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Quantitative Aptitude
List of top Quantitative Aptitude Questions
There are 980 students in a school, of which 50% play cricket, 30% play basketball and 40% play football. If 60 students play cricket and basketball, 48 students play basketball and football, 180 students play cricket and football, and 35 students play all the three games, then how many students play none of the games?
NPAT - 2020
NPAT
Quantitative Aptitude
Set Theory
A person borrows a sum of ₹10,920 at 10% p.a. compounded interest and promises to pay it back in two equal annual instalments. The interest to be paid by him under this instalment scheme is:
NPAT - 2020
NPAT
Quantitative Aptitude
Compound Interest
Let $A = \{2, 4, 6, 9\}$ and $B = \{4, 6, 18, 27, 81\}$. If $C = \{(x, y) \mid x \in A, y \in B$ such that $x$ is a factor of $y$ and $x<y\}$, then $n(C)$ is:
NPAT - 2020
NPAT
Quantitative Aptitude
Functions
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
NPAT - 2020
NPAT
Quantitative Aptitude
Ratio and Proportion
Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( 4\frac{1}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:
NPAT - 2020
NPAT
Quantitative Aptitude
Time, Speed and Distance
Let A =
\(\{2, 3, 4, 8, 10\}\)
, B =
\(\{3, 4, 5, 10, 12\}\)
, and C =
\(\{4, 5, 6, 12, 14\}\)
be the three sets. If $D = ((A \cup B) \cap (A \cup C)) - (B \cap C)$, then the number of elements in D is:
NPAT - 2020
NPAT
Quantitative Aptitude
Set Theory
The number of elements in sets X and Y are $p$ and $q$ respectively. The total number of subsets of X is 112 more than that of Y. What is the value of $(2p - 3q)$?
NPAT - 2020
NPAT
Quantitative Aptitude
Set Theory
A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
NPAT - 2020
NPAT
Quantitative Aptitude
Percentages
Shikha sells an article for ₹253, after giving 12% discount on its marked price. Had she not given any discount, she would have earned a profit of 25% on the cost price. What is the cost price of the article?
NPAT - 2020
NPAT
Quantitative Aptitude
Mixtures & Alligations
Let \( x = -4\sqrt{2} + \sqrt{17(-\sqrt{2})^2 + 2} \). If \( \frac{1}{x} = a + b\sqrt{2} \), then what is the value of \( (a - b) \)?
NPAT - 2020
NPAT
Quantitative Aptitude
Simplification
The sum of the first 10 terms of the series \( \frac{7}{3} + \frac{7}{5} + \frac{1}{5} + \frac{1}{9} + \cdots = \frac{a}{b} \), where HCF(a,b) = 1. What is the value of \( |a - b| \)?
NPAT - 2020
NPAT
Quantitative Aptitude
Sequence and series
The value of \( \frac{0.35 \times 0.7}{0.63 \times 3.6} + 0.27 (0.83 + 0.16) \) is:
NPAT - 2020
NPAT
Quantitative Aptitude
Simplification
In a year, out of 160 games to be played, a cricket team wants to win 80% of them. Out of 90 games already played, the success rate is \( 66\frac{2}{3} %\). What should be the success rate for the remaining games in order to reach the target?
NPAT - 2020
NPAT
Quantitative Aptitude
Probability
The income of A is \( \frac{3}{5} \) of B's income, and the expenditure of A is \( \frac{4}{5} \) of B's expenditure. If A's income is \( \frac{9}{10} \) of B's expenditure, then the ratio of savings of A and B is:
NPAT - 2020
NPAT
Quantitative Aptitude
Ratio and Proportion
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y + \frac{1}{z}} \), where \( x, y, z \) are positive integers, then the value of \( (2x + 3y - 4z) \) is:
NPAT - 2020
NPAT
Quantitative Aptitude
Algebra
The value of \( \left( \frac{5}{13} \cdot \frac{1}{14} + \frac{2}{25} \cdot \frac{3}{10} - \frac{7}{18} \cdot \frac{1}{35} \right) \div \left( \frac{3}{5} \cdot \frac{4}{21} \cdot \frac{2}{5} \right) \) lies between:
NPAT - 2020
NPAT
Quantitative Aptitude
Simplification
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
NPAT - 2020
NPAT
Quantitative Aptitude
Trigonometric Identities
If \( \sec \theta = a + \frac{1}{4a^2} \), \( 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
NPAT - 2020
NPAT
Quantitative Aptitude
Trigonometric Identities
Evaluate: \[ \frac{\sin \theta (1 + \tan \theta) + \cos \theta (1 + \cot \theta)}{(\cos \theta - \sin \theta)(\sec \theta - \cos \theta)(\tan \theta + \cot \theta)} \]
NPAT - 2020
NPAT
Quantitative Aptitude
Trigonometric Identities
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
NPAT - 2020
NPAT
Quantitative Aptitude
Functions
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{-x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?
NPAT - 2020
NPAT
Quantitative Aptitude
Functions
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
NPAT - 2020
NPAT
Quantitative Aptitude
Functions
X and Y are two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are \( 30^\circ \) and \( 60^\circ \) respectively. The distance of Y from the foot of the pole (in m) is:
NPAT - 2020
NPAT
Quantitative Aptitude
Trigonometric Identities
The value of \( \frac{(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta)}{\tan^2 \theta + \cot^2 \theta - \sec^2 \theta \csc^2 \theta} \) is:
NPAT - 2020
NPAT
Quantitative Aptitude
Trigonometric Identities
Let \( A = \{1,2,5,6\}, B = \{1,2,3\} \) and \( C = (A \times B) \cap (B \times A) \). Which of the following is INCORRECT?
NPAT - 2020
NPAT
Quantitative Aptitude
Set Theory
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