Aptitude Overflow - Recent questions tagged cat2018-2
https://aptitude.gateoverflow.in/tag/cat2018-2
Powered by Question2AnswerCAT2018-2: 68
https://aptitude.gateoverflow.in/6149/cat2018-2-68
<p>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?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$5$</li>
<li>$6$</li>
<li>$8$</li>
<li>$7$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6149/cat2018-2-68Fri, 20 Mar 2020 05:48:53 +0000CAT2018-2: 67
https://aptitude.gateoverflow.in/6150/cat2018-2-67
<p>The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$80707$</li>
<li>$80773$</li>
<li>$80730$</li>
<li>$80751$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6150/cat2018-2-67Fri, 20 Mar 2020 05:48:53 +0000CAT2018-2: 69
https://aptitude.gateoverflow.in/6148/cat2018-2-69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6148/cat2018-2-69Fri, 20 Mar 2020 05:48:53 +0000CAT2018-2: 66
https://aptitude.gateoverflow.in/6151/cat2018-2-66
<p>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:</p>
<ol>
<li>$140$ tickets were sold.</li>
<li>The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.</li>
<li>Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.</li>
<li>The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.</li>
</ol>
<p>Which of the following statements $MUST$ be $FALSE$?</p>
<p> </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The numbers of Old and Middle-aged visitors buying Economy tickets were equal</li>
<li>The numbers of Old and Middle-aged visitors buying Platinum tickets were equal</li>
<li>The numbers of Middle-aged and Young visitors buying Gold tickets were equal</li>
<li>The numbers of Gold and Platinum tickets bought by Young visitors were equal</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6151/cat2018-2-66Fri, 20 Mar 2020 05:48:53 +0000CAT2018-2: 74
https://aptitude.gateoverflow.in/6143/cat2018-2-74
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 $f(x)$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6143/cat2018-2-74Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 71
https://aptitude.gateoverflow.in/6146/cat2018-2-71
On a long stretch of east-west road, $A$ and $B$ are two points such that $B$ is $350$ km west of $A$. One car starts from $A$ and another from $B$ at the same time. If they move towards each other, then they meet after $1$ hour. If they both move towards east, then they meet in $7$ hrs. The difference between their speeds, in km per hour, isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6146/cat2018-2-71Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 70
https://aptitude.gateoverflow.in/6147/cat2018-2-70
Gopal borrows Rs. $X$ from Ankit at $8$% annual interest. He then adds Rs. $Y$ of his own money and lends Rs. $X+Y$ to Ishan at $10$% annual interest. At the end of the year, after returning Ankit's dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal Ient Rs. $X+2Y$ to Ishan at $10$%, then the net interest retained by him would have increased by Rs. $150$. If all interests are compounded annually, then find the value of $X+Y$.Quantitative Aptitudehttps://aptitude.gateoverflow.in/6147/cat2018-2-70Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 72
https://aptitude.gateoverflow.in/6145/cat2018-2-72
On a triangle $ABC$, a circle with diameter $BC$ is drawn, intersecting $AB$ and $AC$ at points $P$ and $Q$, respectively. If the lengths of $AB$, $AC$, and $CP$ are $30$ cm, $25$ cm, and $20$ cm respectively, then the length of $BQ$, in cm, isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6145/cat2018-2-72Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 73
https://aptitude.gateoverflow.in/6144/cat2018-2-73
<p>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</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$8$</li>
<li>$6\sqrt2$</li>
<li>$5\sqrt3$</li>
<li>$2\pi$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6144/cat2018-2-73Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 75
https://aptitude.gateoverflow.in/6142/cat2018-2-75
<p>A $20$% ethanol solution is mixed with another ethanol solution, say, $S$ 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 $S$ is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$52$%</li>
<li>$50$%</li>
<li>$55$%</li>
<li>$48$%</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6142/cat2018-2-75Fri, 20 Mar 2020 05:48:52 +0000CAT2018-2: 76
https://aptitude.gateoverflow.in/6141/cat2018-2-76
<p>A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump $A$ or pump $B$ or both start working until the tank is full. On Monday, $A$ alone completed filling the tank at $8$ pm. On Tuesday, $B$ alone completed filling the tank at $6$ pm. On Wednesday, $A$ alone worked till $5$ pm, and then B worked alone from $5$ pm to $7$ pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$4:36$ pm</li>
<li>$4:12$ pm</li>
<li>$4:24$ pm</li>
<li>$4:48$ pm</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6141/cat2018-2-76Fri, 20 Mar 2020 05:48:51 +0000CAT2018-2: 77
https://aptitude.gateoverflow.in/6140/cat2018-2-77
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 $2a-6b$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6140/cat2018-2-77Fri, 20 Mar 2020 05:48:51 +0000CAT2018-2: 78
https://aptitude.gateoverflow.in/6139/cat2018-2-78
A water tank has inlets of two types $A$ and $B$. All inlets of type $A$ when open, bring in water at the same rate. All inlets of type $B$, when open, bring in water at the same rate. The empty tank is completely filled in $30$ minutes if $10$ inlets of type $A$ and $45$ inlets of type $B$ are open, and in $1$ hour if $8$ inlets of type $A$ and $18$ inlets of type $B$ are open. In how many minutes will the empty tank get completely filled if $7$ inlets of type $A$ and $27$ inlets of type $B$ are open?Quantitative Aptitudehttps://aptitude.gateoverflow.in/6139/cat2018-2-78Fri, 20 Mar 2020 05:48:51 +0000CAT2018-2: 83
https://aptitude.gateoverflow.in/6134/cat2018-2-83
<p>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</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$35.2$</li>
<li>$30.3$</li>
<li>$20.5$</li>
<li>$25.4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6134/cat2018-2-83Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 84
https://aptitude.gateoverflow.in/6133/cat2018-2-84
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 level is $153$, while the number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6133/cat2018-2-84Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 79
https://aptitude.gateoverflow.in/6138/cat2018-2-79
If $N$ and $x$ are positive integers such that $N^{N}=2^{160}$ and $N^{2} + 2^{N}$ is an integral multiple of $2^{x}$, then the largest possible $x$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6138/cat2018-2-79Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 82
https://aptitude.gateoverflow.in/6135/cat2018-2-82
<p>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?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$13.5$</li>
<li>$11$</li>
<li>$12$</li>
<li>$14.5$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6135/cat2018-2-82Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 81
https://aptitude.gateoverflow.in/6136/cat2018-2-81
<p>If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$16/5$</li>
<li>$1$</li>
<li>$24/5$</li>
<li>$47/10$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6136/cat2018-2-81Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 80
https://aptitude.gateoverflow.in/6137/cat2018-2-80
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 $k$ equalsQuantitative Aptitudehttps://aptitude.gateoverflow.in/6137/cat2018-2-80Fri, 20 Mar 2020 05:48:50 +0000CAT2018-2: 85
https://aptitude.gateoverflow.in/6132/cat2018-2-85
<p>If $A=\left \{6^{2n} – 35n – 1: n=1,2,3 \dots \right \}$ and $B= \left \{35\left (n – 1 \right ) : n=1,2,3\dots \right \}$ then which of the following is true?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>Neither every member of $A$ is in $B$ nor every member of $B$ is in $A$</li>
<li>Every member of $A$ is in $B$ and at least one member of $B$ is not in $A$</li>
<li>Every member of $B$ is in $A$</li>
<li>At least one member of $A$ is not in $B$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6132/cat2018-2-85Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 86
https://aptitude.gateoverflow.in/6131/cat2018-2-86
<p>A parallelogram $ABCD$ has area $48$ sqcm. If the length of $CD$ is $8$ cm and that of $AD$ is $s$ cm, then which one of the following is necessarily true?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$s\geq6$</li>
<li>$s\neq6$</li>
<li>$s\leq6$</li>
<li>$5\leq s\leq7$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6131/cat2018-2-86Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 87
https://aptitude.gateoverflow.in/6130/cat2018-2-87
<p>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</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$20$</li>
<li>$23$</li>
<li>$48$</li>
<li>$45$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6130/cat2018-2-87Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 88
https://aptitude.gateoverflow.in/6129/cat2018-2-88
Points $A$ and $B$ are $150$ km apart. Cars $1$ and $2$ travel from $A$ to $B$, but car $2$ starts from $A$ when car $1$ is already $20$ km away from $A$. Each car travels at a speed of $100$ kmph for the first $50$ km, at $50$ kmph for the next $50$ km, and at $25$ kmph for the last $50$ km. The distance, in km, between car $2$ and $B$ when car $1$ reaches $B$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6129/cat2018-2-88Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 89
https://aptitude.gateoverflow.in/6128/cat2018-2-89
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 $x$ isQuantitative Aptitudehttps://aptitude.gateoverflow.in/6128/cat2018-2-89Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 90
https://aptitude.gateoverflow.in/6127/cat2018-2-90
<p>If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$-32$</li>
<li>$48$</li>
<li>$64$</li>
<li>$16$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6127/cat2018-2-90Fri, 20 Mar 2020 05:48:49 +0000CAT2018-2: 95
https://aptitude.gateoverflow.in/6122/cat2018-2-95
<p>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</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$5:4$</li>
<li>$8:5$</li>
<li>$4:3$</li>
<li>$3:2$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6122/cat2018-2-95Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 96
https://aptitude.gateoverflow.in/6121/cat2018-2-96
<p>From a rectangle $ABCD$ of area $768$ sq cm, a semicircular part with diameter $AB$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion, in cm, is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$80 + 16\pi$</li>
<li>$86+8\pi$</li>
<li>$82+24\pi$</li>
<li>$88+12\pi$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6121/cat2018-2-96Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 91
https://aptitude.gateoverflow.in/6126/cat2018-2-91
<p>For two sets $A$ and $B$, let $A \triangle B$ denote the set of elements which belong to $A$ or $B$ but not both. If $P= \{1,2,3,4\}, Q =\{2,3,5,6\}, R=\{1,3,7,8,9\}, S =\{2,4,9,10\},$ then the number of elements in $(P\triangle Q) \triangle (R\triangle S)$ is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$9$</li>
<li>$7$</li>
<li>$6$</li>
<li>$8$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6126/cat2018-2-91Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 94
https://aptitude.gateoverflow.in/6123/cat2018-2-94
<p>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</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1:4$</li>
<li>$2:9$</li>
<li>$1:3$</li>
<li>$3:8$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6123/cat2018-2-94Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 92
https://aptitude.gateoverflow.in/6125/cat2018-2-92
<p>The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$33$</li>
<li>$37$</li>
<li>$39$</li>
<li>$35$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6125/cat2018-2-92Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 93
https://aptitude.gateoverflow.in/6124/cat2018-2-93
<p>The strength of a salt solution is $p$% if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions $A, B, C$ 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 resulting solution has strength $30$%. A fourth solution, $D$, is produced by mixing $B$ and $C$ in the ratio $2:7$. The ratio of the strength of $D$ to that of $A$ is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$2:5$</li>
<li>$1:3$</li>
<li>$1:4$</li>
<li>$3:10$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6124/cat2018-2-93Fri, 20 Mar 2020 05:48:48 +0000CAT2018-2: 97
https://aptitude.gateoverflow.in/6120/cat2018-2-97
<p>A triangle $ABC$ has area $32$ sq units and its side $BC$, of length $8$ units, lies on the line $x =4$. Then the shortest possible distance between $A$ and the point $(0,0)$ is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$4$ units</li>
<li>$8$ units</li>
<li>$4\sqrt2$ units</li>
<li>$ 2\sqrt2$ units</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6120/cat2018-2-97Fri, 20 Mar 2020 05:48:47 +0000CAT2018-2: 98
https://aptitude.gateoverflow.in/6119/cat2018-2-98
<p>There are two drums, each containing a mixture of paints $A$ and $B$. In drum $1, A$ and $B$ 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, $A$ and $B$ are in the ratio $13 :7$. In drum $2$, then $A$ and $B$ were in the ratio</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$229:141$</li>
<li>$220:149$</li>
<li>$239: 161$</li>
<li>$251: 163$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6119/cat2018-2-98Fri, 20 Mar 2020 05:48:47 +0000CAT2018-2: 99
https://aptitude.gateoverflow.in/6118/cat2018-2-99
<p>Points $A, P, Q$ and $B$ lie on the same line such that $P, Q$ and $B$ are, respectively, $100$ km, $200$ km and $300$ km away from $A$. Cars $1$ and $2$ leave $A$ at the same time and move towards $B$. Simultaneously, car $3$ leaves $B$ and moves towards $A$. Car $3$ meets car $1$ at $Q$, and car $2$ at $P$. If each car is moving in uniform speed then the ratio of the speed of car $2$ to that of car $1$ is </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1:2$</li>
<li>$2:9$</li>
<li>$1:4$</li>
<li>$2:7$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6118/cat2018-2-99Fri, 20 Mar 2020 05:48:47 +0000CAT2018-2: 100
https://aptitude.gateoverflow.in/6117/cat2018-2-100
<p>$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100}=?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1/2$</li>
<li>$0$</li>
<li>$10$</li>
<li>$-4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6117/cat2018-2-100Fri, 20 Mar 2020 05:48:46 +0000CAT2018-2: 56
https://aptitude.gateoverflow.in/6116/cat2018-2-56
<p>An agency entrusted to accredit colleges looks at four parameters: faculty quality $(F)$, reputation $(R)$. placement quality $(P)$, and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points:$A$ ($50$ points), $B$ ($40$ points), $C$ ($30$ points), $D$ ($20$ points), and $F$ ($0$ points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are $0.1$, $0.2$,$0.3$ and $0.4$ in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:</p>
<p>$\begin{array}{|cl|cl|}\hline<br>
&\text{Range} && \text{Accreditation}\\ \hline<br>
& \text{Overall score $\geq$ 45} & \text{AAA} \\ \hline<br>
& \text{35 $\leq$ Overall score <45} & \text{BAA} \\ \hline<br>
& \text{25 $\leq$ Overall score <35} & \text{BBA} \\ \hline<br>
& \text{15 $\leq$ Overall score <25} & \text{BBB} \\ \hline<br>
&\text{Overall score <15} & \text{Junk} \\ \hline \end{array}$</p>
<p>Eight colleges apply for accreditation, and receive the following grades in the four parameters ($F$, $R$, $P$, and $I$):</p>
<p>$\begin{array}{|cl|cI|cI|cI|}\hline<br>
&\text{} & \text{F} & \text{R} & \text{P} & \text{I} \\ \hline<br>
&\text{A-one} & \text{A} & \text{A} & \text{A} & \text{B} \\ \hline<br>
&\text{Best Ed} & \text{B} & \text{C} & \text{D} & \text{D} \\ \hline<br>
&\text{Cosmopolitan} & \text{B} & \text{D} & \text{D} & \text{C} \\ \hline<br>
&\text{Dominance} & \text{D} & \text{D} & \text{B} & \text{C} \\ \hline<br>
&\text{Education Aid} & \text{A} & \text{A} & \text{B} & \text{A} \\ \hline<br>
&\text{Fancy} & \text{A} & \text{A} & \text{B} & \text{B} \\ \hline<br>
&\text{Global} & \text{C} & \text{F} & \text{D} & \text{D} \\ \hline<br>
&\text{High Q} & \text{C} & \text{D} & \text{D} & \text{B} \\ \hline \end{array}$</p>
<p>It is further known that in terms of overall scores:</p>
<ol>
<li>High $Q$ is better than Best $Ed$;</li>
<li>Best $Ed$ is better than Cosmopolitan; and</li>
<li>Education Aid is better than $A$-one.</li>
</ol>
<p>How many colleges receive the accreditation of $AAA$?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6116/cat2018-2-56Fri, 20 Mar 2020 05:47:32 +0000CAT2018-2: 57
https://aptitude.gateoverflow.in/6115/cat2018-2-57
<p>An agency entrusted to accredit colleges looks at four parameters: faculty quality $(F)$, reputation $(R)$. placement quality $(P)$, and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points:$A$ ($50$ points), $B$ ($40$ points), $C$ ($30$ points), $D$ ($20$ points), and $F$ ($0$ points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are $0.1$, $0.2$,$0.3$ and $0.4$ in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:</p>
<p>$\begin{array}{|cl|cl|}\hline<br>
&\text{Range} && \text{Accreditation}\\ \hline<br>
& \text{Overall score $\geq$ 45} & \text{AAA} \\ \hline<br>
& \text{35 $\leq$ Overall score <45} & \text{BAA} \\ \hline<br>
& \text{25 $\leq$ Overall score <35} & \text{BBA} \\ \hline<br>
& \text{15 $\leq$ Overall score <25} & \text{BBB} \\ \hline<br>
&\text{Overall score <15} & \text{Junk} \\ \hline \end{array}$</p>
<p>Eight colleges apply for accreditation, and receive the following grades in the four parameters ($F$, $R$, $P$, and $I$):</p>
<p>$\begin{array}{|cl|cI|cI|cI|}\hline<br>
&\text{} & \text{F} & \text{R} & \text{P} & \text{I} \\ \hline<br>
&\text{A-one} & \text{A} & \text{A} & \text{A} & \text{B} \\ \hline<br>
&\text{Best Ed} & \text{B} & \text{C} & \text{D} & \text{D} \\ \hline<br>
&\text{Cosmopolitan} & \text{B} & \text{D} & \text{D} & \text{C} \\ \hline<br>
&\text{Dominance} & \text{D} & \text{D} & \text{B} & \text{C} \\ \hline<br>
&\text{Education Aid} & \text{A} & \text{A} & \text{B} & \text{A} \\ \hline<br>
&\text{Fancy} & \text{A} & \text{A} & \text{B} & \text{B} \\ \hline<br>
&\text{Global} & \text{C} & \text{F} & \text{D} & \text{D} \\ \hline<br>
&\text{High Q} & \text{C} & \text{D} & \text{D} & \text{B} \\ \hline \end{array}$</p>
<p>It is further known that in terms of overall scores:</p>
<ol>
<li>High $Q$ is better than Best $Ed$;</li>
<li>Best $Ed$ is better than Cosmopolitan; and</li>
<li>Education Aid is better than $A$-one.</li>
</ol>
<p>what is the highest overall score among the eight colleges?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6115/cat2018-2-57Fri, 20 Mar 2020 05:47:32 +0000CAT2018-2: 58
https://aptitude.gateoverflow.in/6114/cat2018-2-58
<p>An agency entrusted to accredit colleges looks at four parameters: faculty quality $(F)$, reputation $(R)$. placement quality $(P)$, and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points:$A$ ($50$ points), $B$ ($40$ points), $C$ ($30$ points), $D$ ($20$ points), and $F$ ($0$ points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are $0.1$, $0.2$,$0.3$ and $0.4$ in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:</p>
<p>$\begin{array}{|cl|cl|}\hline<br>
&\text{Range} && \text{Accreditation}\\ \hline<br>
& \text{Overall score $\geq$ 45} & \text{AAA} \\ \hline<br>
& \text{35 $\leq$ Overall score <45} & \text{BAA} \\ \hline<br>
& \text{25 $\leq$ Overall score <35} & \text{BBA} \\ \hline<br>
& \text{15 $\leq$ Overall score <25} & \text{BBB} \\ \hline<br>
&\text{Overall score <15} & \text{Junk} \\ \hline \end{array}$</p>
<p>Eight colleges apply for accreditation, and receive the following grades in the four parameters ($F$, $R$, $P$, and $I$):</p>
<p>$\begin{array}{|cl|cI|cI|cI|}\hline<br>
&\text{} & \text{F} & \text{R} & \text{P} & \text{I} \\ \hline<br>
&\text{A-one} & \text{A} & \text{A} & \text{A} & \text{B} \\ \hline<br>
&\text{Best Ed} & \text{B} & \text{C} & \text{D} & \text{D} \\ \hline<br>
&\text{Cosmopolitan} & \text{B} & \text{D} & \text{D} & \text{C} \\ \hline<br>
&\text{Dominance} & \text{D} & \text{D} & \text{B} & \text{C} \\ \hline<br>
&\text{Education Aid} & \text{A} & \text{A} & \text{B} & \text{A} \\ \hline<br>
&\text{Fancy} & \text{A} & \text{A} & \text{B} & \text{B} \\ \hline<br>
&\text{Global} & \text{C} & \text{F} & \text{D} & \text{D} \\ \hline<br>
&\text{High Q} & \text{C} & \text{D} & \text{D} & \text{B} \\ \hline \end{array}$</p>
<p>It is further known that in terms of overall scores:</p>
<ol>
<li>High $Q$ is better than Best $Ed$;</li>
<li>Best $Ed$ is better than Cosmopolitan; and</li>
<li>Education Aid is better than $A$-one.</li>
</ol>
<p>How many colleges have overall scores between $31$ and $40$, both exclusive?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$</li>
<li>$3$</li>
<li>$0$</li>
<li>$2$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6114/cat2018-2-58Fri, 20 Mar 2020 05:47:32 +0000CAT2018-2: 62
https://aptitude.gateoverflow.in/6110/cat2018-2-62
<p>According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as $5688999$ $35$ $1135556678$ $56$ $458$ $13666689$ $1334$ $79$ $13366$</p>
<p>This coding scheme has the following rules:</p>
<ol>
<li>The scheme is case-insensitive (does not distinguish between upper case and lower case letters).</li>
<li>Each letter has a unique code which is a single digit from among $1,2,3$,$\dots$,$9$.</li>
<li>The digit $9$ codes two letters, and every other digit codes there letters.</li>
<li>The code for a word is constructed by arranging the digits corresponding to its letters in a non decreasing sequence.</li>
</ol>
<p>Answer these questions on the basis of this information.</p>
<p>Which set of letters CANNOT be coded with the same digit? </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$S,U,V$</li>
<li>$I,B,M$</li>
<li>$X,Y,Z$</li>
<li>$S,E,Z$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6110/cat2018-2-62Fri, 20 Mar 2020 05:47:31 +0000CAT2018-2: 63
https://aptitude.gateoverflow.in/6109/cat2018-2-63
<p>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:</p>
<ol>
<li>$140$ tickets were sold.</li>
<li>The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.</li>
<li>Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.</li>
<li>The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.</li>
</ol>
<p>If the number of Old visitors buying Platinum tickets was equal to the number of Middle- aged visitors buying Platinum tickets, then which among the following could be the total number of Platinum tickets sold?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$34$</li>
<li>$38$</li>
<li>$32$</li>
<li>$36$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6109/cat2018-2-63Fri, 20 Mar 2020 05:47:31 +0000CAT2018-2: 60
https://aptitude.gateoverflow.in/6112/cat2018-2-60
<p>According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as $5688999$ $35$ $1135556678$ $56$ $458$ $13666689$ $1334$ $79$ $13366$</p>
<p>This coding scheme has the following rules:</p>
<ol>
<li>The scheme is case-insensitive (does not distinguish between upper case and lower case letters).</li>
<li>Each letter has a unique code which is a single digit from among $1,2,3$,$\dots$,$9$.</li>
<li>The digit $9$ codes two letters, and every other digit codes there letters.</li>
<li>The code for a word is constructed by arranging the digits corresponding to its letters in a non decreasing sequence.</li>
</ol>
<p>Answer these questions on the basis of this information.</p>
<p>What best can be concluded about the code for the letter $B$?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$ or $3$ or $4$</li>
<li>$3$</li>
<li>$1$</li>
<li>$3$ or $4$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6112/cat2018-2-60Fri, 20 Mar 2020 05:47:31 +0000CAT2018-2: 61
https://aptitude.gateoverflow.in/6111/cat2018-2-61
<p>According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as $5688999$ $35$ $1135556678$ $56$ $458$ $13666689$ $1334$ $79$ $13366$</p>
<p>This coding scheme has the following rules:</p>
<ol>
<li>The scheme is case-insensitive (does not distinguish between upper case and lower case letters).</li>
<li>Each letter has a unique code which is a single digit from among $1,2,3$,$\dots$,$9$.</li>
<li>The digit $9$ codes two letters, and every other digit codes there letters.</li>
<li>The code for a word is constructed by arranging the digits corresponding to its letters in a non decreasing sequence.</li>
</ol>
<p>Answer these questions on the basis of this information.</p>
<p>For how many digits can the complete list of letters associated with that digit be identified?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$3$</li>
<li>$0$</li>
<li>$1$</li>
<li>$2$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6111/cat2018-2-61Fri, 20 Mar 2020 05:47:31 +0000CAT2018-2: 59
https://aptitude.gateoverflow.in/6113/cat2018-2-59
<p>According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as $5688999$ $35$ $1135556678$ $56$ $458$ $13666689$ $1334$ $79$ $13366$</p>
<p>This coding scheme has the following rules:</p>
<ol>
<li>The scheme is case-insensitive (does not distinguish between upper case and lower case letters).</li>
<li>Each letter has a unique code which is a single digit from among $1,2,3$,$\dots$,$9$.</li>
<li>The digit $9$ codes two letters, and every other digit codes there letters.</li>
<li>The code for a word is constructed by arranging the digits corresponding to its letters in a non decreasing sequence.</li>
</ol>
<p>Answer these questions on the basis of this information.</p>
<p>What best can be concluded about the code for the letter $L$?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$</li>
<li>$1$ or $8$</li>
<li>$6$</li>
<li>$8$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6113/cat2018-2-59Fri, 20 Mar 2020 05:47:31 +0000CAT2018-2: 64
https://aptitude.gateoverflow.in/6108/cat2018-2-64
<p>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:</p>
<ol>
<li>$140$ tickets were sold.</li>
<li>The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.</li>
<li>Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.</li>
<li>The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.</li>
</ol>
<p>If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets, then the number of Old visitors buying Gold tickets was</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6108/cat2018-2-64Fri, 20 Mar 2020 05:47:30 +0000CAT2018-2: 65
https://aptitude.gateoverflow.in/6107/cat2018-2-65
<p>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:</p>
<ol>
<li>$140$ tickets were sold.</li>
<li>The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.</li>
<li>Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.</li>
<li>The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.</li>
</ol>
<p>If the number of Old visitors buying Gold tickets was strickly greater that the number of Young visitors buying Gold tickets, then the number of Middle-aged visitors buying Gold tickets was</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6107/cat2018-2-65Fri, 20 Mar 2020 05:47:30 +0000CAT2018-2: 46
https://aptitude.gateoverflow.in/6106/cat2018-2-46
<p>Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates were required to reach the venue before $8$ am. Immediately upon arrival, they were sent to one of three interview rooms: $101$, $102$, and $103$. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded in the log and have been marked as '?'.</p>
<p>$\begin{array}{|cl|cI|cI|cI|} \hline<br>
&\text{Time} & \text{7:10 am} & \text{7:15 am} &\text{7:25 am} & \text{7:30 am} & \text{7:40 am} & \text{7:45 am} \\ \hline<br>
& \text{Person} & \text{Akil,?} & \text{?} & \text{?} & \text{Chitra} & \text{Fatima} &\text{?} \\ \hline<br>
\end{array}$<br>
</p>
<p>Additionally here are some statements from the candidates:</p>
<p>Balaram: I was the third person to enter Room $101$</p>
<p>Chitra: I was the last person to enter the room I was allotted to.</p>
<p>Erina: I was the only person in the room I was allotted to.</p>
<p>Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.</p>
<p>Ganeshan: I was one among the two candidates allotted to Room $102$.</p>
<p>If Ganeshan entered the venue before Divya, when did Balaram enter the venue?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$7:45$ am</li>
<li>$7:25$ am</li>
<li>$7:15$ am</li>
<li>$7:10$ am</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6106/cat2018-2-46Fri, 20 Mar 2020 05:46:21 +0000CAT2018-2: 47
https://aptitude.gateoverflow.in/6105/cat2018-2-47
<p>The base exchange rate of a currency $X$ with respect to a currency $Y$ is the number of units of currency $Y$ which is equivalent in value to one unit of currency $X$. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.</p>
<p>A currency exchange outlet uses the local currency $L$ to buy and sell three international currencies $A$, $B$, and $C$, but does not exchange one international currency directly with another.<br>
The base exchange rates of $A$, $B$ and $C$ with respect to $L$ are in the ratio $100:120:1$. The buying exchange rates of each of $A$, $B$, and $C$ with respect to $L$ are $5$% below the corresponding base exchange rates, and their selling exchange rates are $10$% above their corresponding base exchange rates.</p>
<p>The following facts are known about the outlet on a particular day:</p>
<ol>
<li>The amount of $L$ used by the outlet to buy $C$ equals the amount of $L$ it received by selling $C$.</li>
<li>The amounts of $L$ used by the outlet to buy $A$ and $B$ are in the ratio $5:3$.</li>
<li>The amounts of $L$ the outlet received from the sales of $A$ and $B$ are in the ratio $5:9$.</li>
<li>The outlet received $88000$ units of $L$ by selling $A$ during the day.</li>
<li>The outlet started the day with some amount of $L$, $2500$ units of $A$, $4800$ units of $B$, and $48000$ units of $C$.</li>
<li>The outlet ended the day with some amount of $L$, $3300$ units of $A$, $4800$ units of $B$, and $51000$ units of $C$.</li>
</ol>
<p>How many units of currency A did the outlet buy on the day?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6105/cat2018-2-47Fri, 20 Mar 2020 05:46:20 +0000CAT2018-2: 48
https://aptitude.gateoverflow.in/6104/cat2018-2-48
<p>The base exchange rate of a currency $X$ with respect to a currency $Y$ is the number of units of currency $Y$ which is equivalent in value to one unit of currency $X$. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.</p>
<p>A currency exchange outlet uses the local currency $L$ to buy and sell three international currencies $A$, $B$, and $C$, but does not exchange one international currency directly with another.<br>
The base exchange rates of $A$, $B$ and $C$ with respect to $L$ are in the ratio $100:120:1$. The buying exchange rates of each of $A$, $B$, and $C$ with respect to $L$ are $5$% below the corresponding base exchange rates, and their selling exchange rates are $10$% above their corresponding base exchange rates.</p>
<p>The following facts are known about the outlet on a particular day:</p>
<ol>
<li>The amount of $L$ used by the outlet to buy $C$ equals the amount of $L$ it received by selling $C$.</li>
<li>The amounts of $L$ used by the outlet to buy $A$ and $B$ are in the ratio $5:3$.</li>
<li>The amounts of $L$ the outlet received from the sales of $A$ and $B$ are in the ratio $5:9$.</li>
<li>The outlet received $88000$ units of $L$ by selling $A$ during the day.</li>
<li>The outlet started the day with some amount of $L$, $2500$ units of $A$, $4800$ units of $B$, and $48000$ units of $C$.</li>
<li>The outlet ended the day with some amount of $L$, $3300$ units of $A$, $4800$ units of $B$, and $51000$ units of $C$.</li>
</ol>
<p>How many units of currency $C$ did the outlet sell on that day?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$19000$</li>
<li>$3000$</li>
<li>$6000$</li>
<li>$22000$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6104/cat2018-2-48Fri, 20 Mar 2020 05:46:20 +0000CAT2018-2: 49
https://aptitude.gateoverflow.in/6103/cat2018-2-49
<p>The base exchange rate of a currency $X$ with respect to a currency $Y$ is the number of units of currency $Y$ which is equivalent in value to one unit of currency $X$. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.</p>
<p>A currency exchange outlet uses the local currency $L$ to buy and sell three international currencies $A$, $B$, and $C$, but does not exchange one international currency directly with another.<br>
The base exchange rates of $A$, $B$ and $C$ with respect to $L$ are in the ratio $100:120:1$. The buying exchange rates of each of $A$, $B$, and $C$ with respect to $L$ are $5$% below the corresponding base exchange rates, and their selling exchange rates are $10$% above their corresponding base exchange rates.</p>
<p>The following facts are known about the outlet on a particular day:</p>
<ol>
<li>The amount of $L$ used by the outlet to buy $C$ equals the amount of $L$ it received by selling $C$.</li>
<li>The amounts of $L$ used by the outlet to buy $A$ and $B$ are in the ratio $5:3$.</li>
<li>The amounts of $L$ the outlet received from the sales of $A$ and $B$ are in the ratio $5:9$.</li>
<li>The outlet received $88000$ units of $L$ by selling $A$ during the day.</li>
<li>The outlet started the day with some amount of $L$, $2500$ units of $A$, $4800$ units of $B$, and $48000$ units of $C$.</li>
<li>The outlet ended the day with some amount of $L$, $3300$ units of $A$, $4800$ units of $B$, and $51000$ units of $C$.</li>
</ol>
<p>What was the base exchange rate of currency $B$ with respect to currency $L$ on that day?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6103/cat2018-2-49Fri, 20 Mar 2020 05:46:20 +0000CAT2018-2: 50
https://aptitude.gateoverflow.in/6102/cat2018-2-50
<p>The base exchange rate of a currency $X$ with respect to a currency $Y$ is the number of units of currency $Y$ which is equivalent in value to one unit of currency $X$. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.</p>
<p>A currency exchange outlet uses the local currency $L$ to buy and sell three international currencies $A$, $B$, and $C$, but does not exchange one international currency directly with another.<br>
The base exchange rates of $A$, $B$ and $C$ with respect to $L$ are in the ratio $100:120:1$. The buying exchange rates of each of $A$, $B$, and $C$ with respect to $L$ are $5$% below the corresponding base exchange rates, and their selling exchange rates are $10$% above their corresponding base exchange rates.</p>
<p>The following facts are known about the outlet on a particular day:</p>
<ol>
<li>The amount of $L$ used by the outlet to buy $C$ equals the amount of $L$ it received by selling $C$.</li>
<li>The amounts of $L$ used by the outlet to buy $A$ and $B$ are in the ratio $5:3$.</li>
<li>The amounts of $L$ the outlet received from the sales of $A$ and $B$ are in the ratio $5:9$.</li>
<li>The outlet received $88000$ units of $L$ by selling $A$ during the day.</li>
<li>The outlet started the day with some amount of $L$, $2500$ units of $A$, $4800$ units of $B$, and $48000$ units of $C$.</li>
<li>The outlet ended the day with some amount of $L$, $3300$ units of $A$, $4800$ units of $B$, and $51000$ units of $C$.</li>
</ol>
<p>What was the buying exchange rate of currency $C$ with respect to currency $L$ on that day?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$0.95$</li>
<li>$1.10$</li>
<li>$1.90$</li>
<li>$2.20$</li>
</ol>Logical Reasoninghttps://aptitude.gateoverflow.in/6102/cat2018-2-50Fri, 20 Mar 2020 05:46:20 +0000