Hanhpt23/IQBench huggingface dataset:
Topic: Mechanical Deductive Reasoning Test
Question: The smaller gear makes 36 revolutions by the time the larger ones make 18.
If the smaller gear makes 56 revolutions, how many turns will the larger one make?
A. 24 
B. 26 
C. 28 
D. 25 

Answer: C
Explanation: Explanation:
\[
u = \frac{18}{36} = 0.5
\]
\[
n_{\text{larger}} = u \cdot 56 = 28
\]
Topic: Mechanical Deductive Reasoning Test
Question: Gear A: 5 teeth 
Gear B: 50 teeth 
Gear C: 20 teeth 
Gear D: 10 teeth
How many revolutions per second is gear C turning?
A. 5
B. 10
C. 15
D. 20

Answer: B
Explanation: If a cog with 5 teeth can do a full 40 revolutions in a second, a cog with four times as many teeth will take 4 times as long to do a full revolution. This means, it will do 4 times fewer revolutions. So the correct answer is 10.
Topic: Mechanical Deductive Reasoning Test
Question: Which image is the front view of the given part in the direction of the arrow?
Answer: B
Explanation: The front view is determined by looking in the direction of the arrow.
Option A shows a circle, which represents the top view.
Option C makes the cylinder appear too small, which is inaccurate.
Option B correctly shows the rectangular base with the cylinder as a smaller rectangle on top.
Conclusion: The correct answer is B.
Topic: Mechanical Deductive Reasoning Test
Question: In which direction will the orange gear rotate?
A. Clockwise 
B. Counterclockwise
C. No rotation

Answer: A
Explanation: The driving gear and the orange gear are connected through an intermediate gear, so the orange gear rotates in the same direction as the driving gear.
Topic: Mechanical Deductive Reasoning Test
Question: In which direction will the orange gear rotate?
A. Clockwise 
B. Counterclockwise
C. No rotation
Answer: B
Explanation: the driving gear rotates clockwise (CW), the orange gear will rotate counterclockwise (CCW).
Topic: Mechanical Deductive Reasoning Test
Question: In which direction will the orange gear rotate?
A. Clockwise 
B. Counterclockwise
C. No rotation
Answer: B
Explanation: The driving gear and the orange gear are continuously meshed through two intermediate gears. Therefore, the orange gear rotates in the opposite direction of the driving gear.
Topic: Mechanical Deductive Reasoning Test
Question: In which direction will the orange gear rotate?
A. Clockwise 
B. Counterclockwise
C. No rotation
Answer: B
Explanation: The driving rack moves to the right, causing the meshing gear to rotate clockwise. The orange gear is connected to this gear through two intermediate gears. Therefore, the orange gear rotates counterclockwise.
Topic: Mechanical Deductive Reasoning Test
Question: In which direction will the orange gear rotate?
A. Clockwise 
B. Counterclockwise
C. No rotation
Answer: B
Explanation: The driving gear rotates counterclockwise and transmits motion through a belt to the large gear, which also rotates counterclockwise. This large gear meshes with a smaller gear, making it rotate clockwise. The small gear then drives another gear, causing it to rotate counterclockwise. Finally, the orange gear meshes with this last gear, making it rotate counterclockwise
Topic: Mechanical Deductive Reasoning Test
Question: The scale is balanced. What is the weight of the weight with the question mark? 
A. 4 kg 
B. 10 kg 
C. 20 kg 
D. 40 kg 
E. 50 kg 

Answer: A
Explanation: \[
m = \frac{10 \cdot 2}{5} = 4 \, \text{kg}
\]
Topic: Mechanical Deductive Reasoning Test
Question: On which pole does the weight press harder? 
A. (A) 
B. (B) 
C. None 

Answer: B
Explanation: (B) experiences greater force because it is closer to the fulcrum of the heavier mass (A).
Topic: Mechanical Deductive Reasoning Test
Question: What pulleys turn in the same direction as 1?
A. 2 and 8
B. 6 and 4
C. 2, 3, 7 and 8
D. 4, 5 and 6

Answer: B
Explanation: Pulley 1 rotates clockwise. 
Pulley 2 and 8 rotate in the opposite directions to pulley 1. 
Pulley 8 and 7 rotate in the same direction. 
Pulley 2 and 3 rotate in the same direction. 
Pulley 3 and 4 rotate in opposite directions. 
Pulley 6 and 7 rotate in opposite directions. 
Pulley 5 and 6 rotate in opposite directions.
Topic: Mechanical Deductive Reasoning Test
Question: Consider the following pulley system. Pulley A is fixed, and Pulley B is moveable. If the system is balanced, how much does the weight with the question mark weigh?
A. 5 kg
B. 10 kg
C. 20 kg
D. 40 kg
E. 50 kg


Answer: C
Explanation: 
The force transmitted on a single rope is the same. Pulley B has two ropes, so the mass of the object to be found is: 

\[ 
m = 2 \cdot 10 = 20 \, \text{kg} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: What is the weight of the weight with the question mark?
A. 15 kg
B. 20 kg
C. 25 kg
D. 30 kg
E. 35 kg

Answer: E
Explanation: \[
m = \frac{20 \cdot 6 + 30 \cdot 3}{6} = 35 \ \text{kg}
\]
Topic: Mechanical Deductive Reasoning Test
Question: Which is the side view projection of the given part according to the first angle projections?
Answer: B
Explanation: According to the first angle projections, the side view projection is seen from the left. Therefore, the correct answer is B.
Topic: Mechanical Deductive Reasoning Test
Question: What weight does the blue box have to be in order for the seesaw to be in equilibrium?
A. 20 kg
B. 30 kg
C. 40 kg
D. None

Answer: D
Explanation: In order for the seesaw to be in equilibrium, the net force must equal zero. Moment of a force = force x distance to pivot. Therefore, the moment of a force on the left side of the seesaw is 10 kg x 5 = 50. The right side must equal 50 for the seesaw to be balanced, therefore 50 divided by 2 (2 meters distance from pivot) = 25.
Topic: Mechanical Deductive Reasoning Test
Question: Consider two spheres as shown in the figure. Sphere 1 moves and undergoes a perfectly elastic head-on collision with sphere 2. Determine the direction of motion of sphere 1 after the collision.
A. Opposite to the initial direction
B. Same as the initial direction
C. None of the answers

Answer: A
Explanation: Since the collision is central and perfectly elastic, the total momentum before and after the collision must be equal:

\[
m_1 \cdot v_1(0) + m_2 \cdot v_2(0) = m_1 \cdot v_1 + m_2 \cdot v_2
\]

Since the collision is perfectly elastic, kinetic energy is also conserved:

\[
\frac{1}{2} \cdot m_1 \cdot v_1(0)^2 + \frac{1}{2} \cdot m_2 \cdot v_2(0)^2 = \frac{1}{2} \cdot m_1 \cdot v_1^2 + \frac{1}{2} \cdot m_2 \cdot v_2^2
\]

Solving for \( v_1 \), we get:

\[
v_1 = -\frac{5}{3} \, \text{m/s}
\]

Hence, option A is the correct choice.
Topic: Mechanical Deductive Reasoning Test
Question: A speeding motorist travelling passes a stopped police car. The police car immediately begins to chase the speeder, accelerating at a constant 2.5 m/s2. How long does it take for the police car to intercept the speeder?
A. 25.6 s
B. 26.6 s
C. 27.6 s
D. 28.6 s
Answer: B
Explanation: The speeder’s car's equation of motion is given by: 

\[ 
X_s \coloneqq \frac{120 \cdot 1000 \cdot t}{3600} = \frac{100}{3} \cdot t, \, \text{m/s} 
\] 

The police car's equation of motion is: 

\[ 
X_{\text{police}} = 0.5 \cdot 2.5 \cdot t^2 
\] 

When the two vehicles are at the same position: 

\[ 
X_s = X_{\text{police}} 
\] 

Solving for time \( t \), we get: 

\[ 
t = \frac{33.3}{0.5 \cdot 2.5} = 26.6 \, \text{s} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: A child pulls a heavy object using a rope that passes over a pulley. Neglect the mass of the pulley and assume the rope remains taut throughout the motion. What is the minimum force the child must exert in order to lift the object upward?
A. 49 N
B. 50 N
C. 51 N
D. 52 N

Answer: B
Explanation: The minimum force the child must exert in order to lift the object upward is:

\[
F = g \cdot m = 9.81 \cdot 5 = 49.05 \, \text{N}
\]

Hence, option B is the correct answer, with:

\[
F = 50 \, \text{N}
\]
Topic: Mechanical Deductive Reasoning Test
Question: The angular velocity of the disk is defined by like the picture. Determine the magnitudes of the velocity of point A on the disk when t = 0.5 s. _x000B_
A. 2.5 m/s
B. 2.6 m/s
C. 2.7 m/s
D. 2.8 m/s
Answer: B
Explanation: V_A = \omega \cdot 0.8 = \left(2 \cdot 0.5^2 + 2\right) \cdot 0.8 = 2.6 \, \text{m/s}
Topic: Mechanical Deductive Reasoning Test
Question: The disk is originally rotating at 𝜔_0. If it is
subjected to a constant angular acceleration, determine the magnitudes of the normal component of acceleration of point A at the
instant t = 2 s.
A. 1350 m/s^2
B. 1352 m/s^2
C. 1354 m/s^2
D. 1356 m/s^2
Answer: B
Explanation: 
The angular velocity of the disk can be determined using :\\
\[
\omega = \omega_0 + \alpha t = 12 + 20 \ast 2 = 52 \, \text{rad/s}
\]

The normal component of acceleration are:\\
\[
a_n = \omega^2 R = 1352 \, \text{m/s}^2
\]
Topic: Mechanical Deductive Reasoning Test
Question: If gear A rotates with a constant angular acceleration of starting from rest, determine the angular velocity of gear B if the angular velocity of gear A is 600 rpm. 
A. 180 rad/s
B. 190 rad/s
C. 200 rad/s
D. 210 rad/s
Answer: A
Explanation: \[ 
\omega_B = \frac{15\omega_A}{50} = 180 \, \text{rad/s} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: The power of a bus engine is transmitted using the belt-andpulley arrangement shown. Determine the angular velocities of the generator pulley B when t = 3 s.
A. 300 rad/s
B. 320 rad/s
C. 340 rad/s
D. 360 rad/s
Answer: A
Explanation: \text{When } t = 3 \, \text{s} 
\[ 
\omega_A = 20(3) + 40 = 100 \, \text{rad/s} 
\] 

\text{The speed of a point } P \text{ on the belt wrapped around } A \text{ is} 
\[ 
v_P = \omega_A r_A = 100(0.075) = 7.5 \, \text{m/s} 
\] 

\[ 
\omega_B = \frac{v_P}{r_D} = \frac{7.5}{0.025} = 300 \, \text{rad/s} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: If the motor turns gear A with an angular acceleration and the angular velocity, determine the angular velocity of gear D.
A. 2 rad/s
B. 3 rad/s
C. 4 rad/s
D. 5 rad/s
Answer: C
Explanation: \textbf{Angular Motion:} \text{ The angular velocity and acceleration of gear } B \text{ must be determined first. Here, } 
\omega_A r_A = \omega_B r_B \text{ and } \alpha_A r_A = \alpha_B r_B. \text{ Then,} 

\[ 
\omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{40}{100} \right)(20) = 8.00 \, \text{rad/s} 
\] 

\[ 
\alpha_B = \frac{r_A}{r_B} \alpha_A = \left( \frac{40}{100} \right)(2) = 0.800 \, \text{rad/s}^2 
\] 

\text{Since gear } C \text{ is attached to gear } B, \text{ then } \omega_C = \omega_B = 8 \, \text{rad/s and } 
\alpha_C = \alpha_B = 0.8 \, \text{rad/s}^2. \text{ Realizing that } \omega_C r_C = \omega_D r_D \text{ and } 
\alpha_C r_C = \alpha_D r_D, \text{ then} 

\[ 
\omega_D = \frac{r_C}{r_D} \omega_C = \left( \frac{50}{100} \right)(8.00) = 4.00 \, \text{rad/s} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: The gear A on the drive shaft of the outboard motor has a radius 𝑟_𝐴=0.5 in. and the meshed pinion gear B on the propeller shaft has a radius 𝑟_𝐵=1.2 in. Determine the angular velocity of the propeller in t=1.5 𝑠, if the drive shaft rotates with an angular acceleration 𝛼=〖400𝑡〗^3 𝑟𝑎𝑑/𝑠^2 , where t is in seconds. The propeller is originally at rest and the motor frame does not move. _x000B_
A. 209 m/s^2
B. 211 m/s^2
C. 213 m/s^2
D. 215 m/s^2
Answer: B
Explanation: \textbf{Angular Motion:} \text{ The angular velocity of gear } A \text{ at } t = 1.5 \, \text{s must be determined first. Applying Eq. 16--2, we have} 

\[ 
d\omega = \alpha dt 
\] 

\[ 
\int_0^{\omega_A} d\omega = \int_0^{1.5 \, s} 400t^3 \, dt 
\] 

\[ 
\omega_A = 100t^4 \big|_0^{1.5 \, s} = 506.25 \, \text{rad/s} 
\] 

\text{However, } \omega_A r_A = \omega_B r_B \text{ where } \omega_B \text{ is the angular velocity of propeller. Then,} 

\[ 
\omega_B = \frac{r_A}{r_B} \omega_A = \left( \frac{0.5}{1.2} \right)(506.25) = 211 \, \text{rad/s} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: The pinion gear A on the motor shaft is given a constant angular acceleration 𝛼. If the gears A and B have the dimensions shown, determine the angular velocity of the output shaft C, when t=2s starting from rest. The shaft is fixed to B and turns with it. 
A. 1.62 rad/s
B. 1.64 rad/s
C. 1.66 rad/s
D. 1.68 rad/s
Answer: D
Explanation: \begin{align*} 
\omega &= \omega_0 + \alpha_c t \\ 
\omega_A &= 0 + 3(2) = 6 \, \text{rad/s} \\ 
\\ 
\theta &= \theta_0 + \omega_0 t + \frac{1}{2} \alpha_c t^2 \\ 
\theta_A &= 0 + 0 + \frac{1}{2}(3)(2)^2 \\ 
\theta_A &= 6 \, \text{rad} \\ 
\\ 
\omega_A r_A &= \omega_B r_B \\ 
6(35) &= \omega_B (125) \\ 
\omega_C = \omega_B &= 1.68 \, \text{rad/s} 
\end{align*}
Topic: Mechanical Deductive Reasoning Test
Question: Which piece corresponds to the given solid?
Answer: C
Explanation: The third piece corresponds to the given solid
Topic: Mechanical Deductive Reasoning Test
Question: Which picture can be formed with the given pieces? 

Answer: C
Topic: Mechanical Deductive Reasoning Test
Question: To which object does the given top view correspond? 

Answer: A
Topic: Mechanical Deductive Reasoning Test
Question: Which of these image is the top view of the given object?
Answer: B
Topic: Mechanical Deductive Reasoning Test
Question: For protection, the barrel barrier is placed in front of the bridge pier. If the relation between the force and deflection of the barrier is lb, where is in ft, determine the car’s maximum penetration in the barrier. The car has a weight of 4000 lb and it is traveling with a constant speed before it hits the barrier.
A. 3.20 ft
B. 3.22 ft
C. 3.24 ft
D. 3.26 ft
Answer: C
Explanation: \[
T_{1}+\Sigma U_{12}=T_{2}
\]
\[
0.5\cdot \left(\frac{4000}{ 32.2}\right)\cdot \left(75^{2}\right)+\int_{0}^{x_{\max}}90\cdot 10^{3}\cdot x^{ 0.5}d{x}=0
\]
\[
x_{\max}= 3.24 \text{ ft}
\]
Topic: Mechanical Deductive Reasoning Test
Question: A man kicks the ball such that it leaves the ground at an angle and strikes the ground at the same elevation a distance of Sx m away. Determine the impulse of his foot on the ball at A. Neglect the impulse caused by the ball’s weight while it’s being kicked. 
A. 1.75 N.s
B. 1.76 N.s
C. 1.77 N.s
D. 1.78 N.s
Answer: A
Explanation: Consider the vertical motion of the ball, where:

\[
S_y = v \cdot \sin(60^\circ) \cdot t + \frac{1}{2} \cdot (-9.81) \cdot t^2 = 0
\]

Factorizing the equation:

\[
t \left( v \cdot \sin(60^\circ) - 4.905 \cdot t \right) = 0
\]

Since \( t \ne 0 \), we solve:

\[
v \cdot \sin(60^\circ) - 4.905 \cdot t = 0
\]

\[
t \approx \frac{v \cdot \sin(60^\circ)}{4.905}
\]

\[
t \approx 0.1766v
\]

\section*{Horizontal Motion of the Ball}

\[
S_x = v \cdot \cos(60^\circ) \cdot t = 12
\]

\[
t = \frac{12}{v \cdot \cos(60^\circ)} = \frac{24}{v}
\]

Equating the two expressions for \( t \):

\[
0.1766v = \frac{24}{v}
\]

Solving for \( v \):

\[
v^2 = \frac{24}{0.1766} \Rightarrow v \approx 11.66 \, \text{m/s}
\]

\section*{Principle of Impulse and Momentum}

\[
I = m (v_2 - v_1) = m \cdot v = 1.75 \, \text{N$\cdot$s}
\]
Topic: Mechanical Deductive Reasoning Test
Question: The jet car is initially traveling at a initial velocity when it is subjected to the acceleration shown. Determine the car's maximum velocity and the time 𝑡' when it comes to a stop. Assume that when t=0, the displacement s=0.
A. 𝑉_𝑚𝑎𝑥=100 m/s; 𝑡′=40 s
B. 𝑉_𝑚𝑎𝑥=102 m/s; 𝑡′=42 s
C. 𝑉_𝑚𝑎𝑥=104 m/s; 𝑡′=44 s
D. 𝑉_𝑚𝑎𝑥=106 m/s; 𝑡′=46 s


Answer: A
Explanation: Because acceleration is constant, the equation of car motion is:

\[
v = 10 + a \cdot t
\]

The maximum velocity is:

\[
V_{\text{max}} = 10 + 6 \cdot 15 = 100 \, \text{m/s}
\]

When the jet car stops:

\[
0 = 100 - 4 \cdot (t' - 15)
\]

Solving for \( t' \):

\[
t' = \frac{160}{4} = 40 \, \text{s}
\]
Topic: Mechanical Deductive Reasoning Test
Question: Determine the minimum initial velocity 𝑣_0 at which the ball must be kicked.
A. 𝑣_0=22.5 m/s
B. 𝑣_0=23.5 m/s
C. 𝑣_0=24.5 m/s
D. 𝑣_0=25.5 m/s



Answer: A
Explanation: Time to reach the horizontal position:

\[
x = v_0 \cdot t \cdot \cos(30^\circ) = 6
\]

The vertical position at that time:

\[
y = v_0 \cdot t \cdot \sin(30^\circ) - 0.5 \cdot g \cdot t^2 = 3
\]

From these two equations, we can determine:

\[
v_0 = 22.5 \, \text{m/s}
\]
Topic: Mechanical Deductive Reasoning Test
Question: A golf ball is struck with a velocity as shown. Determine the distance d to where it will land. 
A. 𝑑=156 ft
B. 𝑑=166 ft
C. 𝑑=176 ft
D. 𝑑=186 ft

Answer: B
Explanation: Given the following equations:

\[
d \cdot \cos(10^\circ) = 80 \cdot \cos(55^\circ) \cdot t \text{ (1)}
\]

\[
d \cdot \sin(10^\circ) = 80 \cdot \sin(55^\circ) \cdot t - 0.5 \cdot (32.5) \cdot t^2 \text{ (2)}
\]

Solving these equations, we get the result:

\[
d = 166 \, \text{ft}
\]
Topic: Mechanical Deductive Reasoning Test
Question: A passenger in an automobile observes that raindrops make an angle with the horizontal as the auto travels forward with a constant speed as shown. Compute the terminal (constant) velocity of the rain if it is assumed to fall vertically.
A. 33.6 km/h
B. 34.6 km/h
C. 35.6 km/h
D. 36.6 kh/h

Answer: B
Explanation: The relative velocity is given by:

\[
V_r = 60 \cdot \tan(30^\circ) = 34.6 \, \text{km/h}
\]
Topic: Mechanical Deductive Reasoning Test
Question: If the coefficient of kinetic friction between the crate and the ground is 𝜇 as shown. Determine the distance traveled by the crate at 
𝑡=t', if it starts from rest..
A. 5.01 m
B. 5.02 m
C. 5.03 m
D. 5.04 m

Answer: D
Explanation: The acceleration of the crate is given by:

\[
a = \frac{200 \cdot \cos(30^\circ) - 0.3 \cdot (-200 \cdot \sin(30^\circ) + 9.81 \cdot 50)}{50} = 1.121 \, \text{m/s}^2
\]

The motion equation is:

\[
s = 0.5 \cdot a \cdot t^2 = 0.5 \cdot 1.121 \cdot 9 = 5.04 \, \text{m}
\]
Topic: Mechanical Deductive Reasoning Test
Question: The conveyor belt is moving. If the coeffcient of static friction between the conveyor and the package B is 𝜇 as shown, determine the shortest time the belt can stop so that the package does not slide on the belt.
A. 2.02 s
B. 2.04 s
C. 2.06 s
D. 2.08 s

Answer: B
Explanation: When the conveyor belt decelerates, the package wants to keep moving due to inertia. Static friction must provide the force to decelerate the package at the same rate as the belt, to avoid sliding.

The maximum static friction force is given by:

\[
f = 0.2 \cdot 10 \cdot 9.81 = 19.62 \, \text{N}
\]

This force is responsible for the maximum possible deceleration:

\[
a = \frac{19.62}{10} = 1.962 \, \text{m/s}^2
\]

To find the shortest time to stop, we use kinematics:

\[
v = 4 - a \cdot t = 0
\]

Solving for time:

\[
t_{\text{min}} = \frac{4}{1.962} = 2.04 \, \text{s}
\]
Topic: Mechanical Deductive Reasoning Test
Question: Determine the magnitude of the resultant force Fr.

A. 392 lb
B. 393 lb
C. 394 lb
D. 395 lb

Answer: B
Explanation: The resultant force \( F_r \) is given by the equation:

\[
F_r = \sqrt{F_1^2 + F_2^2 - 2 \cdot F_1 \cdot F_2 \cdot \cos(75^\circ)} = 393 \, \text{lb}
\]
Topic: Mechanical Deductive Reasoning Test
Question: A vertical force F acts downward on the two-membered frame. Determine the magnitudes of the two components of F directed along the axes of members AB and AC. 
A. 𝐹_𝐴𝐵=366 N; 𝐹_𝐴𝐶=448 N
B. 𝐹_𝐴𝐵=448 N; 𝐹_𝐴𝐶=366 N
C. 𝐹_𝐴𝐵=446 N; 𝐹_𝐴𝐶=368 N
D. 𝐹_𝐴𝐵=368 N; 𝐹_𝐴𝐶= 448 N

Answer: B
Explanation: he forces \( F_{ab} \) and \( F_{ac} \) are calculated as follows: 

\[ 
F_{ab} = \frac{500 \cdot \sin(60^\circ)}{\sin(75^\circ)} = 448 \, \text{N} 
\] 

\[ 
F_{ac} = \frac{500 \cdot \sin(45^\circ)}{\sin(75^\circ)} = 366 \, \text{N} 
\]
Topic: Mechanical Deductive Reasoning Test
Question: If the resultant force of the two tugboats is required to be directed towards the positive 𝑥 axis, and 𝐹_𝐵 is to be a minimum, determine the magnitude of the resultant force 𝐹_𝑅 and 𝐹_𝐵 and the angle 𝜃._x000B_
A. 𝜃=70^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN
B. 𝜃=80^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN
C. 𝜃=90^𝑜;𝐹_𝑅=1.73 kN; 𝐹_𝐵=1 kN
D. 𝜃=100^𝑜;𝐹_𝑅=1 kN; 𝐹_𝐵= 1.73 kN

Answer: C
Explanation: For \( F_R \) to be minimum, it has to be directed perpendicular to \( F_R \). Thus, 

\[
\theta = 90^\circ
\]

The forces \( F_R \) and \( F_B \) are calculated as follows:

\[
F_R = F_A \cdot \cos(30^\circ) = 1.73 \, \text{kN}
\]

\[
F_B = F_A \cdot \sin(30^\circ) = 1 \, \text{kN}
\]
Topic: Mechanical Deductive Reasoning Test
Question: A non-pressurized cylindrical metal tank filled with air is submerged underwater. As the air escapes, the tank gradually moves deeper underwater. Which statement provides the best reason for this motion?

A. The bubbles provide a downward thrust on the tank
B. The metal increases in density so it gets heavier
C. The bubbles lower the density of the water which lowers its buoyancy
D. Water replaces the air in the tank which makes it heavier
E. Impossible to tell

Answer: D
Explanation: As air escapes the available space is quickly replaced with water, so the tank's density becomes the same as that of the water and with the added weight and density of the tank itself continues to sink.
Topic: Mechanical Deductive Reasoning Test
Question: There are two identical cars along a bridge. If the bridge has the same thickness along it, which part(s) of the bridge would undergo the most deflection?
A. Under the towers
B. Below the cars
C. Middle of the bridge
D. All of the above will have equal deflection
E. Impossible to tell

Answer: C
Explanation: The middle of the bridge would undergo the most deflection because it is furthest away from the towers and pillars supporting the bridge. Imagine a piece of string held at either end over a gap between two tables. The point right in the middle would droop the most.
Topic: Mechanical Deductive Reasoning Test
Question: Convex mirrors are used for rear-view mirrors of vehicles. What is the advantage of using a convex mirror instead of a flat mirror?
A. It provides a clearer reflection
B. It has a more accurate reflection
C. The wider angle of view reduces blind spots
D. It is easier to clean a convex mirror
E. A convex mirror provides no advantage

Answer: C
Explanation: A convex mirror has a wider field of view because of its shape. A wider field of view can eliminate blind spots or reduce the size of the area that's not easily visible.
Topic: Mechanical Deductive Reasoning Test
Question: It is a cold winter outside and a well-insulated house has its heater turned on. The front door is opened and cold air rushes in. If the wind speed outside is very low, how would the cold air enter the house?
A. Scenario A, the cold air will flow towards the floor
B. Scenario B, the cold air will flow towards the ceiling
C. A combination of A and B
D. The cold air will not enter the house
E. Impossible to tell

Answer: A
Explanation: Cold air sinks, whereas hot air rises. The house and the air inside it are warmer than the outside air temperature, so if these two systems (house and outside) were to be suddenly connected (door opening) the cold air would sink and the hot air would sit above the cold air until the heat transferred between the two.
Topic: Mechanical Deductive Reasoning Test
Question: A bucket of water has a leak on its lower side. As the water level goes down, what happens to the speed of the water coming out of the hole?
A. It increases
B. It stays the same
C. It decreases
D. It reverses
E. Impossible to tell

Answer: C
Explanation: The speed of the water exiting the bucket by the hole is proportional to the pressure exerted upon it. When the bucket is full there is a greater volume of water trying to exit the bucket via the hole. A greater volume of water is a greater mass of water and therefore exerts a greater pressure, the greater pressure translates to faster speed. As more water leaves the bucket via the hole the volume decreased, therefore so does the mass of the water and the pressure then drops.
Topic: Mechanical Deductive Reasoning Test
Question: Three identical candles were lit and covered by individual jars at the same time. Which candle would have its flame extinguish first?
A. A, candle in a small sealed jar
B. B, candle in a big sealed jar
C. C, candle in a small jar with holes
D. They will all extinguish at the same time
E. Impossible to tell

Answer: A
Explanation: A flame needs fuel and oxygen to continue burning. The wax provides the fuel in all of three instances. There is air exchange in jar C, so more oxygen can be used by the candle to continue burning. Jars A and B are closed systems. No oxygen can get in. Once the oxygen is used up the flame will suffocate itself. The air available in the small jar, A, is less than that in the large jar, B, therefore A shall be extinguished first.
Topic: Mechanical Deductive Reasoning Test
Question: Fire doors have a spring which automatically pushes and forces shut the door when it's open. If the springs were made thicker, what effect would this have on how the door closes?
A. The door will close slower 
B. The door will not fully close 
C. The door will make a screeching noise as it closes 
D. The door will close faster 
E. It will not make a difference 

Answer: D
Explanation: The spring forces the door shut. A thicker spring is stronger which will shut the door more forcefully than before.
Topic: Mechanical Deductive Reasoning Test
Question: A bolt cutter has long handles with handle grips that are located as far away as possible from the neck. Which statement provides the best reason for this design?

A. Longer handles make the cutting blade move faster
B. It provides mechanical advantage which allows cutting through thick bolts.
C. The appearance of the tool is significantly more aesthetic with longer handles
D. It makes the bolt cutter more durable when dropped accidentally
E. Longer handles are more ergonomic and allows easier storage

Answer: B
Explanation: The further the distance that the force is applied to the pivot point, the less force that's required to cut through the bolts, or the stronger the force that can be applied to the bolts is. This is the advantage in having long handles on many tools.
Topic: Mechanical Deductive Reasoning Test
Question: A car is behind a moving fire engine on a motorway. The fire engine is traveling at a speed of 60 mph. If the distance between the two moving vehicles is not changing, what is the car's speed?

A. 80 mph
B. 70 mph
C. 60 mph
D. 50 mph
E. Impossible to tell

Answer: C
Explanation: If the distance between the two vehicles remains the same, they must be traveling at the same speed. The car is therefore also traveling at 60mph. Note: This is not the same as how much energy is required to get the vehicles moving at the same speed. This depends on a lot of factors, mostly; air resistance and mass of each vehicle, which is not what's being asked in this question.
Topic: Mechanical Deductive Reasoning Test
Question: Firefighters use a halligan to forcibly enter locked doors during fire rescue operations. Which halligan would require the least effort to forcibly open the door?
A. Figure A
B. Figure B
C. Figure C
D. Figure D
Answer: D
Explanation: Halligan D would require the least effort to forcibly open the door because it has the longest distance from the point where the force is applied to where it is being leveraged.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\equiv$, B: $\Sigma$, C: $\neq$, D: $\pi$
Answer: D
Explanation: Row 6 contains $\neq$, $\sqrt$, $\Sigma$, missing $\pi$. Column 2 contains $\equiv$, $\neq$, $\sqrt$, $\Sigma$, $\approx$, missing $\pi$. Thus, the answer is $\pi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 13, C: 9, D: 12
Answer: D
Explanation: Row 3 contains 14, 20, 13, 1, 11, missing 12. Column 6 contains 9, 14, 20, 13, missing 12. Thus, the answer is 12.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\phi$, C: $\lambda$, D: $\theta$
Answer: D
Explanation: Row 2 contains $\lambda$, $\iota$, missing $\theta$. Column 3 contains $\lambda$, $\iota$, $\phi$, missing $\theta$. Thus, the answer is $\theta$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\tau$, B: $\upsilon$, C: $\mu$, D: $\kappa$
Answer: C
Explanation: Row 5 contains $\upsilon$, $\chi$, $\kappa$, $\tau$, missing $\mu$. Column 6 contains $\omicron$, $\upsilon$, $\rho$, $\chi$, $\tau$, $\omega$, missing $\mu$. Thus, the answer is $\mu$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 8, C: 6, D: 16
Answer: C
Explanation: Row 1 contains 14, 4, 10, 8, 5, missing 6. Column 2 contains 4, 17, 10, 8, 16, 3, 5, 14, missing 6. Thus, the answer is 6.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\blacktriangledown$, C: $\bigstar$, D: $\bullet$
Answer: D
Explanation: Row 1 contains $\blacktriangledown$, $\triangleright$, o, $\blacksquare$, $\bigstar$, missing $\bullet$. Column 2 contains $\blacklozenge$, $\triangleright$, $\blacktriangle$, $\lozenge$, $\blacktriangledown$, missing $\bullet$. Thus, the answer is $\bullet$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 18, B: 19, C: 17, D: 8
Answer: C
Explanation: Row 5 contains 19, 8, 6, missing 17. Column 6 contains 1, 18, 3, 19, missing 17. Thus, the answer is 17.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangle$, B: $\blacklozenge$, C: o, D: $\bigstar$
Answer: A
Explanation: Row 2 contains o, $\blacklozenge$, $\blacktriangledown$, $\bigstar$, missing $\blacktriangle$. Column 1 contains $\bigstar$, o, $\blacktriangledown$, $\bullet$, missing $\blacktriangle$. Thus, the answer is $\blacktriangle$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacksquare$, B: $\bigstar$, C: $\bullet$, D: $\triangleright$
Answer: C
Explanation: Row 4 contains $\blacksquare$, $\triangleright$, missing $\bullet$. Column 2 contains $\bigstar$, $\triangleright$, $\blacksquare$, missing $\bullet$. Thus, the answer is $\bullet$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 2, C: 8, D: 11
Answer: A
Explanation: Row 5 contains 8, 11, 2, missing 14. Column 4 contains 2, 8, 3, missing 14. Thus, the answer is 14.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pm$, B: $\infty$, C: $\int$, D: $\div$
Answer: A
Explanation: Row 3 contains $\int$, $\div$, missing $\pm$. Column 3 contains $\int$, $\div$, $\infty$, missing $\pm$. Thus, the answer is $\pm$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 1, B: 15, C: 19, D: 8
Answer: C
Explanation: Row 1 contains 8, 1, 12, 4, missing 19. Column 5 contains 6, 4, 15, 1, missing 19. Thus, the answer is 19.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: e, B: r, C: a, D: c
Answer: B
Explanation: Row 4 contains e, c, a, missing r. Column 4 contains c, a, missing r. Thus, the answer is r.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\upsilon$, B: $\lambda$, C: $\alpha$, D: $\eta$
Answer: C
Explanation: Row 2 contains $\beta$, $\textvarsigma$, $\lambda$, $\phi$, $\eta$, $\upsilon$, $\sigma$, missing $\alpha$. Column 5 contains $\phi$, $\omicron$, $\upsilon$, $\sigma$, $\textvarsigma$, $\lambda$, missing $\alpha$. Thus, the answer is $\alpha$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\bullet$, C: $\blacklozenge$, D: $\blacktriangledown$
Answer: B
Explanation: Row 5 contains $\blacksquare$, $\blacklozenge$, o, $\blacktriangledown$, missing $\bullet$. Column 2 contains $\lozenge$, $\blacktriangledown$, $\triangleright$, $\triangleleft$, $\bigstar$, $\blacklozenge$, missing $\bullet$. Thus, the answer is $\bullet$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\pm$, D: $\int$
Answer: C
Explanation: Row 8 contains $\infty$, $\approx$, $\pi$, $\sqrt$, $\int$, $\times$, missing $\pm$. Column 7 contains $\infty$, $\approx$, $\equiv$, $\int$, missing $\pm$. Thus, the answer is $\pm$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\pi$, B: $\div$, C: $\int$, D: $\equiv$
Answer: C
Explanation: Row 1 contains $\equiv$, $\div$, missing $\int$. Column 4 contains $\pi$, $\div$, missing $\int$. Thus, the answer is $\int$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\triangleright$, B: o, C: $\blacktriangledown$, D: $\lozenge$
Answer: C
Explanation: Row 9 contains $\lozenge$, $\bullet$, o, $\triangleright$, $\blacksquare$, $\blacklozenge$, $\blacktriangle$, missing $\blacktriangledown$. Column 4 contains $\triangleleft$, $\blacklozenge$, $\lozenge$, o, missing $\blacktriangledown$. Thus, the answer is $\blacktriangledown$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\sqrt$, B: $\equiv$, C: $\div$, D: $\Sigma$
Answer: A
Explanation: Row 5 contains $\equiv$, $\approx$, $\pi$, $\neq$, $\Delta$, $\div$, $\Sigma$, $\int$, missing $\sqrt$. Column 5 contains $\approx$, $\pi$, $\neq$, $\Delta$, $\int$, missing $\sqrt$. Thus, the answer is $\sqrt$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: c, B: f, C: a, D: l
Answer: B
Explanation: Row 5 contains c, a, l, s, missing f. Column 1 contains a, h, s, c, missing f. Thus, the answer is f.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\div$, C: $\infty$, D: $\Sigma$
Answer: B
Explanation: Row 8 contains $\Sigma$, $\approx$, $\equiv$, $\int$, $\sqrt$, missing $\div$. Column 2 contains $\approx$, $\int$, $\infty$, $\pi$, $\Sigma$, missing $\div$. Thus, the answer is $\div$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\phi$, D: $\xi$
Answer: D
Explanation: Row 4 contains $\tau$, $\iota$, missing $\xi$. Column 1 contains $\phi$, missing $\xi$. Thus, the answer is $\xi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: o, B: $\triangleright$, C: $\lozenge$, D: $\bullet$
Answer: B
Explanation: Row 1 contains $\lozenge$, o, missing $\triangleright$. Column 2 contains o, $\bullet$, missing $\triangleright$. Thus, the answer is $\triangleright$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\times$, B: $\div$, C: $\sqrt$, D: $\neq$
Answer: A
Explanation: Row 5 contains $\Sigma$, $\Delta$, $\sqrt$, $\div$, missing $\times$. Column 3 contains $\neq$, $\Sigma$, $\Delta$, $\sqrt$, missing $\times$. Thus, the answer is $\times$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacktriangledown$, B: $\blacktriangle$, C: o, D: $\lozenge$
Answer: D
Explanation: Row 5 contains o, $\blacktriangle$, $\blacksquare$, $\bigstar$, missing $\lozenge$. Column 8 contains $\blacklozenge$, $\blacksquare$, $\bigstar$, $\blacktriangledown$, $\bullet$, missing $\lozenge$. Thus, the answer is $\lozenge$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: q, B: k, C: y, D: p
Answer: B
Explanation: Row 4 contains e, p, y, q, missing k. Column 1 contains p, e, missing k. Thus, the answer is k.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftrightarrow$, B: $\swarrow$, C: $\downarrow$, D: $\searrow$
Answer: D
Explanation: Row 4 contains $\swarrow$, missing $\searrow$. Column 2 contains $\leftrightarrow$, $\downarrow$, $\swarrow$, missing $\searrow$. Thus, the answer is $\searrow$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 11, B: 10, C: 8, D: 2
Answer: C
Explanation: Row 3 contains 10, 11, 14, missing 8. Column 3 contains 2, 10, 14, missing 8. Thus, the answer is 8.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 20, C: 11, D: 1
Answer: B
Explanation: Row 4 contains 15, 17, 11, 1, 14, 16, missing 20. Column 1 contains 9, 14, 15, 17, 11, 1, missing 20. Thus, the answer is 20.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 15, B: 7, C: 14, D: 4
Answer: B
Explanation: Row 2 contains 15, 14, 4, missing 7. Column 3 contains 14, 4, 15, missing 7. Thus, the answer is 7.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\Delta$, B: $\neq$, C: $\approx$, D: $\div$
Answer: C
Explanation: Row 5 contains $\Delta$, $\div$, $\sqrt$, missing $\approx$. Column 5 contains $\neq$, $\div$, $\sqrt$, missing $\approx$. Thus, the answer is $\approx$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\rho$, B: $\pi$, C: $\kappa$, D: $\sigma$
Answer: B
Explanation: Row 4 contains $\kappa$, $\rho$, $\sigma$, missing $\pi$. Column 1 contains $\kappa$, $\rho$, missing $\pi$. Thus, the answer is $\pi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 17, B: 9, C: 14, D: 19
Answer: D
Explanation: Row 6 contains 18, 14, 17, 6, 9, missing 19. Column 3 contains 17, 6, missing 19. Thus, the answer is 19.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: t, B: e, C: d, D: f
Answer: B
Explanation: Row 2 contains f, p, missing e. Column 5 contains p, t, d, missing e. Thus, the answer is e.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\int$, B: $\Sigma$, C: $\neq$, D: $\approx$
Answer: D
Explanation: Row 1 contains $\times$, $\neq$, $\Delta$, $\equiv$, $\int$, missing $\approx$. Column 6 contains $\equiv$, $\int$, $\div$, $\pm$, $\neq$, $\Sigma$, missing $\approx$. Thus, the answer is $\approx$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\alpha$, B: $\textvarsigma$, C: $\eta$, D: $\phi$
Answer: D
Explanation: Row 2 contains $\textvarsigma$, $\iota$, $\omicron$, $\psi$, $\tau$, missing $\phi$. Column 1 contains $\eta$, $\textvarsigma$, $\omega$, $\omicron$, $\psi$, $\tau$, $\alpha$, missing $\phi$. Thus, the answer is $\phi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{laughingface}$, B: $\text{joy}$, C: $\text{blush}$, D: $\text{smileface}$
Answer: B
Explanation: Row 6 contains $\text{smileyface}$, $\text{grinningface}$, $\text{smileface}$, $\text{laughingface}$, missing $\text{joy}$. Column 1 contains $\text{blush}$, missing $\text{joy}$. Thus, the answer is $\text{joy}$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\leftarrow$, B: $\rightarrow$, C: $\updownarrow$, D: $\nearrow$
Answer: C
Explanation: Row 3 contains $\uparrow$, $\rightarrow$, $\downarrow$, $\nearrow$, $\nwarrow$, $\swarrow$, $\leftarrow$, $\leftrightarrow$, missing $\updownarrow$. Column 7 contains $\nwarrow$, $\leftarrow$, $\leftrightarrow$, $\rightarrow$, $\downarrow$, $\nearrow$, missing $\updownarrow$. Thus, the answer is $\updownarrow$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: w, B: t, C: s, D: p
Answer: B
Explanation: Row 6 contains v, p, w, s, missing t. Column 6 contains v, u, b, s, missing t. Thus, the answer is t.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\chi$, B: $\pi$, C: $\iota$, D: $\lambda$
Answer: B
Explanation: Row 1 contains $\psi$, $\lambda$, $\iota$, missing $\pi$. Column 1 contains $\chi$, $\mu$, $\psi$, $\lambda$, $\iota$, missing $\pi$. Thus, the answer is $\pi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\blacklozenge$, B: $\triangleleft$, C: $\blacksquare$, D: o
Answer: C
Explanation: Row 1 contains o, $\bullet$, $\blacklozenge$, $\triangleleft$, missing $\blacksquare$. Column 1 contains o, missing $\blacksquare$. Thus, the answer is $\blacksquare$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: n, B: c, C: g, D: r
Answer: D
Explanation: Row 3 contains a, n, missing r. Column 5 contains c, n, g, y, a, missing r. Thus, the answer is r.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: d, B: u, C: h, D: t
Answer: B
Explanation: Row 3 contains h, j, d, t, missing u. Column 5 contains d, t, h, missing u. Thus, the answer is u.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\iota$, B: $\tau$, C: $\upsilon$, D: $\xi$
Answer: D
Explanation: Row 8 contains $\tau$, $\upsilon$, $\iota$, $\chi$, $\eta$, $\epsilon$, $\nu$, missing $\xi$. Column 4 contains $\eta$, $\epsilon$, $\mu$, $\tau$, $\iota$, $\chi$, missing $\xi$. Thus, the answer is $\xi$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 14, B: 3, C: 1, D: 12
Answer: C
Explanation: Row 7 contains 7, 14, 12, 3, 2, 20, 13, 11, missing 1. Column 6 contains 14, 3, 13, missing 1. Thus, the answer is 1.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\lozenge$, B: $\bullet$, C: $\blacksquare$, D: $\triangleleft$
Answer: A
Explanation: Row 5 contains $\bullet$, $\blacksquare$, missing $\lozenge$. Column 5 contains $\triangleleft$, $\bullet$, $\blacktriangle$, $\blacksquare$, missing $\lozenge$. Thus, the answer is $\lozenge$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: 13, B: 4, C: 18, D: 8
Answer: B
Explanation: Row 3 contains 3, 8, 9, 18, 13, missing 4. Column 6 contains 13, 8, 9, missing 4. Thus, the answer is 4.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{sweatsmile}$, B: $\text{joy}$, C: $\text{smileface}$, D: $\text{laughingface}$
Answer: D
Explanation: Row 3 contains $\text{sweatsmile}$, $\text{smileface}$, $\text{joy}$, missing $\text{laughingface}$. Column 2 contains $\text{joy}$, missing $\text{laughingface}$. Thus, the answer is $\text{laughingface}$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\text{joy}$, B: $\text{grinningface}$, C: $\text{blush}$, D: $\text{sweatsmile}$
Answer: D
Explanation: Row 6 contains $\text{joy}$, $\text{grinningface}$, missing $\text{sweatsmile}$. Column 4 contains $\text{blush}$, $\text{grinningface}$, $\text{smileyface}$, $\text{joy}$, $\text{beamingface}$, $\text{innocent}$, missing $\text{sweatsmile}$. Thus, the answer is $\text{sweatsmile}$.
Topic: Deductive Reasoning Test with Figures
Question: Select the correct symbol (A, B, C, or D) to replace the question mark. Each row and column must contain unique symbols. Options: A: $\theta$, B: $\zeta$, C: $\sigma$, D: $\gamma$
Answer: B
Explanation: Row 2 contains $\theta$, $\sigma$, $\mu$, $\gamma$, missing $\zeta$. Column 5 contains $\gamma$, $\sigma$, $\mu$, missing $\zeta$. Thus, the answer is $\zeta$.
Topic: Figure Series Test
Question: Choose the most appropriate image from options A to F to fill in the question mark so that the figures follow a certain pattern.
Answer: B
Explanation: Figures in the same horizontal row share the same shape. The black part's position is consistent in vertical columns. Therefore, the missing figure is a circle with the black part in the bottom right.
Topic: Figure Series Test
Question: Choose the most appropriate image from options A to F to fill in the question mark so that the figures follow a certain pattern.
Answer: E
Explanation: Each figure in a row combines two of these six: circle, square, cross, black dot, star, or diamond. No repeats in a row! That means the missing figure has a black dot and a star.