# Recent questions tagged quantitative-aptitude

81

If a certain weight of an alloy of silver and copper is mixed with $3 \; \text{kg}$ of pure silver, the resulting alloy will have $90 \%$ silver by weight. If the same we...

82

One day, Rahul started a work at $9 \; \text{AM}$ and Gautam joined him two hours later. They then worked together and completed the work at $5 \; \text{PM}$ the same day...

83

A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying elect...

84

The total of male and female populations in a city increased by $25 \%$ from $1970$ to $1980.$ During the same period, the male population increased by $40 \%$ while the ...

85

If $n$ is a positive integer such that $( \sqrt[7]{10}) ( \sqrt[7]{10})^{2} \dots ( \sqrt[7]{10})^{n} 999,$ then the smallest value of $n$ is

86

If $3x + 2|y| + y = 7$ and $ x + |x| + 3y = 1,$ then $x + 2y$ is$\frac{8}{3}$$1$$ – \frac{4}{3}$$0$

87

A tea shop offers tea in cups of three different sizes. The product of the prices, in $\text{INR},$ of three different sizes is equal to $800.$ The prices of the smallest...

88

One part of a hostel’s monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects $ ₹ \; 1600$ per month from ea...

89

In a tournament, a team has played $40$ matches so far and won $30 \%$ of them. If they win $60 \%$ of the remaining matches, their overall win percentage will be $50 \%....

90

Consider the pair of equations: $x^{2} – xy – x = 22$ and $y^{2} – xy + y = 34.$ If $x>y,$ then $x – y$ equals$7$$8$$6$$4$

91

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is $70 \%.$ His...

92

If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is$\sqrt{13} + \sqrt{12}$$\sqrt{37} +...

93

The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four ba...

94

For a sequence of real numbers $x_{1}, x_{2}, \dots , x_{n},$ if $x_{1} – x_{2} + x_{3} – \dots + (-1)^{n+1} x_{n} = n^{2} + 2n$ for all natural numbers $n,$ then the...

95

For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if$9 < x < 14$$6 < x < 11$$7 < x < 12$$10 < x < 15$

96

A box has $450$ balls, each either white or black, there being as many metallic white balls as metallic black balls. If $40 \%$ of the white balls and $50 \%$ of the blac...

97

The sides $\text{AB}$ and $\text{CD}$ of a trapezium $\text{ABCD}$ are parallel, with $\text{AB}$ being the smaller side. $\text{P}$ is the midpoint of $\text{CD}$ and $\...

98

Raj invested ₹$10000$ in a fund. At the end of first year, he incurred a loss but his balance was more than ₹$5000.$ This balance, when invested for another year, gre...

99

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$

100

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 $10$ matc...

101

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

102

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 hi...

103

Let $\text{D}$ and $\text{E}$ be points on sides $\text{AB}$ and $\text{AC},$ respectively, of a triangle $\text{ABC},$ such that $\text{AD}$ : $\text{BD} = 2 : 1$ and $...

104

For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is$ \left(\frac{3}{7}, \frac{1}{2} \right)$$ \left[\frac{3}{7}, \fr...

105

Suppose one of the roots of the equation $ax^{2} – bx + c = 0$ is $2 + \sqrt{3},$ where $a, b$ and $c$ are rational numbers and $a \neq 0.$ If $b = c^{3}$ then $|a|$ eq...

106

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...

107

If $\log_{2} [3+ \log_{3} \{ 4+ \log_{4} (x-1) \}] – 2 = 0$ then $4x$ equals

108

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 $...

109

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...

110

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 $15,$ an...

111

How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?

112

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...

113

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$$...

114

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 $16$ m...

115

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 alter...

116

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 al...

117

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 \sqr...

118

$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if$ – 2 < x < 3 \; \text{or} \; x 9 $$ x < – 5 \; \text{or} \; 3 < x < 9 $$ – 5 < x...

119

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 ...

120

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...