Aptitude Overflow - Recent questions tagged numerical-answer
https://aptitude.gateoverflow.in/tag/numerical-answer
Powered by Question2AnswerCAT2019-2: 34
https://aptitude.gateoverflow.in/6218/cat2019-2-34
<p>The four sentences (labelled $1, 2, 3, 4$) given below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequence of the order of the sentences and key in the sequence of the four numbers as your answer.</p>
<ol start="1" style="list-style-type:decimal">
<li>Conceptualisations of ‘women’s time’ as contrary to clock-time and clock-time as synonymous with economic rationalism are two of the deleterious results of this representation</li>
<li>While dichotomies of ‘men’s time’, ‘women’s time’, clock-time, and caring time can be analytically useful, this article argues that everyday caring practices incorporate a multiplicity of times; and both men and women can engage in these multiple-times</li>
<li>When the everyday practices of working sole fathers and working sole mothers are carefully examined to explore conceptualisations of gendered time, it is found that caring time is often more focused on the clock than generally theorised</li>
<li>Clock-time has been consistently represented in feminist literature as a masculine artefact representative of a ‘time is money’ perspective</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/6218/cat2019-2-34Fri, 20 Mar 2020 07:16:51 +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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 51
https://aptitude.gateoverflow.in/6101/cat2018-2-51
<p>Fun Sports $(FS)$ provides training in three sports-Gilli-danda $(G)$, Kho-Kho $(K)$, and Ludo $(L)$. Currently it has an enrollment of $39$ students each of whom is enrolled in at least one of the three sports. The following details are known:</p>
<ol>
<li>The number of students enrolled only in L is double the number of students enrolled in all the three sports.</li>
<li>There are a total of $17$ students enrolled in $G$.</li>
<li>The number of students enrolled only in $G$ is one less than the number of students enrolled only in $L$.</li>
<li>The number of students enrolled only in $K$ is cqual to the number of students who are enrolled in both $K$ and $L$</li>
<li>The maximum student enrollment is in $L$.</li>
<li>Ten students enrolled in $G$ are also enrolled in at least one more sport.</li>
</ol>
<p>What is the minimum number of students enrolled in both $G$ and $L$ but not in $K$?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6101/cat2018-2-51Fri, 20 Mar 2020 05:46:19 +0000CAT2018-2: 53
https://aptitude.gateoverflow.in/6099/cat2018-2-53
<p>Fun Sports $(FS)$ provides training in three sports-Gilli-danda $(G)$, Kho-Kho $(K)$, and Ludo $(L)$. Currently it has an enrollment of $39$ students each of whom is enrolled in at least one of the three sports. The following details are known:</p>
<ol>
<li>The number of students enrolled only in L is double the number of students enrolled in all the three sports.</li>
<li>There are a total of $17$ students enrolled in $G$.</li>
<li>The number of students enrolled only in $G$ is one less than the number of students enrolled only in $L$.</li>
<li>The number of students enrolled only in $K$ is equal to the number of students who are enrolled in both $K$ and $L$</li>
<li>The maximum student enrollment is in $L$.</li>
<li>Ten students enrolled in $G$ are also enrolled in at least one more sport.</li>
</ol>
<p>Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in $G$ was six less than the number of students enrolled in $L$, while the number of students enrolled in $K$ went down by one. After the withdrawal, how many students were enrolled in both $G$ and $K$?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6099/cat2018-2-53Fri, 20 Mar 2020 05:46:19 +0000CAT2018-1: 61
https://aptitude.gateoverflow.in/6050/cat2018-1-61
<p>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 of her marks in the other two sections. Candidates who score less than $70\%$ marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p>
<p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p>
<ol>
<li>No two candidates had the same composite score.</li>
<li>Ajay was the unique highest scorer in WE.</li>
<li>Among the four recruited, Geeta had the lowest composite score.</li>
<li>Indu was recruited.</li>
<li>Danish, Harini, and Indu had scored the same marks the in GA.</li>
<li>Indu and Jatin both scored $100\%$ in exactly one section and Jatin’s composite score was 10 more than Indu’s.</li>
</ol>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=12094401443843151087"></p>
<p>If all the candidates except Ajay and Danish had different marks in DI, and Bala's composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI? ________</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6050/cat2018-1-61Thu, 19 Mar 2020 22:39:11 +0000CAT2018-1: 62
https://aptitude.gateoverflow.in/6049/cat2018-1-62
<p>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 of her marks in the other two sections. Candidates who score less than $70\%$ marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p>
<p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p>
<ol>
<li>No two candidates had the same composite score.</li>
<li>Ajay was the unique highest scorer in WE.</li>
<li>Among the four recruited, Geeta had the lowest composite score.</li>
<li>Indu was recruited.</li>
<li>Danish, Harini, and Indu had scored the same marks the in GA.</li>
<li>Indu and Jatin both scored $100\%$ in exactly one section and Jatin’s composite score was $10$ more than Indu’s.</li>
</ol>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=12094401443843151087"></p>
<p>If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE? _____</p>
<p> </p>Logical Reasoninghttps://aptitude.gateoverflow.in/6049/cat2018-1-62Thu, 19 Mar 2020 22:39:10 +0000CAT2018-1: 64
https://aptitude.gateoverflow.in/6047/cat2018-1-64
<p>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, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p>
<ol>
<li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is $75\%$ of the number of bureaucrats in the administration committee.</li>
<li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li>
<li>$60\%$ of the politicians are in the administration committee, and $20\%$ are in the teaching committee.</li>
</ol>
<p>What is the number of bureaucrats in the administration committee?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6047/cat2018-1-64Thu, 19 Mar 2020 22:39:10 +0000CAT2018-1: 65
https://aptitude.gateoverflow.in/6046/cat2018-1-65
<p>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, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p>
<ol>
<li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is $75\%$ of the number of bureaucrats in the administration committee.</li>
<li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li>
<li>$60\%$ of the politicians are in the administration committee, and $20\%$ are in the teaching committee.</li>
</ol>
<p>What is the number of educationalists in the research committee?</p>Logical Reasoninghttps://aptitude.gateoverflow.in/6046/cat2018-1-65Thu, 19 Mar 2020 22:39:10 +0000CAT2018-1: 68
https://aptitude.gateoverflow.in/6043/cat2018-1-68
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, but this time becomes $60$ hours when $5$ filling and $6$ draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?Quantitative Aptitudehttps://aptitude.gateoverflow.in/6043/cat2018-1-68Thu, 19 Mar 2020 22:39:09 +0000CAT2018-1: 70
https://aptitude.gateoverflow.in/6041/cat2018-1-70
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 _________.Quantitative Aptitudehttps://aptitude.gateoverflow.in/6041/cat2018-1-70Thu, 19 Mar 2020 22:39:09 +0000CAT2018-1: 79
https://aptitude.gateoverflow.in/6032/cat2018-1-79
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 _________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6032/cat2018-1-79Thu, 19 Mar 2020 22:39:08 +0000CAT2018-1: 81
https://aptitude.gateoverflow.in/6030/cat2018-1-81
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 ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6030/cat2018-1-81Thu, 19 Mar 2020 22:39:07 +0000CAT2018-1: 83
https://aptitude.gateoverflow.in/6028/cat2018-1-83
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 $Y$?Quantitative Aptitudehttps://aptitude.gateoverflow.in/6028/cat2018-1-83Thu, 19 Mar 2020 22:39:07 +0000CAT2018-1: 84
https://aptitude.gateoverflow.in/6027/cat2018-1-84
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 _________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6027/cat2018-1-84Thu, 19 Mar 2020 22:39:07 +0000CAT2018-1: 86
https://aptitude.gateoverflow.in/6025/cat2018-1-86
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 ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6025/cat2018-1-86Thu, 19 Mar 2020 22:39:06 +0000CAT2018-1: 91
https://aptitude.gateoverflow.in/6020/cat2018-1-91
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?Quantitative Aptitudehttps://aptitude.gateoverflow.in/6020/cat2018-1-91Thu, 19 Mar 2020 22:39:05 +0000CAT2018-1: 92
https://aptitude.gateoverflow.in/6019/cat2018-1-92
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 _______Quantitative Aptitudehttps://aptitude.gateoverflow.in/6019/cat2018-1-92Thu, 19 Mar 2020 22:39:05 +0000CAT2018-1: 93
https://aptitude.gateoverflow.in/6018/cat2018-1-93
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 ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6018/cat2018-1-93Thu, 19 Mar 2020 22:39:05 +0000CAT2018-1: 96
https://aptitude.gateoverflow.in/6015/cat2018-1-96
John borrowed Rs.$2,10,000$ from a bank at an interest rate of $10\%$ per annum, compounded annually. The loan was repaid in two equal installments, the first after one year and the second after another year. The first installment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each installment, in Rs., is ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6015/cat2018-1-96Thu, 19 Mar 2020 22:39:04 +0000CAT2018-1: 97
https://aptitude.gateoverflow.in/6014/cat2018-1-97
Let $f(x) = \text{min }\{2x^2, 52−5x\}$, where $x$ is any positive real number. Then the maximum possible value of $f(x)$ is ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6014/cat2018-1-97Thu, 19 Mar 2020 22:39:04 +0000CAT2018-1: 27
https://aptitude.gateoverflow.in/5990/cat2018-1-27
<p>The four sentences (labeled $1,2,3$ and $4$) given in this question, when properly sequenced, from a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.</p>
<ol start="1" style="list-style-type:decimal">
<li>The woodland’s canopy receives most of the sunlight that falls on the trees.</li>
<li>Swifts do not confine themselves to woodlands, but hunt wherever there are insects in the air.</li>
<li>With their streamlined bodies, swifts are agile flyers, ideally adapted to twisting and turning through the air as they chase flying insects – the creatures that form their staple diet.</li>
<li>Hundreds of thousands of insects fly in the sunshine up above the canopy, some falling prey to swifts and swallows.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5990/cat2018-1-27Thu, 19 Mar 2020 02:52:58 +0000CAT2018-1: 26
https://aptitude.gateoverflow.in/5991/cat2018-1-26
<p>Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.</p>
<ol>
<li>Translators are like bumblebees.</li>
<li>Though long since scientifically disproved, this factoid is still routinely trotted out.</li>
<li>Similar pronouncements about the impossibility of translation have dogged practitioners since Leonardo Bruni’s De interpretatione recta, published in $1424$.</li>
<li>Bees, unaware of these deliberations, have continued to flit from flower to flower, and translators continue to translate.</li>
<li>In $1934$, the French entomologist August Magnan pronounced the flight of the bumblebee to be aerodynamically impossible.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5991/cat2018-1-26Thu, 19 Mar 2020 02:52:58 +0000CAT2018-1: 25
https://aptitude.gateoverflow.in/5992/cat2018-1-25
<p>The four sentences (labelled $1,2,3,4$) given in this question, when properly sequenced, from a coherent paragraph. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer.</p>
<ol>
<li>Impartiality and objectivity are fiendishly difficult concepts that can cause all sorts of injustices even if transparently implemented.</li>
<li>It encourages us into bubbles of people we know and like, while blinding us to different perspectives, but the deeper problem of ‘transparency’ lies in the words “...and much more”.</li>
<li>Twitter’s website says that “tweets you are likely to care about most will show up first in your timeline...based on accounts you interact with most, tweets you engage with, and much more.”</li>
<li>We are only told some of the basic principles, and we can’t see the algorithm itself, making it hard for citizens to analyze the system sensibly or fairly or be convinced of its impartiality and objectivity.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5992/cat2018-1-25Thu, 19 Mar 2020 02:52:58 +0000CAT2018-1: 31
https://aptitude.gateoverflow.in/5986/cat2018-1-31
<p>he four sentences (labelled $1,2,3,4$) given in this question, when properly sequenced, from a coherent paragraph. Decide on the proper order of the sentences and key in this sequence of four numbers as your answer.</p>
<ol>
<li>But now we have another group: the unwitting enablers.</li>
<li>Democracy and high levels of inequality of the kind that have come to characterize the United States are simply incompatible.</li>
<li>Believing these people are working for a better world, they are, actually, at most, chipping away at the margins, making slight course corrections, ensuring the system goes on as it is, uninterrupted.</li>
<li>Very rich people will always use money to maintain their political and economic power.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5986/cat2018-1-31Thu, 19 Mar 2020 02:52:57 +0000CAT2018-1: 32
https://aptitude.gateoverflow.in/5985/cat2018-1-32
<p>Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.</p>
<ol>
<li>In many cases time inconsistency is what prevents our going from intention to action.</li>
<li>For people to continuously postpone getting their children immunized, they would need to be constantly fooled by themselves.</li>
<li>In the specific case of immunization, however, it is hard to believe that time inconsistency by itself would be sufficient to make people permanently postpone the decision if they were fully cognizant of its benefits.</li>
<li>In most cases, even a small cost of immunization was large enough to discourage most people.</li>
<li>Not only do they have to think that they prefer to spend time going to the camp next month rather than today, they also have to believe that they will indeed go next month.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5985/cat2018-1-32Thu, 19 Mar 2020 02:52:57 +0000CAT2018-1: 33
https://aptitude.gateoverflow.in/5984/cat2018-1-33
<p>Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.</p>
<ol>
<li>Displacement in Bengal is thus not very significant in view of its magnitude.</li>
<li>A factor of displacement in Bengal is the shifting course of the Ganges leading to erosion of river banks.</li>
<li>The nature of displacement in Bengal makes it an interesting case study.</li>
<li>Since displacement due to erosion is well spread over a long period of time, it remains invisible.</li>
<li>Rapid displacement would have helped senitize the public to its human costs.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5984/cat2018-1-33Thu, 19 Mar 2020 02:52:57 +0000CAT2018-1: 34
https://aptitude.gateoverflow.in/5983/cat2018-1-34
<p>The four sentences (labeled $1,2,3$ and $4$) given in this question, when properly sequenced, from a coherent paragraph. Decide on the proper order for the sentence and key in this sequence of four numbers as your answer.</p>
<ol>
<li>The eventual diagnosis was skin cancer and after treatment all seemed well.</li>
<li>The viola player didn’t know what it was; nor did her GP.</li>
<li>Then a routine scan showed it had come back and spread to her lungs.</li>
<li>It started with a lump on Cathy Perkins’ index finger.</li>
</ol>English Languagehttps://aptitude.gateoverflow.in/5983/cat2018-1-34Thu, 19 Mar 2020 02:52:57 +0000CAT2018-1: 43
https://aptitude.gateoverflow.in/5974/cat2018-1-43
An ATM dispenses exactly Rs. $5000$ per withdrawal using $100, 200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.<br />
<br />
In how many different ways can the ATM serve a customer who gives $500$ rupee notes as her preference?Logical Reasoninghttps://aptitude.gateoverflow.in/5974/cat2018-1-43Thu, 19 Mar 2020 02:52:55 +0000CAT2018-1: 44
https://aptitude.gateoverflow.in/5973/cat2018-1-44
An ATM dispenses exactly Rs. $5000$ per withdrawal using $100, 200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.<br />
<br />
If the ATM could serve only $10$ customers with a stock of fifty $500$ rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these $10$ who could have given $500$ rupee notes as their preferences?Logical Reasoninghttps://aptitude.gateoverflow.in/5973/cat2018-1-44Thu, 19 Mar 2020 02:52:55 +0000CAT2018-1: 51
https://aptitude.gateoverflow.in/5966/cat2018-1-51
You are given an $n\times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.<br />
<br />
What is the minimum number of different numerals needed to fill a $3\times 3$ square matrix?Logical Reasoninghttps://aptitude.gateoverflow.in/5966/cat2018-1-51Thu, 19 Mar 2020 02:52:54 +0000CAT2018-1: 52
https://aptitude.gateoverflow.in/5965/cat2018-1-52
You are given an $n\times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.<br />
<br />
What is the minimum number of different numerals needed to fill a $5\times 5$ square matrix?Logical Reasoninghttps://aptitude.gateoverflow.in/5965/cat2018-1-52Thu, 19 Mar 2020 02:52:54 +0000CAT2017-1: 61
https://aptitude.gateoverflow.in/5793/cat2017-1-61
<p>A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.</p>
<p>The underlying principle that they are working on is the following:</p>
<p>Any person staying in any of these $10$ cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.</p>
<p>Suppose the $10$ cities are divided into $4$ distinct groups $G1,G2,G3,G4$ having $3, 3, 2$ and $2$ cities respectively and that $G1$ consists of cities named $A, B$ and $C$. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>Both cities are in $G1$</li>
<li>Between $A$ and any city in $G2$</li>
<li>Between $B$ and any city in $G3$</li>
<li>Between $C$ and any city in $G4$</li>
</ol>
<p>Then the minimum number of direct flights that satisfies the underlying principle of the airline is ___________</p>Logical Reasoninghttps://aptitude.gateoverflow.in/5793/cat2017-1-61Fri, 13 Mar 2020 07:23:51 +0000CAT2015: 55
https://aptitude.gateoverflow.in/5597/cat2015-55
<p><img alt="CAT2015-55" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=16059172063250258373"></p>
<p>Answer the question on the basis of the information given below:</p>
<p>Mathematicians are assigned a number called Zohos number (named after the famous mathematician, Paul Zohos). Only Paul Zohos himself has an Zohos number of zero. Any mathematician who has written a research paper with Zohos has an Zohos number of $1$. For other mathematicians, the calculation of his/her Zohos number is illustrated below:</p>
<p>Suppose that a mathematician $X$ has co-authored papers with several other mathematicians. From among them, mathematician $Y$ has the smallest Zohos number. Let the Zohos number be $Y$ and $y$. Then $X$ has an Zohos number of $y+1$. Hence any mathematician with no co-authorship chain connected to Zohos has an Zohos number of infinity.</p>
<p>In a seven day long mini-conference organized in memory of Paul Zohos, a close group of eight mathematicians, call them $A, B, C, D, E, F, G$ and $H$, discussed some research problems. At the beginning of conference, $A$ was the only participant who had a infinite Zohos number. Nobody had an Zohos number less than that of $F$.</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>On the third day of the conference $F$ co-authored a paper jointly with $A$ and $C$. This reduced the average Zohos number of the group of eight mathematicians to $3$. The Zohos numbers of $B, D, E, G $ and $H$ remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Zohos number of the group of eight to as low as $3$.</li>
<li>At the end of the third day, five members of this group had identical Zohos numbers while the other three had Zohos numbers distinct from each other.</li>
<li>On the fifth day, $E$ co-authored a paper with $F$ which reduced the group’s average Zohos number by $0.5$. The Zohos numbers of the remaining six were unchanged with the writing of this paper.</li>
<li>No other paper was written during the conference.</li>
</ol>
<p>How many participants in the conference did not change their Zohos number during the conference?_________</p>Logical Reasoninghttps://aptitude.gateoverflow.in/5597/cat2015-55Mon, 09 Mar 2020 09:50:00 +0000