# Recent questions tagged quantitative-aptitude 1 vote
41
Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x > 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals $12$ $8$ $14$ $10$
1 vote
42
In a football tournament, a player has played a certain number of matches and $10$ more matches are to be played. If he scores a total of one goal over the next $10$ matches, his overall average will be $0.15$ goals per match. On the other hand, if he scores a total of two goals over the next $10$ matches, his overall average will be $0.2$ goals per match. The number of matches he has played is
1 vote
43
For all possible integers $n$ satisfying $2.25 \leq 2 + 2^{n+2} \leq 202,$ the number of integer values of $3 + 3^{n+1}$ is
1 vote
44
Anil can paint a house in $60 \; \text{days}$ while Bimal can paint it in $84 \; \text{days}.$ Anil starts painting and after $10 \; \text{days},$ Bimal and Charu join him. Together, they complete the painting in $14$ more days. If they are paid a total of $₹ \; 21000$ for the job, then the share of Charu, $\text{in INR},$ proportionate to the work done by him, is $9150$ $9100$ $9000$ $9200$
1 vote
45
Two trains $\text{A}$ and $\text{B}$ were moving in opposite directions, their speeds being in the ratio $5:3.$ The front end of $\text{A}$ crossed the rear end of $\text{B} \; 46 \; \text{seconds}$ ... cross each other. The ratio of length of train $\text{A}$ to that of train $\text{B}$ is $2:3$ $2:1$ $3:2$ $5:3$
1 vote
46
If $\log_{2} [3+ \log_{3} \{ 4+ \log_{4} (x-1) \}] – 2 = 0$ then $4x$ equals
1 vote
47
Two pipes $\text{A}$ and $\text{B}$ are attached to an empty water tank. Pipe $\text{A}$ fills the tank while pipe $\text{B}$ drains it. If pipe $\text{A}$ is opened at $2 \; \text{pm}$ and pipe $\text{B}$ is opened at $3 \; \text{pm},$ then the tank becomes full ... $\text{B}$ is not opened at all, then the time, in minutes, taken to fill the tank is $140$ $264$ $144$ $120$
1 vote
48
From a container filled with milk, $9 \; \text{litres}$ of milk are drawn and replaced with water. Next, from the same container, $9 \; \text{litres}$ are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of $16:9,$ then the capacity of the container, in $\text{litres},$ is
1 vote
49
For a $4$-digit number, the sum of its digits in the thousands, hundreds and tens places is $14,$ the sum of its digits in the hundreds, tens and units places is $15,$ and the tens place digit is $4$ more than the units place digit. Then the highest possible $4$-digit number satisfying the above conditions is
1 vote
50
How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?
51
A basket of $2$ apples, $4$ oranges and $6$ mangoes costs the same as a basket of $1$ apple, $4$ oranges and $8$ mangoes, or a basket of $8$ oranges and $7$ mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is : $12$ $10$ $11$ $13$
1 vote
52
The natural numbers are divided into groups as $(1), (2,3,4), (5,6,7,8,9), \dots$ and so on. Then, the sum of the numbers in the $15 \text{th}$ group is equal to $6090$ $4941$ $6119$ $7471$
1 vote
53
Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in $1 \; \text{year},$ Akbar and Anthony can complete in $16$ months, Anthony and Amar can complete in $2 \; \text{years}.$ If the person who is neither the faster nor the slowest works alone, the time in months he will take to complete the project is
1 vote
54
Anu, Vinu and Manu can complete a work alone in $15 \; \text{days}, 12 \; \text{days}$ and $20 \; \text{days},$ respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is $6$ $5$ $8$ $7$
1 vote
55
The amount Neeta and Geeta together earn in a day equals what Sita alone earns in $6 \; \text{days}.$The amount Sita and Neeta together earn in a day equals what Geeta alone earns in $2 \; \text{days}.$ The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is $7 : 3$ $3 : 2$ $11 : 3$ $11 : 7$
1 vote
56
If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12 \; \text{cm},$ then the length, in cm, of each side of the hexagon is $6 \sqrt{6}$ $2 \sqrt{6}$ $4 \sqrt{6}$ $\sqrt{6}$
1 vote
57
$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $– 2 < x < 3 \; \text{or} \; x > 9$ $x < – 5 \; \text{or} \; 3 < x < 9$ $– 5 < x < – 2 \; \text{or} \; 3 < x < 9$ $x < – 5 \; \text{or} \; – 2 < x < 3$
1 vote
58
Amal purchases some pens at $₹ \; 8$ each. To sell these, he hires an employee at a fixed wage. He sells $100$ of these pens at $₹ \; 12$ each. If the remaining pens are sold at $₹ \; 11$ each, then he makes a net profit of $₹ \; 300,$ while he makes a net loss of $₹ \; 300$ if the remaining pens are sold at $₹ \; 9$ each. The wage of the employee, in $\text{INR},$ is
1 vote
59
The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7,$ and $8$ so that the groups always include $3$ and $5,$ while $7$ and $8$ are never included together is
1 vote
60
The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100 \; \text{cc}$ of water. Two $800 \; \text{cc}$ bottles are filled with indigo solutions of strengths $33 \%$ and $17 \%,$ respectively. A part of the solution ... the indigo solution in the first bottle has now changed to $21 \%$ then the volume, in cc, of the solution left in the second bottle is
1 vote
61
Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in cm},$ is $\sqrt{15}$ $\sqrt{13}$ $\sqrt{12}$ $\sqrt{14}$
1 vote
62
If $r$ is a constant such that $|x^{2} – 4x -13| = r$ has exactly three distinct real roots, then the value of $r$ is $15$ $18$ $17$ $21$
1 vote
63
If $x_{0} = 1, x_{1} = 2$ and $x_{n+2} = \dfrac{1 + x_{n+1}}{x_{n}}, n = 0, 1, 2, 3, \dots ,$ then $x_{2021}$ is equal to $1$ $3$ $4$ $2$
1 vote
64
If $5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}},$ then $100x$ equals
1 vote
65
Suppose hospital $\text{A}$ admitted $21$ less Covid infected patients than hospital $\text{B},$ and all eventually recovered. The sum of recovery days for patients in hospitals $\text{A}$ and $\text{B}$ were $200$ and $152,$ respectively. If the average recovery days for ... $\text{A}$ was $3$ more than the average in hospital $\text{B}$ then the number admitted in hospital $\text{A}$ was
66
The number of integers $n$ that satisfy the inequalities $|n – 60| < |n – 100| < |n – 20|$ is $18$ $19$ $21$ $20$
1 vote
67
Two trains cross each other in $14 \; \text{seconds}$ when running in opposite directions along parallel tracks. The faster train is $160 \; \text{m}$ long and crosses a lamp post in $12 \; \text{seconds}.$ If the speed of the other train is $6 \; \text{km/hr}$ less than the faster one, its length, in $\text{m},$ is $190$ $192$ $184$ $180$
1 vote
68
Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are $₹ \; 806.25$ and $₹ \; 866.72,$ respectively, the interest accrued, in $\text{INR},$ during the fourth year is nearest to $934.65$ $929.48$ $926.84$ $931.72$
1 vote
69
A circle of diameter $8 \; \text{inches}$ is inscribed in a triangle $\text{ABC}$ where $\angle \text{ABC} = 90^{\circ}.$ If $\text{BC} = 10 \; \text{inches}$ then the area of the triangle in $\text{square inches}$ is
1 vote
70
Onion is sold for $5$ consecutive months at the rate of $\text{Rs}\; 10, 20, 25, 25,$ and $50 \; \text{per kg},$ respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next ... for onion, $\text{in rupees per kg},$ for the family over these $5 \; \text{months}$ is closest to $18$ $16$ $26$ $20$
1 vote
71
Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price $\text{per gram}$ of chocolate in the large box is $12 \%$ less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to $135$ $127$ $144$ $124$
72
If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B}$ and $\log_{2} a = 1/3,$ then $\log_{3}a$ equals $\frac{2}{\text{A + B}} \;– 3$ $\frac{\text{A + B} - 3}{2}$ $\frac{2}{\text{A + B} – 3}$ $\frac{\text{A + B}}{2}\; – 3$
73
Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average age of all three, then Harry’s age, in years, is
1 vote
74
Let $k$ be a constant. The equations $kx + y= 3$ and $4x + ky= 4$ have a unique solution if and only if $|k| \neq 2$ $|k| = 2$ $k \neq 2$ $k= 2$
1 vote
75
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m,$ then $x_{100}$ equals $– 5151$ $– 5150$ $– 5051$ $– 5050$
76
Vimla starts for office every day at $9 \; \text{am}$ and reaches exactly on time if she drives at her usual speed of $40 \; \text{km/hr}.$ She is late by $6 \; \text{minutes}$ if she drives at $35 \; \text{km/hr}.$ One day, she covers two-thirds of her ... $\text{km/hr},$ at which she should drive the remaining distance to reach office exactly on time is $29$ $27$ $28$ $26$
77
A man buys $35 \; \text{kg}$ of sugar and sets a marked price in order to make a $20\%$ profit. He sells $5 \; \text{kg}$ at this price, and $15 \; \text{kg}$ at a $10\%$ discount. Accidentally, $3 \; \text{kg}$ of sugar is wasted. He sells the remaining sugar by raising the marked price by $p$ percent so as to make an overall profit of $15\%.$ Then $p$ is nearest to $31$ $22$ $35$ $25$
1 vote
If $f(x+y) = f(x) f(y)$ and $f(5) = 4,$ then $f(10) – f(-10)$ is equal to $0$ $15.9375$ $3$ $14.0625$
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
A contractor agreed to construct a $6 \; \text{km}$ road in $200 \; \text{days}.$ He employed $140$ persons for the work. After $60 \; \text{days},$ he realized that only $1.5 \; \text{km}$ road has been completed. How many additional people would he need to employ in order to finish the work exactly on time $?$