# Recent questions and answers in Quantitative Aptitude

1
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$ $n^{4}$ $4^{n}$ $2^{2n-1}$ $4^{n-1}$
2
There are $3$ Indians and $3$ Chinese in a group of $6$ people. How many subgroups of this group can we choose so that every subgroup has at least one Indian? $56$ $52$ $48$ $44$
1 vote
3
What is the total number of ways to reach from $A$ to $B$ in the network given? $12$ $16$ $20$ $22$
4
A tiger is $50$ leaps of its own behind a tree. The tiger takes $5$ leaps per minute to the deer's $4.$ If the tiger and the deer cover $8$ meter and $5$ meter per leap respectively, what distance in meters will the tiger have to run before it catches the deer$?$
5
What is the radix of the numbers if the solution to the quadratic equation $x^2-10x+26=0$ is $x=4$ and $x=7$? $8$ $9$ $10$ $11$
6
Ten teams participate in a tournament. Every team plays each of the other teams twice. The total number of matches to be played is $20$ $45$ $60$ $90$
7
P, Q, R and S are working on a project. Q can finish the task in $25$ days, working alone for $12$ hours a day. R can finish the task in $50$ days, working alone for $12$ hours per day. Q worked $12$ ... . What is the ratio of work done by Q and R after $7$ days from the start of the project? $10:11$ $11:10$ $20:21$ $21:20$
8
Two machine $M1$ and $M2$ are able to execute any of four jobs $P,Q,R$ and $S$. The machines can perform one job on one object at a time. Jobs $P,Q,R$ and $S$ take $30$ minutes, $20$ minutes, $60$ minutes and $15$ minutes each respectively. There are $10$ objects each ... Job $S$ on $4$ objects. What is the minimum time needed to complete all the jobs? $2$ hours $2.5$ hours $3$ hours $3.5$ hours
9
Ananth takes $6$ hours and Bharath takes $4$ hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace. $1$ $2$ $3$ $4$
10
In a college, there are three student clubs, $60$ students are only in the Drama club, $80$ students are only in the Dance club, $30$ students are only in Maths club, $40$ students are in both Drama and Dance clubs, $12$ ... the college are not in any of these clubs, then the total number of students in the college is _____. $1000$ $975$ $900$ $225$
11
Pick the odd one from the following options. $CADBE$ $JHKIL$ $XVYWZ$ $ONPMQ$
1 vote
12
Two trains started at $7$AM from the same point. The first train travelled north at a speed of $80$km/h and the second train travelled south at a speed of $100$km/h. The time at which they were $540$ km apart is ________ AM. $9$ $10$ $11$ $11.30$
1 vote
13
If $2a+3b+c=0$, then at least one root of the equation $ax^2+bx+c=0$, lies in the interval: $(0,1)$ $(1,2)$ $(2,3)$ $(1,3)$
14
A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth $11$ marks each. How many multiple choice questions does the exam have? $12$ $15$ $18$ $19$
1 vote
15
Five numbers $10,7,5,4$ and $2$ are to be arranged in a sequence from left to right following the directions given below: No two odd or even numbers are next to each other. The second number from the left is exactly half of the left-most number. The middle number is exactly twice the right-most number. Which is the second number from the right? $2$ $4$ $7$ $10$
16
There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box ... of all three boxes? The box labeled Apples' The box labeled Apples and Oranges' The box labeled Oranges' Cannot be determined
1 vote
17
A wire would enclose an area of 1936 $m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters? 1096 1111 1243 2486
1 vote
18
Suresh wanted to lay a new carpet in his new mansion with an area of $70\times 55$ sq.mts. However an area of $550$ sq. mts. had to be left out for flower pots. If the cost carpet is Rs.$50$ sq. mts. how much money (in Rs.) will be spent by Suresh for the carpet now? $Rs.1,65,000$ $Rs.1,92,500$ $Rs.2,75,000$ $Rs.1,27,500$
19
There are five buildings called $V$, $W$, $X$, $Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W$. $Z$ is to the East of $X$ and the West of $V$. $W$ is to the West of $Y$. Which is the building in the middle? $V$ $W$ $X$ $Y$
20
Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs. $150$ more. The cost of the gift was Rs. ____ $666$ $3000$ $6000$ $12000$
21
Which number does not belong in the series below? $\qquad2, 5, 10, 17, 26, 37, 50, 64$ $17$ $37$ $64$ $26$
1 vote
22
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$
23
A container originally contains $10$ litres of pure spirit. From this container, $1$ litre of spirit replaced with $1$ litre of water. Subsequently, $1$ litre of the mixture is again replaced with $1$ litre of water and this process is repeated one more time. How much spirit is now left in the container? $7.58$ litres $7.84$ litres $7$ litres $7.29$ litres
24
What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly? Is $5000*(1+4/100)^{1.5} - 5000$ wrong for calculating CI yearly?
25
Given that $a$ and $b$ are integers and $a+a^2 b^3$ is odd, which of the following statements is correct? $a$ and $b$ are both odd $a$ and $b$ are both even $a$ is even and $b$ is odd $a$ is odd and $b$ is even
26
Four cards lie on table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are $2,3,$ red, and blue. Proposition: If a card has an even value on one side, then its opposite face is red. The card which MUST be turned over to verify the above proposition are $2,$ red $2,3,$ red $2,$ blue $2,$ red, blue
1 vote
27
The number of $3$-digit numbers such that the digit $1$ is never to the immediate right of $2$ is $781$ $791$ $881$ $891$
28
The graph of a cubic polynomial $f(x)$ is shown below. If $k$ is a constant such that $f(x)=k$ has three real solutions, which of the following could be a possible value of $k$? $3$ $0$ $-7$ $-3$
1 vote
29
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
30
A 5-card poker hand is said to be a full house if it consists of 3 cards of the same denomination and 2 other cards of the same denomination (of course, different from the first denomination). Thus, one kind of full house is three of a kind plus a pair. What is the probability that one is dealt a full house?
1 vote
31
There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one student who is a member of more than half of the committees.
32
Suppose there are $n$ positive real numbers such that their sum is 20 and the product is strictly greater than 1. What is the maximum possible value of n? 18 19 20 21
33
Evaluate the sum $S=1+1+\dfrac{3}{2^{2}}+\dfrac{3}{2^{3}}+\dfrac{5}{2^{4}}+\dots$ $1$ $2$ $3$ $4$
34
A can is filled with $5$ paise coins. Another can is filled with $10$ paise coins. Another can is filled with $25$ paise coins. All the cans are given wrong labels. If the can labeled $25$ paise is not having the $10$ paise coins, what will the can, labeled $10$ paise have? $25$ paise $5$ paise $10$ paise cannot be determined
1 vote
35
Find the smallest number $y$ such that $y\times 162$ ($y$ multiplied by $162$) is a perfect cube $24$ $27$ $36$ $38$
1 vote
36
When the sum of all possible two digit numbers formed from three different one digit natural numbers are divided by sum of the original three numbers, the result is $26$ $24$ $20$ $22$
37
What is the maximum number of distinct handshakes that can happen in the room with $5$ people in it? $15$ $10$ $6$ $5$
The percentage profit earned by selling an article for $\text{Rs.}1,920$ is equal to the percentage loss incurred by selling the same article for $\text{Rs.}1,280$. At what price should the article be sold to make $25\%$ profit? $\text{Rs.}2,000$ $\text{Rs.}2,200$ $\text{Rs.}2,400$ Data inadequate
The present ages of three persons in proportions $4:7:9$. Eight years ago, the sum of their ages was $56$. Find their present ages (in years). $8,20,28$ $16,28,36$ $20,35,45$ None of the above options
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$