# Recent questions tagged quantitative-aptitude

121

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...

122

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 ...

123

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$

124

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$

125

If $5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}},$ then $100x$ equals

126

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 ho...

127

The number of integers $n$ that satisfy the inequalities $ |n – 60| < |n – 100| < |n – 20|$ is$18$$19$$21$$20$

128

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 ...

129

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 ₹ $866.72,$ res...

130

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 ar...

131

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 ...

132

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 gr...

133

If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B} $ and $\log_{2} a = 1/3,$ then $\log_{3}a $ equals$ \dfrac{2}{\text{A + B}} \;– 3 $ $ \dfrac{\text{A + B} - 3}...

134

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

135

$\text{A}$ 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...

136

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$

137

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 $

138

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{min...

139

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 $10\%$...

140

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$

141

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

142

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...

143

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 $7$...

144

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 $\te...

145

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 r...

146

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$

147

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...

148

How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$

149

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 $\...

150

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$...

151

How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$$2017$$2019$$2020$$2018$

152

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...

153

How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$$40$$42$$43$$41$

154

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 $\text{A}$ suc...

155

$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals

156

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 i...

157

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...

158

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$$...

159

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...

160

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 $\text{C}$...