# Numerical Ability

 Question 1
Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?
 A $2:3$ B $1:1$ C $3:2$ D $2:1$
GATE ME 2022 SET-2   General Aptitude
Question 1 Explanation:

$2d=1\Rightarrow d=\frac{1}{2}$
Area of circle $=\frac{\pi d^2}{4}=\frac{\pi}{16}$
Total circle area $= 4 \times \frac{\pi}{16}=\frac{\pi}{4}$

$3d=1\Rightarrow d=\frac{1}{3}$
Area of circle $=\frac{\pi d^2}{4}=\frac{\pi}{36}$
Total circle area $= 9 \times \frac{\pi}{36}=\frac{\pi}{4}$
$\frac{\text{Unshaded area M}}{\text{Unshaded area N}}=\frac{1^2-\frac{\pi}{4}}{1-\frac{\pi}{4}}=\frac{1}{1}=1:1$
 Question 2
Four cities P, Q, R and S are connected through oneway routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train. If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?

 A 6 hours 30 minutes B 3 hours 45 minutes C 4 hours 30 minutes D 5 hours 15 minutes
GATE ME 2022 SET-2   General Aptitude
Question 2 Explanation:
R at 7 am
1 hour journey
Reached Q at 8 am
At Q buses available timings are 5 am, 7am, 9 am ..
Person started at Q at 9 am
1 hour journey reached P at 10 am.
Buses timings at P are 8 am, 9:30am, 11 am, 12:30 pm...
Person started at P at 11 am
1 hour journey
Reached S at 12 noon.
Buses timings at S are
8am, 8:45 am, 9:30 am, 10:15 am, 11am, 11:45 am, 12:30pm ....
Person started at S at 12:30 pm
1 hour journey
Reached R at 1:30 pm
Minimum Total time = 1:30 pm - 7 am
= 6 hrs 30 min
 Question 3
Consider the following functions for non-zero positive integers, $p$ and $q$

$f(p,q)=\underbrace{p \times p \times p \times ...p}_{q \;\;times} =p^q;\;\; f(p,1)=p$
$g(p,q)=p^{p^{p^{\vdots ^{q \;\;times}}}};\;\; g(p,1)=p$

Which one of the following options is correct based on the above?
 A $f(2,2)=g(2,2)$ B $f(g(2,2),2) \lt f(2,g(2,2))$ C $g(2,1) \neq f(2,1)$ D $f(3,2) \gt g(3,2)$
GATE ME 2022 SET-2   General Aptitude
Question 3 Explanation:
f(2,2) = 2 x 2 = 4
g(2,2) = 4
f(2,2) = g(2,2)
 Question 4
For the past m days, the average daily production at a company was 100 units per day.
If today's production of 180 units changes the average to 110 units per day, what is the value of m?
 A 18 B 10 C 7 D 5
GATE ME 2022 SET-2   General Aptitude
Question 4 Explanation:
Total production = Average x No. of days
P= 100 m
and
P + 180 = 110 (m+1)
Solving, m = 7
 Question 5

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other?
(rotation and translation operations may be used).

 A A B B C C D D
GATE ME 2022 SET-2   General Aptitude
Question 5 Explanation:
Priority: Shape, position and size.
As per size point of view parallelogram is not suitable.
 Question 6
If $f(x)=2 \ln\sqrt{e^x}$ what is the area bounded by $f(x)$ for the interval $[0,2]$ on the $x-$axis?
 A $\frac{1}{2}$ B $1$ C $2$ D $4$
GATE ME 2022 SET-2   General Aptitude
Question 6 Explanation:
\begin{aligned} f(x)&=2 \ln ( \sqrt{e^x})\\ &=2 \ln (e^{x/2})=2 \log _e e^{x/2}\\ f(x)&=2\left ( \frac{x}{2} \right )=x \end{aligned}

Area =(1/2) x 2 x 2=2
 Question 7
Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality $2-5x\leq -\frac{6x-5}{3}$on the real number line?

 A A B B C C D D
GATE ME 2022 SET-2   General Aptitude
Question 7 Explanation:
\begin{aligned} 2-5x \leq -\frac{6x-5}{3}\\ 1-9x\leq 0\\ \Rightarrow 1\leq 9x\Rightarrow x\geq \frac{1}{9} \end{aligned}
 Question 8
In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?
 A 11 B 12 C 144 D 2
GATE ME 2022 SET-1   General Aptitude
Question 8 Explanation:
3 pm - 3am = 12 hrs
Coincide is
11 times in 12 hours
 Question 9
An equilateral triangle, a square and a circle have equal areas.
What is the ratio of the perimeters of the equilateral triangle to square to circle?
 A $3\sqrt{3}: 2: \sqrt{\pi}$ B $\sqrt{3\sqrt{3}}: 2: \sqrt{\pi}$ C $\sqrt{3\sqrt{3}}: 4: 2\sqrt{\pi}$ D $\sqrt{3\sqrt{3}}: 2: 2\sqrt{\pi}$
GATE ME 2022 SET-1   General Aptitude
Question 9 Explanation:

\begin{aligned} \frac{\sqrt{3}}{4}a^2 &=s^2 &=\pi r^2&=k\\ a&=\sqrt{\frac{4k}{\sqrt{3}}}&s=\sqrt{k} &\;\;\; r=\sqrt{\frac{\pi}{k}}\\ &\text{Perimeters:}\\ 3a&:&4a&:&2 \pi ^2\\ 3\frac{2\sqrt{k}}{3^{1/4}}&:&4\sqrt{k}&:&2 \pi \frac{\sqrt{k}}{\sqrt{\pi}}\\ 3^{3/4}&:&2&:&\sqrt{\pi} \end{aligned}
 Question 10

A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.
Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?

 A A B B C C D D
GATE ME 2022 SET-1   General Aptitude
Question 10 Explanation:
View from arrow direction is

There are 10 questions to complete.

### 6 thoughts on “Numerical Ability”

1. Answer to 113 question is option b plz correct it

• Thank You Hania,