they completed the work in $17$ days instead of $16$ days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work? $13.5$ $11$ $12$ $14.5$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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3 votes

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17

CAT 2018 Set-2 | Question: 81
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$ $1$ $24/5$ $47/10$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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18

CAT 2018 Set-2 | Question: 80
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals

go_editor asked in Quantitative Aptitude Mar 20, 2020

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19

CAT 2018 Set-2 | Question: 79
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest possible $x$ is _______

go_editor asked in Quantitative Aptitude Mar 20, 2020

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3 votes

2 answers

20

CAT 2018 Set-2 | Question: 90
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product? $-32$ $48$ $64$ $16$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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21

CAT 2018 Set-2 | Question: 89
The arithmetic mean of $x,y$ and $z$ is $80$, and that of $x,y,z,u$ and $v$ is $75$, where $u=\left (x+y \right)/2$ and $v=\left (y+z \right)/2$. If $x\geq z$, then the minimum possible value of $x$ is ____________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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22

CAT 2018 Set-2 | Question: 88
Points $\text{A}$ and $\text{B}$ are $150$ km apart. Cars $1$ and $2$ travel from $\text{A}$ to $\text{B}$, but car $2$ starts from $\text{A}$ when car $1$ is already $20$ km away from $\text{A}$. Each car travels at a speed of $100$ kmph ... $25$ kmph for the last $50$ km. The distance, in km, between car $2$ and $\text{B}$ when car $1$ reaches $\text{B}$ is ________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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23

CAT 2018 Set-2 | Question: 87
Let $a_{1},a_{2},\dots , a_{52}$ be a positive integers such that $a_{1}<a_{2}<\dots < a_{52}$. Suppose, their arithmetic mean is one less than the arithmetic mean of $a_{2},a_{3},\dots , a_{52}$. If $a_{52}=100$ , then the largest possible value of $a_{1}$ is ________ $20$ $23$ $48$ $45$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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24

CAT 2018 Set-2 | Question: 86
A parallelogram $\text{ABCD}$ has area $48$ sqcm. If the length of $\text{CD}$ is $8$ cm and that of $\text{AD}$ is $s$ cm, then which one of the following is necessarily true? $s\geq6$ $s\neq6$ $s\leq6$ $5\leq s\leq7$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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25

CAT 2018 Set-2 | Question: 85
If $\text{A}=\left \{6^{2n} - 35n - 1: n=1,2,3 \dots \right \}$ and $\text{B}= \left \{35\left (n - 1 \right ) : n=1,2,3\dots \right \}$ then which of the following is true? Neither every member of $\text{A}$ is in $\text{B}$ nor every member of ... $\text{A}$ Every member of $\text{B}$ is in $\text{A}$ At least one member of $\text{A}$ is not in $\text{B}$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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2 votes

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26

CAT 2018 Set-2 | Question: 96
From a rectangle $\text{ABCD}$ of area $768$ sq cm, a semicircular part with diameter $\text{AB}$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion, in cm, is $80 + 16\pi$ $86+8\pi$ $82+24\pi$ $88+12\pi$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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2 votes

1 answer

27

CAT 2018 Set-2 | Question: 95
The scores of Amal and Bimal in an examination are in the ratio $11: 14$. After an appeal, their scores increase by the same amount and their new scores are in the ratio $47 : 56$. The ratio of Bimal's new score to that of his original score is $5:4$ $8:5$ $4:3$ $3:2$

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

302 views

3 votes

1 answer

28

CAT 2018 Set-2 | Question: 94
The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio $1:4$ $2:9$ $1:3$ $3:8$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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29

CAT 2018 Set-2 | Question: 93
The strength of a salt solution is $p\%$ if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions $\text{A, B, C}$ are mixed in the proportion $1:2:3$, then the resulting solution has strength $20\%$. If instead the proportion is $3:2:1$, then the ... $\text{D}$ to that of $\text{A}$ is $2:5$ $1:3$ $1:4$ $3:10$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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2 votes

1 answer

30

CAT 2018 Set-2 | Question: 91
For two sets $\text{A}$ and $\text{B}$, let $\text{A} \triangle \text{B}$ denote the set of elements which belong to $\text{A}$ or $\text{B}$ ... $(\text{P} \triangle \text{Q}) \triangle (\text{R}\triangle \text{S})$ is $9$ $7$ $6$ $8$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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1 answer

31

CAT 2018 Set-2 | Question: 92
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to $33$ $37$ $39$ $35$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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32

CAT 2018 Set-2 | Question: 99
Points $\text{A, P, Q}$ and $\text{B}$ lie on the same line such that $\text{P, Q}$ and $\text{B}$ are, respectively, $100$ km, $200$ km and $300$ km away from $\text{A}$. Cars $1$ and $2$ leave $\text{A}$ ... car is moving in uniform speed then the ratio of the speed of car $2$ to that of car $1$ is $1:2$ $2:9$ $1:4$ $2:7$

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

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1 vote

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33

CAT 2018 Set-2 | Question: 98
There are two drums, each containing a mixture of paints $\text{A}$ and $\text{B}$. In drum $1, \text{A}$ and $\text{B}$ are in the ratio $18: 7$. The mixtures from drums $1$ and $2$ are mixed in the ratio $3: 4$ and in this final mixture, $\text{A}$ and ... $2$, then $\text{A}$ and $\text{B}$ were in the ratio $229:141$ $220:149$ $239: 161$ $251: 163$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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2 votes

1 answer

34

CAT 2018 Set-2 | Question: 97
A triangle $\text{ABC}$ has area $32$ sq units and its side $\text{BC}$, of length $8$ units, lies on the line $x =4$. Then the shortest possible distance between $\text{A}$ and the point $(0,0)$ is $4$ units $8$ units $4\sqrt2$ units $ 2\sqrt2$ units

go_editor asked in Quantitative Aptitude Mar 20, 2020

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3 votes

1 answer

35

CAT 2018 Set-2 | Question: 100
$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100}=?$ $1/2$ $0$ $10$ $-4$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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36

CAT 2018 Set-2 | Question: 58
An agency entrusted to accredit colleges looks at four parameters: faculty quality $\text{(F)}$, reputation $\text{(R)},$ placement quality $\text{(P)}$, and infrastructure $\text{(I)}.$ The four parameters are used to arrive at an overall score, which the agency ... $31$ and $40$, both exclusive? $1$ $3$ $0$ $2$

go_editor asked in Data Interpretation Mar 20, 2020

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37

CAT 2018 Set-2 | Question: 56
An agency entrusted to accredit colleges looks at four parameters: faculty quality $\text{(F)}$, reputation $\text{(R)},$ placement quality $\text{(P)}$, and infrastructure $\text{(I)}.$ The four parameters are used to arrive at an overall ... Cosmopolitan; and Education Aid is better than $\text{A}$-one. How many colleges receive the accreditation of $\text{AAA}?$

go_editor asked in Data Interpretation Mar 20, 2020

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38

CAT 2018 Set-2 | Question: 57
An agency entrusted to accredit colleges looks at four parameters: faculty quality $\text{(F)}$, reputation $\text{(R)},$ placement quality $\text{(P)}$, and infrastructure $\text{(I)}.$ The four parameters are used to arrive at an ... than Cosmopolitan; and Education Aid is better than $\text{A}$-one. What is the highest overall score among the eight colleges?

go_editor asked in Data Interpretation Mar 20, 2020

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39

CAT 2018 Set-2 | Question: 63
Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day: $140$ tickets ... tickets, then which among the following could be the total number of Platinum tickets sold? $34$ $38$ $32$ $36$

go_editor asked in Logical Reasoning Mar 20, 2020

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40

CAT 2018 Set-2 | Question: 62
According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as $5688999\;35\;1135556678\;56\;458\;13666689\;1334\;79\;13366$ This coding scheme has the following rules: The scheme is case-insensitive (does not distinguish between upper case and lower case ... $\text{S, U, V}$ $\text{I, B, M}$ $\text{X, Y, Z}$ $\text{S, E, Z}$

go_editor asked in Logical Reasoning Mar 20, 2020

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