# Recent questions tagged quantitative-aptitude

1

For any natural numbers $\mathrm{m}, \mathrm{n}$, and $\mathrm{k}$, such that $\mathrm{k}$ divides both $m+2 n$ and $3 m+4 n \mathrm{k}$ must be a common divisor of$m$ an...

2

If $x$ and $y$ are real numbers such that $x^{2}+(x-2 y-1)^{2}=-4 y(x+y)$, then the value $x-2 y$ is$1$$2$$-1$$0$

3

If $\sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2})$, then $\sqrt{10 x+9}$ is equal to$3 \sqrt{7}$$4 \sqrt{5}$$3 \sqrt{31}$$2 \sqrt{7}$

4

If $x$ and $y$ are positive real numbers such that $\log _{x}\left(x^{2}+12\right)=4$ and $3 \log _{y} x=1$, then $x+y$ equals$11$$20$$10$$68$

5

The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is

6

Let $\alpha$ and $\beta$ be the two distinct roots of the equation $2 x^{2}-6 x+k=0$, such that $(\alpha+\beta)$ and $\alpha \beta$ are the distinct roots of the equation...

7

In an examination, the average marks of $4$ girls and $6$ boys is $24$. Each of the girls has the same marks while each of the boys has the same marks. If the marks of an...

8

The minor angle between the hours hand and minutes hand of a clock was observed at $8:48$ am. The minimum duration, in minutes, after $8.48$ am when this angle increases ...

9

A container has 20 L of milk. 4 L of milk is replaced with an equal quantity of water. What was will be the final quantity of milk in the container if the process is repe...

10

If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value$-60$ $-50$ $60$ $-70$

11

A group of $\mathrm{N}$ people worked on a project. They finished $35 \%$ of the project by working $7$ hours a day for $10$ days. Thereafter, $10$ people left the group ...

12

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio $5: 8: 10$. They accept a job which they can finish in $4$ days if they all work...

13

Mr. Pinto invests one-fifth of his capital at $6 \%$, one-third at $10 \%$ and the remaining at $1 \%$, each rate being simple interest per annum. Then, the minimum numbe...

14

Regular polygons $\mathrm{A}$ and $\mathrm{B}$ have number of sides in the ratio $1: 2$ and interior angles in the ratio $3: 4$. Then the number of sides of $\mathrm{B}$ ...

15

The number of distinct integer values of $n$ satisfying $\frac{4-\log 2 n}{3-\log _{4} n}<0$, is

16

The average of a non-decreasing sequence of $\mathrm{N}$ numbers $a_{1}, a_{2}, \ldots \ldots, a_{N}$ is $300$ . If $a_{1}$ is replaced by $6 a_{1}$, the new average beco...

17

If $a$ and $b$ are non-negative real numbers such that $a+2 b=6$, then the average of the maximum and minimum possible values of $(a+b)$ is$3.5$$4.5$$3$$4$

18

The length of each side of an equilateral triangle $\mathrm{A B C}$ is $3 \mathrm{~cm}$. Let $\mathrm{D}$ be a point on $\mathrm{B C}$ such that the area of triangle $\ma...

19

The number of integers greater than $2000$ that can be formed with the digits $0,1,2,3,4,5$, using each digit at most once, is$1480$$1440$$1200$$1420$

20

Let $f(x)$ be a quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. If $f(2)=0$ and $f(4)=6$, then $f(-2)$ is equal to$36$$12$$24$$6$

21

Manu earns ₹$4000$ per month and wants to save an average of ₹$550$ per month in a year. In the first nine months, his monthly expense was ₹$3500$, and he foresees ...

22

In an election, there were four candidates and $80 \%$ of the registered voters casted their votes. One of the candidates received $30 \%$ of the casted votes while the o...

23

On day one, there are $100$ particles in a laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total num...

24

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first co...

25

Five students, including Amit, appear for an examination in which possible marks are integers between $0$ and $50$ , both inclusive. The average marks for all the student...

26

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are $60 \mathrm{~km}$ apar...

27

For some natural number $n$, assume that $(15,000) !$ is divisible by $(n !) !$. The largest possible value of $n$ is$5$$4$$6$$7$

28

Suppose for all integers $x$, there are two functions $f$ and $g$ such that $f(x)+$ $f(x-1)-1=0$ and $g(x)=x^{2}$. If $f\left(x^{2}-x\right)=5$, then the value of the sum...

29

In triangle $\mathrm{A B C}$, altitudes $\mathrm{A D}$ and $\mathrm{B E}$ are drawn to the corresponding bases. If $\angle \mathrm{B A C}=45^{\circ}$ and $\angle \mathrm{...

30

The number of integer solutions of the equation $\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$ is

31

Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals$4$$-4$$-\frac{9}{2}$$\frac{9}{2}$

32

Consider the arithmetic progression $3,7,11, \ldots$ and let $A_{n}$ denote the sum of the first $\mathrm{n}$ terms of this progression. Then the value of $1^{25}, A$ is$...

33

In an examination, there were $75$ questions. $3$ marks were awarded for each correct answer, $1$ mark was deducted for each wrong answer and $1$ mark was awarded for eac...

34

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the q...

35

The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite number of solutions for $x$ is$2$$-1$$0$$1$

36

The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$...

37

Let $A$ be the largest positive integer that divides all the numbers of the form $3^{k}+4^{k}+5^{k}$, and $B$ be the largest positive integer that divides all the numbers...

38

In a village, the ratio of number of males to females is $5: 4$. The ratio of number of literate males to literate females is $2: 3$. The ratio of the number of illiterat...

39

Let $\text{A B C D}$ be a parallelogram such that the coordinates of its three vertices $\text{A, B, C}$ are $(1,1),(3,4)$ and $(-2,8)$, respectively. Then, the coordinat...

40

Alex invested his savings in two parts. The simple interest earned on the first part at $15 \%$ per annum for 4 years is the same as the simple interest earned on the sec...