# Recent questions tagged quantitative-aptitude

1
Answer the following questions based on the information given below. The petrol consumption rate of a new model car 'Palto' depends on its speed and may be described by the graph below. Manasa would like to minimize the fuel consumption for the trip by driving at the ... . How should she change the speed? Increase the speed Decrease the speed Maintain the speed at $60$ km/hour Cannot be determined
2
The batting average $\text{(BA)}$ of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner: $r_1$ = number of runs scored in completed innings; $n_1$ = number of completed innings $r_2$ = ... $\text{MBA}_1$ and $\text{MBA}_2$ None of these
3
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of $n$ turns (in other words, the string s length is ... , not drawn to scale). How is $h$ related to $n?$ $h=\sqrt{2}n$ $h=\sqrt{17}n$ $h=n$ $h=\sqrt{13}n$
4
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of $n$ turns (in other words, the string ... see figure, not drawn to scale). The length of the string, in cms, is $\sqrt{2}n$ $\sqrt{12}n$ $n$ $\sqrt{13}n$
5
Answer the questions on the basis of the information given below: In an examination, there are $100$ questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries $1$ mark, each question in group B carries $2$ marks and ... best describes the number of questions in group B? $11$ or $12$ $12$ or $13$ $13$ or $14$ $14$ or $15$
6
Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x$ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$
1 vote
7
Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, \dots$ such that $x_{n+1} = x_{n} + n – 1$ for all $n \geq 1.$ If $x_{1} = -1$ then $x_{100}$ is equal to $4950$ $4850$ $4849$ $4949$
1 vote
8
Anil can paint a house in $12 \; \text{days}$ while Barun can paint it in $16 \; \text{days}.$ Anil, Barun, and Chandu undertake to paint the house for $₹ \; 24000$ and the three of them together complete the painting in $6 \; \text{days}.$ If Chandu is paid in proportion to the work done by him, then the amount in $\text{INR}$ received by him is
1 vote
9
For a real number $a,$ if $\dfrac{\log_{15}a + \log_{32}a}{(\log_{15}a)(\log_{32}a)} = 4$ then $a$ must lie in the range $a>5$ $3<a<4$ $4<a<5$ $2<a<3$
1 vote
10
In a triangle $\text{ABC}, \angle \text{BCA} = 50^{\circ}. \text{D}$ and $\text{E}$ are points on $\text{AB}$ and $\text{AC},$ respectively, such that $\text{AD = DE}.$ If $\text{F}$ is a point on $\text{BC}$ such that $\text{BD = DF},$ then $\angle \text{FDE, in degrees},$ is equal to $96$ $72$ $80$ $100$
1 vote
11
Bank $\text{A}$ offers $6 \%$ interest rate per annum compounded half yearly. Bank $\text{B}$ and Bank $\text{C}$ offer simple interest but the annual interest rate offered by Bank $\text{C}$ is twice that of Bank $\text{B}.$ ... same amount in Bank $\text{A}$ for one year. The interest accrued, in $\text{INR},$ to Rupa is $3436$ $2436$ $2346$ $1436$
1 vote
12
Let $\text{ABCD}$ be a parallelogram. The lengths of the side $\text{AD}$ and the diagonal $\text{AC}$ are $10 \; \text{cm}$ and $20 \; \text{cm},$ respectively. If the angle $\angle \text{ADC}$ is equal to $30^{\circ}$ then the area of the parallelogram, in sq. cm, is $\frac{25(\sqrt{5} + \sqrt{15})}{2}$ $25 (\sqrt{5} + \sqrt{15})$ $\frac{25 (\sqrt{3} + \sqrt{15})}{2}$ $25 (\sqrt{3} + \sqrt{15})$
1 vote
13
A shop owner bought a total of $64$ shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was $\text{INR} \; 50$ less than that of a large shirt. She paid a total of $\text{INR} \; 5000$ for the large shirts, and a total of ... for the small shirts. Then, the price of a large shirt and a small shirt together, in $\text{INR},$ is $200$ $175$ $150$ $225$
1 vote
14
The arithmetic mean of scores of $25$ students in an examination is $50.$ Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being $30,$ then the maximum possible score of the toppers is
1 vote
15
Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in $45 \; \text{minutes},$ Amal completes exactly $3$ more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after $3 \; \text{minutes}.$ The number of rounds Mira walks in one hour is
16
The number of distinct pairs of integers $(m,n)$ satisfying $|1 + mn| < |m + n| < 5$ is
1 vote
17
The cost of fencing a rectangular plot is $₹ \; 200 \; \text{per ft}$ along one side, and $₹ \; 100 \; \text{per ft}$ along the three other sides. If the area of the rectangular plot is $60000 \; \text{sq. ft},$ then the lowest possible cost of fencing all four sides, in $\text{INR},$ is $160000$ $100000$ $120000$ $90000$
1 vote
18
If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $-16$ $-15$ $-20$ $-12$
1 vote
19
A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is
1 vote
20
If a certain weight of an alloy of silver and copper is mixed with $3 \; \text{kg}$ of pure silver, the resulting alloy will have $90 \%$ silver by weight. If the same weight of the initial alloy is mixed with $2 \; \text{kg}$ of another alloy which has $90 \%$ silver by ... resulting alloy will have $84 \%$ silver by weight. Then, the weight of the initial alloy, in kg, is $4$ $2.5$ $3$ $3.5$
1 vote
21
One day, Rahul started a work at $9 \; \text{AM}$ and Gautam joined him two hours later. They then worked together and completed the work at $5 \; \text{PM}$ the same day. If both had started at $9 \; \text{AM}$ and worked together, the work would have been ... $10$ $12$ $12.5$ $11.5$
1 vote
22
A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying electric wires along its two diagonals, at the rate of $₹ \; 125 \; \text{per m},$ is
23
The total of male and female populations in a city increased by $25 \%$ from $1970$ to $1980.$ During the same period, the male population increased by $40 \%$ while the female population increased by $20 \%.$ From $1980$ to $1990,$ the female population increased by $25 \%.$ ... in the total of male and female populations in the city from $1970$ to $1990$ is $69.25$ $68.75$ $68.50$ $68.25$
1 vote
24
If $n$ is a positive integer such that $( \sqrt[7]{10}) ( \sqrt[7]{10})^{2} \dots ( \sqrt[7]{10})^{n} > 999,$ then the smallest value of $n$ is
1 vote
25
If $3x + 2|y| + y = 7$ and $x + |x| + 3y = 1,$ then $x + 2y$ is $\frac{8}{3}$ $1$ $– \frac{4}{3}$ $0$
1 vote
26
A tea shop offers tea in cups of three different sizes. The product of the prices, in $\text{INR},$ of three different sizes is equal to $800.$ The prices of the smallest size and the medium size are in the ratio $2:5.$ If the shop owner decides to increase ... largest size unchanged, the product then changes to $3200.$ The sum of the original prices of three different sizes, in $\text{INR},$ is
27
One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects $₹ \; 1600$ per month from each boarder. When the number of boarders is $50,$ the profit of the hostel is $₹ \; 200$ per boarder, and ... the number of boarders is $80,$ the total profit of the hostel, in $\text{INR},$ will be $20800$ $20200$ $20000$ $20500$
1 vote
28
In a tournament, a team has played $40$ matches so far and won $30 \%$ of them. If they win $60 \%$ of the remaining matches, their overall win percentage will be $50 \%.$ Suppose they win $90 \%$ of the remaining matches, then the total number of matches won by the team in the tournament will be $80$ $84$ $78$ $86$
1 vote
29
Consider the pair of equations: $x^{2} – xy – x = 22$ and $y^{2} – xy + y = 34.$ If $x>y,$ then $x – y$ equals $7$ $8$ $6$ $4$
1 vote
30
Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is $70 \%.$ His share of profit decreases by $₹ \; 420$ if the overall profit goes down from $18 \%$ to $15 \%.$ Chintu's share of ... goes up from $15 \%$ to $17 \%.$ The amount, $\text{in INR},$ invested by Bobby is $2400$ $2200$ $2000$ $1800$
1 vote
31
If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is $\sqrt{13} + \sqrt{12}$ $\sqrt{37} + \sqrt{13}$ $\frac{\sqrt{37} + \sqrt{13}}{2}$ $\frac{\sqrt{13} + \sqrt{12}}{2}$
1 vote
32
The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is
1 vote
33
For a sequence of real numbers $x_{1}, x_{2}, \dots , x_{n},$ if $x_{1} – x_{2} + x_{3} – \dots + (-1)^{n+1} x_{n} = n^{2} + 2n$ for all natural numbers $n,$ then the sum $x_{49} + x_{50}$ equals $2$ $-2$ $200$ $-200$
1 vote
34
For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if $9 < x < 14$ $6 < x < 11$ $7 < x < 12$ $10 < x < 15$
1 vote
35
A box has $450$ balls, each either white or black, there being as many metallic white balls as metallic black balls. If $40 \%$ of the white balls and $50 \%$ of the black balls are metallic, then the number of non-metallic balls in the box is
1 vote
36
The sides $\text{AB}$ and $\text{CD}$ of a trapezium $\text{ABCD}$ are parallel, with $\text{AB}$ being the smaller side. $\text{P}$ is the midpoint of $\text{CD}$ and $\text{ABPD}$ is a parallelogram. If the difference between the areas of the parallelogram $\text{ABPD}$ and the ... $\text{in sq cm},$ of the trapezium $\text{ABCD}$ is $25$ $30$ $40$ $20$
1 vote
37
Raj invested $₹ \; 10000$ in a fund. At the end of first year, he incurred a loss but his balance was more than $₹ \; 5000.$ This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the ... the initial investment over the two period is $35 \%,$ then the percentage of loss in the first year is $15$ $10$ $70$ $5$
1 vote
Let $\text{D}$ and $\text{E}$ be points on sides $\text{AB}$ and $\text{AC},$ respectively, of a triangle $\text{ABC},$ such that $\text{AD}$ : $\text{BD} = 2 : 1$ and $\text{AE}$ : $\text{CE} = 2 : 3.$ If the area of the triangle $\text{ADE}$ is $8 \; \text{sq cm},$ then the area of the triangle $\text{ABC, in sq cm},$ is
For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $\left(\frac{3}{7}, \frac{1}{2} \right)$ $\left[\frac{3}{7}, \frac{1}{2} \right)$ $\left[\frac{3}{7}, \frac{8}{9} \right)$ $\left[\frac{4}{9}, \frac{8}{9} \right]$
Suppose one of the roots of the equation $ax^{2} – bx + c = 0$ is $2 + \sqrt{3},$ where $a, b$ and $c$ are rational numbers and $a \neq 0.$ If $b = c^{3}$ then $|a|$ equals $2$ $4$ $1$ $3$