# Numerical Ability

 Question 1
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

 A P B Q C R D S
GATE ME 2023   General Aptitude
 Question 2
How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?
 A 729 B 728 C 665 D 664
GATE ME 2023   General Aptitude
Question 2 Explanation:
Take one element {1}
$T=\phi ,S=\phi \rightarrow (\phi, \phi ) \Rightarrow 1\; pair$

$T=1,S=\phi \rightarrow (\phi, 1 ),(1,1) \Rightarrow 2\; pair$
For 1 element total pair $= 3^1$
Similarly
For 2 element total pair $= 3^2$
For 3 element total pair $= 3^3$
For 4 element total pair $= 3^4$
For 5 element total pair $= 3^5$
For 6 element total pair $= 3^6=729$

 Question 3
Consider the following inequalities

$p^2-4q \lt 4$
$3p+2q \lt 6$

where $p$ and $q$ are positive integers.
The value of $(p+q)$ is _______.
 A 2 B 1 C 3 D 4
GATE ME 2023   General Aptitude
Question 3 Explanation:
\begin{aligned} p^2-4q &\lt 4 \\ p^2-4&\ lt 4q \;\;...(i)\\ 3p+2Q& \lt 6 \\ 6p-12 &\lt -4q\;\;...(ii)\\ &\text{by equation (i) + (ii)} \\ p^2+6p-16 &\lt 0 \\ (p+8)(p-2)& \lt 0 \\ \therefore \; p&\in (-8,2) \end{aligned}
Given p is positive integer
$\therefore \;p=1$
Now, from equation (i), $1-4 \lt 4q$
$q \gt \frac{-3}{4}$
from equation (ii),
$q \lt 3/2$
$\therefore \; \frac{-3}{4} \lt q \lt \frac{3}{2}$
Given q is positive integer
$\therefore \;\; q=1$
Thus $p + q = 1+1 = 2$
 Question 4
The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.
 A 30 B 15 C 29 D 31
GATE ME 2023   General Aptitude
Question 4 Explanation:
After 09:15:00 AM every minute, minute and second hand cross each other once (1) times.
So, 09:16:00 to 09:45:00 minute hand and second hand cross each other 30 times.
 Question 5
A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.
What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

 A 22.7 B 23.7 C 15 D 66.8
GATE ME 2023   General Aptitude
Question 5 Explanation:
$\frac{ \text{7\% of 504 + 23 \% of 25951} }{504 + 25951}=22.7 \%$

There are 5 questions to complete.

### 6 thoughts on “Numerical Ability”

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

• Thank You Hania,