Recent questions and answers in Numerical Ability

1
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
2
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. ____ $666$ $3000$ $6000$ $12000$
1 vote
3
The number of $3$-digit numbers such that the digit $1$ is never to the immediate right of $2$ is $781$ $791$ $881$ $891$
4
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?
5
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
6
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
7
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
8
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.
9
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
10
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. $1$ $2$ $3$ $4$
11
Suppose there are $n$ guests at a party (and no hosts). As the night progresses, the guests meet each other and shake hands. The same pair of guests might shake hands multiple times. for some parties stretch late into the night , and it is hard to keep track.Still, they don't shake hands with ... $2 \mid \text{Even} \mid - \mid \text{Odd} \mid$ $2 \mid \text{Odd} \mid - \mid \text{Even} \mid$
12
Given a positive integer $m$, we define $f(m)$ as the highest power of $2$ that divides $m$. If $n$ is a prime number greater than $3$, then $f(n^3-1) = f(n-1)$ $f(n^3-1) = f(n-1) +1$ $f(n^3-1) = 2f(n-1)$ None of the above is necessarily true
13
One needs to choose six real numbers $x_1, x_2, . . . , x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
14
How many triplets of real numbers $(x,y,z)$ are simultaneous solutions of the equations $x+y=2$ and $xy-z^2=1$? $0$ $1$ $2$ infinitely many
15
Car parking along St. John street is charged at flat X dollar for any amount of time up to these hours, and 1/5 of X dollar each hour or fraction of an hour after the first three hours. How much does it cost to park for 5 hours and 30 minutes?
1 vote
16
The number of isosceles (but not equilateral) triangles with integer sides and no side exceeding $10$ is $65$ $75$ $81$ $90$
17
Let $n> 1$ be an odd integer. The number of zeros at the end of the number $99^{n}+1$ is. $1$ $2$ $3$ $4$ None of the above.
18
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
19
Four squares of sides $x$ cm each are cut off from the four corners of a square metal sheet having side $100$ cm. The residual sheet is then folded into an open box which is then filled with a liquid costing Rs. $x^2$ with $cm^3$. The value of $x$ for which the cost of filling the box completely with the liquid is maximized, is $100$ $50$ $30$ $10$
20
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_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
21
The inequality $\mid x^2 -5x+4 \mid > (x^2-5x+4)$ holds if and only if $1 < x < 4$ $x \leq 1$ and $x \geq 4$ $1 \leq x \leq 4$ $x$ takes any value except $1$ and $4$
1 vote
22
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 $26$ $24$ $20$ $22$
23
Let $a$ and $b$ be two positive integers such that $a = k_1b + r_1$ and $b = k_2r_1 + r_2,$ where $k_1,k_2,r_1,r_2$ are positive integers with $r_2 < r_1 < b$ Then $\text{gcd}(a, b)$ is same as $\text{gcd}(r_1,r_2)$ $\text{gcd}(k_1,k_2)$ $\text{gcd}(k_1,r_2)$ $\text{gcd}(r_1,k_2)$
24
A person moving through a tuberculosis prone zone has a $50$% probability of becoming infected. However, only $30$% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? $15$ $33$ $35$ $37$
25
A function $f(x)$ is linear and has a value of 29 at $x=-2$ and 39 at $x=3$. Find its value at $x=5$. $59$ $45$ $43$ $35$
26
The exponent of $3$ in the product $100!$ is $27$ $33$ $44$ $48$ None of the above.
27
If $z=\dfrac{\sqrt{3}-i}{2}$ and $\large(z^{95}+ i^{67})^{97}= z^{n}$, then the smallest value of $n$ is? $1$ $10$ $11$ $12$ None of the above.
28
How many $0$’s are there at the end of $50!$?
29
At what time between $6$ a. m. and $7$ a. m. will the minute hand and hour hand of a clock make an angle closest to $60°$? $6: 22$ a.m. $6: 27$ a.m. $6: 38$ a.m. $6: 45$ a.m.
30
If $\mid -2X+9\mid =3$ then the possible value of $\mid -X\mid -X^2$ would be: $30$ $-30$ $-42$ $42$
31
If $l=1+a+a^2+ \dots$, $m=1+b+b^2+ \dots$, and $n=1+c+c^2+ \dots$, where $\mid a \mid <1, \: \mid b \mid < 1, \: \mid c \mid <1$ and $a,b,c$ are in arithmetic progression, then $l, m, n$ are in arithmetic progression geometric progression harmonic progression none of these
1 vote
32
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
33
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes? $21$ $18$ $16$ $14$
34
Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is $2$ $3$ $4$ Cannot be determined
35
In the figure below, $\angle DEC + \angle BFC$ is equal to _____ $\angle BCD - \angle BAD$ $\angle BAD + \angle BCF$ $\angle BAD + \angle BCD$ $\angle CBA + \angle ADC$
36
What would be the smallest natural number which when divided either by $20$ or by $42$ or by $76$ leaves a remainder of $7$ in each case? $3047$ $6047$ $7987$ $63847$
37
The Fibonacci sequence is the sequence of integers 1, 3, 5, 7, 9, 11, 13 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 0, 1, 3, 4, 7, 11, 18, 29, 47 0, 1, 3, 7, 15
Hema's age is $5$ years more than twice Hari's age. Suresh's age is $13$ years less than 10 times Hari's age. If Suresh is $3$ times as old as Hema, how old is Hema? $14$ $17$ $18$ $19$
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses $7$ trucks, then at the end of the $4^{th}$ day he can clear all the orders. Alternatively, if he uses only $3$ trucks, then all the orders are ... minimum number of trucks required so that there will be no pending order at the end of $5^{th}$ day? $4$ $5$ $6$ $7$
Let $x$ be a positive real number. Then $x^2+\pi ^2 + x^{2 \pi} > x \pi+ (\pi + x) x^{\pi}$ $x^{\pi}+\pi^x > x^{2 \pi} + \pi ^{2x}$ $\pi x +(\pi+x)x^{\pi} > x^2+\pi ^2 + x^{2 \pi}$ none of the above