# Recent questions tagged quantitative-aptitude 1 vote
121
If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$?______
1 vote
122
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals_______
123
Let $A$ and $B$ be two regular polygons having $a$ and $b$ sides, respectively. If $b= 2a$ and each interior angle of $B$ is $3/2$ times each interior angle of $A$, then each interior angle, in degrees, of a regular polygon with $a + b$ sides is_____
1 vote
124
The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is $18$ $19$ $21$ $20$
1 vote
125
Amal invests Rs $12000$ at $8$% interest, compounded annually, and Rs $10000$ at $6$% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at $7.5$% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is ______
126
Given the quadratic equation $x^2 – (A – 3)x – (A – 2)$, for what value of $A$ will the sum of the squares of the roots be zero? $-2$ $3$ $6$ $\text{None of these}$
127
If both $a$ and $b$ belong to the set $\{1,2,3,4\}$, then the number of equations of the form $ax^2+bx+1=0$ having real roots is _____
128
If $m$ and $n$ are integers such that $(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt{64})$ then $m$ is $-20$ $-12$ $-24$ $-16$
1 vote
129
The income of Amala is $20$% more than that of Bimala and $20$% less than that of Kamala. If kamala’s income goes down by $4$% and Bimala’s goes up by $10$%, then the percentage by which kamala’s income would exceed Bimala’s is nearest to $31$ $28$ $32$ $29$
130
In a class, $60$% of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68$% of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is____
1 vote
131
On selling a pen at $5$% loss and a book at $15$% gain, Karim gains Rs. $7$. If he sells the pen at $5$% gain and the book at $10$% gain, he gains Rs. $13$. What is the cost price of the book in Rupees? $80$ $85$ $95$ $100$
1 vote
132
Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is $5:6$ $4:5$ $3:4$ $2:3$
133
Let $S$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented by $S$ equals _____
1 vote
134
Ramesh and Gautam are among $22$ students who write an examination. Ramesh scores $82.5$. The average score of the $21$ students other than Gautam is $62$. The average score of all the $22$ students is one more than the average score of the $21$ students other than Ramesh. The score of Gautam is $49$ $48$ $51$ $53$
135
At their usual efficiency levels, A and B together finish a task in $12$ days. If A had worked half as efficiency as she usually does, and B had worked thrice as efficiency as he usually does, the task would have been completed in $9$ days. How many days would A take to finish the task if she works alone at her usual efficiency? $24$ $18$ $12$ $36$
1 vote
136
If $a_{1},a_{2}\dots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$ $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$ $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$ $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$
1 vote
137
In a circle of radius $11$ cm, CD is a diameter and AB is a chord of length $20.5$ cm. If AB and CD intersect at a point E inside the circle and CE has length $7$ cm, then the difference of the lengths of BE and AE, in cm, is $2.5$ $3.5$ $0.5$ $1.5$
138
With rectangular axes of coordinates, the number of paths from $(1,1)$ to $(8,10)$ via $(4,6)$, where each step from any point $(x,y)$ is either to $(x,y+1)$ or to $(x+1, y)$, is ____
1 vote
139
Amala, Bina, and Gouri invest money in the ratio $3:4:5$ in fixed deposits having respective annual interest rates in the ratio $6:5:4$. what is their total interest income (in Rs) after a year, if Bina’s interest income exceeds Amala’s by Rs $250$? $6350$ $7250$ $7000$ $6000$
1 vote
140
A club has $256$ members of whom $144$ can play football, $123$ can play tennis, and $132$ can play cricket. Moreover, $58$ members can play both football and tennis, $25$ can play both cricket and tennis, while $63$ can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is $45$ $38$ $32$ $43$
141
Let T be the triangle formed by the straight line $3x+5y-45=0$ and T the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is ______
142
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in $13$ days, then how many men can finish the job in $13$ days?______
1 vote
143
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is $-8$ $-24$ $-4$ $-16$
1 vote
144
Two cars travel the same distance starting at $10:00$ am and $11:00$ am, respectively, on the same day. They reach their common destination at the same point of time. If the first car traveled for at least $6$ hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is $30$ $25$ $10$ $20$
145
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$
146
The wheel of bicycles $A$ and $B$ have radii $30$ cm and $40$ cm, respectively. While traveling a certain distance, each wheel of $A$ required $5000$ more revolutions than each wheel of $B$. If bicycle $B$ traveled this distance in $45$ minutes, then its speed, in km per hour, was $18\pi$ $12\pi$ $16\pi$ $14\pi$
147
$AB$ is a diameter of a circle of radius $5$ cm. Let $P$ and $Q$ be two points on the circle so that the length of $PB$ is $6$ cm, and the length of $AP$ is twice that of $AQ$. Then the length, in cm, of $QB$ is nearest to $7.8$ $8.5$ $9.1$ $9.3$
148
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals____
149
A chemist mixes two liquids $1$ and $2$. One litre of liquid $1$ weighs $1$ kg and one litre of liquid $2$ weighs $800$ gm. If half litre of the mixture weighs $480$ gm, then the percentage of liquid $1$ in the mixture, in terms of volume, is $85$ $70$ $75$ $80$
150
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______
1 vote
151
If $a_{1}+a_{2}+a_{3}+\dots+a_{n}=3(2^{n+1}-2)$, for every $n\geq 1$, then $a_{11}$ equals ____
152
The number of the real roots of the equation $2\cos (x(x+1))=2^{x}+2^{-x}$ is $2$ $1$ infinite $0$
1 vote
153
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-log_{2}3$. Then xy equals $250$ $25$ $100$ $150$
154
One can use three different transports which move at $10,20$, and $30$ kmph, respectively. To reach from $A$ to $B$, Amal took each mode of transport $\frac{1}{3}$ of his total journey time, while Bimal took each mode of transport $\frac{1}{3}$ of the total distance. The percentage by which Bimal’s travel time exceeds Amal’s travel time is nearest to $21$ $22$ $20$ $19$
155
If the rectangular faces of a brick have their diagonals in the ratio $3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is $\sqrt{3}:2$ $2:\sqrt{5}$ $1:\sqrt{3}$ $\sqrt{2}:\sqrt{3}$
1 vote
156
If the population of a town is $p$ in the beginning of any year then it becomes $3+2p$ in the beginning of the next year. If the population in the beginning of $2019$ is $1000$, then the population in the beginning of $2034$ will be $(997)2^{14}+3$ $(1003)^{15}+6$ $(1003)2^{15}-3$ $(997)^{15}-3$
157
A person invested a total amount of Rs $15$ lakh. A part of it was invested in a fixed deposit earning $6$% annual interest, and the remaining amount was invested in two other deposits in the ratio $2:1$, earning annual interest at the rates of $4$% and $3$%, respectively. If the total annual interest income is Rs $76000$ then the amount (in Rs lakh) invested in the fixed deposit was___
Meena scores $40$% in an examination and after review, even though her score is increased by $50$%, she fails by $35$ marks. If her post-review score is increased by $20$%, she will have $7$ marks more than the passing score. The percentage score needed for passing the examination is $70$ $60$ $75$ $80$
In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in metres,of the racecourse? ____
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _____.