# Recent questions tagged quantitative-aptitude 1 vote
81
$\text{A}$ and $\text{B}$ are two railway stations $90 \; \text{km}$ apart. A train leaves $\text{A}$ at $9:00 \; \text{am},$ heading towards $\text{B}$ at a speed of $40 \; \text{km/hr}.$ Another train leaves $\text{B}$ at $10:30 \; \text{am},$ heading towards $\text{A}$ at a ... trains meet each other at $11:45 \; \text{am}$ $10:45 \; \text{am}$ $11:20 \; \text{am}$ $11:00 \; \text{am}$
1 vote
82
Let $\text{m}$ and $\text{n}$ be positive integers, If $x^{2} + mx + 2n = 0$ and $x^{2} + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is $7$ $8$ $5$ $6$
1 vote
83
A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became $\text{Rs} \; 18522.$ The amount, in rupees, that the person had invested is
84
Anil, Sunil, and Ravi run along a circular path of length $3 \; \text{km},$ starting from the same point at the same time, and going in the clockwise direction. If they run at speed of $15 \; \text{km/hr}, 10 \; \text{km/hr},$ and $8 \; \text{km/hr},$ respectively, how ... $?$ $4.2$ $5.2$ $4.8$ $4.6$
85
The area, in $\text{sq. units},$ enclosed by the lines $x = 2, y = |x – 2| + 4,$ the X-axis and the Y-axis is equal to $8$ $12$ $10$ $6$
86
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$ $\frac{12 \pi}{5}$ $\frac{123 \pi}{7}$ $\frac{205 \pi}{9}$
87
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$
88
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} > 25,$ then how many distinct values are possible for $\text{N} ?$
89
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$ $14$ $13$ $15$
90
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$
91
In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5 \; \text{cm}, \; \text{BC} = 4 \; \text{cm},$ the area of the trapezium in $\text{sq. cm}$ is
92
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$ $40$ $42$ $43$ $41$
93
Two alcohol solutions, $\text{A}$ and $\text{B},$ are mixed in the proportion $1:3$ by volume. The volume of the mixture is then doubled by adding solution $\text{A}$ such that the resulting mixture has $72\%$ alcohol. If solution $\text{A}$ has $60\%$ alcohol, then the percentage of alcohol in solution $\text{B}$ is $94\%$ $92\%$ $90\%$ $89\%$
94
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals
95
A batsman played $n + 2$ innings and got out on all occasions. His average score in these $n + 2$ innings was $29$ runs and he scored $38$ and $15$ runs in the last two innings. The batsman scored less than $38$ runs in each of the first $n$ innings. In these $n$ innings, his average score was $30$ runs and lowest score was $x$ runs. The smallest possible value of $x$ is $2$ $3$ $4$ $1$
96
In the final examination, Bishnu scored $52\%$ and Asha scored $64\%.$ The marks obtained by Bishnu is $23$ less, and that by Asha is $34$ more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored $84\%,$ is $439$ $399$ $357$ $417$
97
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$ $4$ $1$ $2$
98
The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area, $\text{R},$ of the rectangle, both in $\text{sq cm},$ ... the sides of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is $24$ $27$ $21$ $18$
99
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent $₹150$ more due to price increase of rice and wheat by $20\%$ and $12\%,$ respectively. If John had spent $₹450$ on rice in April, then how much did he spend on wheat in May $?$ $₹580$ $₹570$ $₹560$ $₹590$
100
In a car race, car $\text{A}$ beats car $\text{B}$ by $45 \; \text{km},$ car $\text{B}$ beats car $\text{C}$ by $50 \; \text{km},$ and car $\text{A}$ beats car $\text{C}$ by $90\;\text{km}.$ The distance $\text{(in km)}$ over which the race has been conducted is $500$ $475$ $550$ $450$
1 vote
101
John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone $?$
102
Let the $\text{m-th}$ and $\text{n-th}$ terms of a geometric progression be $\frac{3}{4}$ and $12,$ respectively, where $\text{m < n}.$ If the common ratio of the progression is an integer $\textsf{r},$ then the smallest possible value of $\textsf{r+n-m}$ is $- 2$ $2$ $6$ $– 4$
103
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{x}} \right) \left( 1 + \frac{1}{\textsf{y}} \right)$ is
104
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $1 < a \leq b$ cannot be equal to $– 0.5$ $1$ $0$ $– 1$
105
In how many ways can a pair of integers $\textsf{(x , a)}$ be chosen such that $x^{2} – 2 |x| + |a-2| = 0 ?$ $4$ $5$ $6$ $7$
1 vote
106
Students in a college have to choose at least two subjects from chemistry, mathematics, and physics. The number of students choosing all three subjects is $18,$ choosing mathematics as one of their subjects is $23$ and choosing physics as one of their subjects is $25.$ The smallest possible number of students who could choose chemistry as one of their subjects is $20$ $22$ $19$ $21$
107
For real $\textsf{x}$ , the maximum possible value of $\frac{x}{\sqrt{1+x^{4}}}$ is $\frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
1 vote
108
Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and $10$ less sharpeners. If the cost of one sharpener is $₹\:2$ more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is $30$ $33$ $27$ $36$
109
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is $3:2,$ while the ratio of the shares of Sunil and Mita is $4:5.$ If the difference between the largest and the smallest of these three shares is $\text{Rs.} 400,$ then Sunil’s share, in rupees, is
1 vote
110
Anil buys $12$ toys and labels each with the same selling price. He sells $8$ toys initially at $20\%$ discount on the labeled price. Then he sells the remaining $4$ toys at an additional $25\%$ discount on the discounted price. Thus, he gets a total of $\text{Rs }2112,$ and makes a $10\%$ profit. With no discounts, his percentage of profit would have been $60$ $55$ $50$ $54$
111
Two circular tracks $\text{T}1$ and $\text{T}2$ of radii $100 \; \text{m}$ and $20 \; \text{m},$ respectively touch at a point $\text{A}.$ Starting from $\text{A}$ at the same time, Ram and Rahim are walking on track $\text{T}1$ and track $\text{T}2$ at ... $4$ $3$ $2$ $5$
112
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$
1 vote
113
The number of pairs of integers $(x,y)$ satisfying $x \geq y \geq – 20$ and $2x + 5y = 99$ is
114
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ equals
115
The distance from $\text{B}$ to $\text{C}$ is thrice that from $\text{A}$ to $\text{B}.$ Two trains travel from $\text{A}$ to $\text{C}$ via $\text{B}.$ The speed of train $2$ is double that of train $1$ while traveling from $\text{A}$ to $\text{B}$ and their speeds are ... taken by train $1$ to that taken by train $2$ in traveling from $\text{A}$ to $\text{C}$ is $1:4$ $7:5$ $5:7$ $4:1$
116
Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and $\text{B}$ where $\text{A}$ is located $4 \; \text{meters}$ north of $\text{O}$ and $\text{B}$ is located $3 \; \text{meters}$ east of $\text{O}.$ Then, the length of $\text{PQ}$, in meters, is nearest to $7.2$ $7.8$ $6.6$ $8.8$
117
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$
Let $f(x) = x^{2} + ax + b$ and $g(x) = f(x+1) – f(x-1).$ If $f(x) \geq 0$ for all real $x,$ and $g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$
Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$ has length $6 \; \text{cm}$ and is a tangent to $\text{C}2,$ then the diameter, in $\text{cm},$ of $\text{C}1$ is
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s.$ Then the area of the triangle is $\frac{\sqrt{3}s^{2}}{2}$ $\frac{s^{2}}{\sqrt{3}}$ $\frac{2s^{2}}{\sqrt{3}}$ $\frac{s^{2}}{2 \sqrt{3}}$