Question 1

Given :

1) The number is in consecutive order from left to right
2) The number is in ascending order.

The method used to solve this problem is based on counting principles and combinatorics. Combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects,

To start, let us generate as many numbers as possible according to the given properties in this question. 1 observation we can make is that the final digit cannot be less than 4, as that would result in a number below 0. Similarly, the digit cannot exceed 9, as this would lead to a two-digit number. Consequently, the permissible options for the final digit are 4, 5, 6, 7, 8, and 9. This implies that we can create a total of 6 numbers.

Question 2

To determine the percentage of the figure that is shaded in the case of concentric circles with lines passing through their common center, you would likely need to use geometric principles. Geometric principles involve the study and application of fundamental concepts and properties related to shapes, sizes, positions, and the spatial relationships between objects, providing a framework for understanding and solving problems in geometry.

Consider this question logically: if we divide the circle in half, you’ll notice that the white areas in one half perfectly correspond to the black spaces in the other. Therefore, if we were to overlay the black spaces from one half onto the white spaces in the other, we would observe that 50% or half of the circle is shaded.

Thus, making E our answer!

Question 3

In analyzing this question, it becomes evident that the final puzzle pieces will be the edge pieces labeled 2 and 2. To establish a connection with the piece marked as 2, we require a puzzle piece with a left-sided inward projection, denoted by the symbol ‘-‘. Consequently, this particular puzzle piece should align with the 2 pieces.

Subsequently, we need a puzzle piece with an outward projection. Considering both options, 0 and 1, connecting the 0 proves incompatible with linking to the 1. Therefore, we must connect the 1 to the puzzle piece marked with ‘-‘. Following this logic, the piece labeled 2 should connect to 0.

In summary, the arrangement follows the sequence 2 – 102, resulting in the equation 2 – 102, which simplifies to -100.

Thus Making A the answer!!

Question 4

This problem involves knowing about Volume, Dimensions and symmetry. Volume is the amount of space occupied by an object, and it is measured in cubic unit

s. Dimensions refer to the measurements that define the size and shape of an object, usually represented by its length, width, and height in three-dimensional space.Symmetry is a property in which an object or a shape looks the same when certain transformations, such as reflection, rotation, or translation, are applied to it. In simpler terms, if you could fold, turn, or slide an object, and it still appears unchanged, it is considered symmetrical.

Shapes B, C, and E exhibit symmetry, meaning they have a central axis along which the forms are mirror images of each other. In such cases, when water is poured into these vases, the level will rise evenly up to the line of symmetry. However, Shapes A and D lack this symmetry.

For Shape A, as there is no line of symmetry, the water distribution will be uneven. The midpoint of the vase will have a higher water level because the bottom portion does not hold as much water as the upper part.

On the other hand, Shape D’s lack of symmetry implies that the water level will not rise uniformly. The midpoint will be lower since the wider bottom of the vase has a greater capacity to hold water compared to the narrower top.

In conclusion, due to the absence of symmetry, Shapes A and D will exhibit non-uniform water levels. Among them, Shape A is expected to have the highest water level, as its midpoint will likely be elevated due to the reduced capacity at the bottom.

Question 5

Let us employ a guess-and-check method for this problem.

Starting with option A, the transition from 6 to 0 requires 6 turns, while the shift from 3 to 8 demands 5 turns, making option A unsuitable.

Moving on to option B, the change from 6 to 1 involves 5 turns, and similarly, the transition from 3 to 8 also requires 5 turns. This consistency suggests that option B is a viable answer, but it’s prudent to assess the other choices for confirmation.

Considering option C, the journey from 6 to 1 takes 5 turns, yet moving from 6 to 9 demands 7 turns, making option C improbable.

Now, evaluating option D, the shift from 6 to 4 necessitates 2 turns, but transitioning from 6 to 8 demands 8 turns, rendering option D implausible.

Lastly, examining option E, the transition from 6 to 8 requires 8 turns, whereas moving from 3 to 8 involves 5 turns, indicating that option E is not the answer.

Consequently, through this process of elimination, it is determined that option B is the most fitting solution for this question.

Question 6

The approach to solving this problem involves a combination of algebraic manipulation and logical deduction. It utilizes the given relationships between the letters (A, B, C, D) to determine the values they represent, specifically the sums of B and D and A and C.

In addressing this question, we observe that the sum of B and D is 7, while the sum of A and C is 13. Keeping this information in mind, we proceed to solve ADCB + CBAD. Since B and D together equal 7, the last digit is determined to be 7. Now, focusing on A and D, which sum to 13, and considering the carryover to the tens place, it should be 3. Eliminating choices with a last digit of 4, we are left with D and B. Considering the carryover of 1, the hundred place becomes 8. Therefore, B emerges as the answer.

Question 7

To solve this problem we can analyze the characteristics of the cubes presented and deduce a logical pattern.

We can observe that the gray section displays a zigzag pattern, with only cubes D and E exhibiting this pattern. Furthermore, atop the pattern, there is a single cube, indicating that E is likely the correct answer.

Question 8

If Neil consumed 12 squares from two rows, it implies that from one row, there are 6 squares. Additionally, it’s mentioned that another size comprises 9 squares. Combining the 9 squares with the remaining two strips results in a deduction of 12 squares. Thus, subtracting 21 from 66 yields 45, indicating that D is the correct answer.

Question 9

Given:

A jar one-fifth filled with water weighs 560 g.
The same jar four-fifth filled with water weighs 740 g.

We denote the weight of the empty jug as X and the weight of the water that can be filled in the jug as Y.

First, we set up our equations:
– From the first scenario where one-fifth of the jug is filled, we have the equation (X+Y) /5 = 560
– From the second scenario where four-fifths of the jug is filled, we have the equation (X+ 4Y) /5 = 740

To eliminate the fraction, we multiply the first equation by 4, yielding (4X + 4Y)/5 = 2240 .

Now, we subtract the second equation from the modified equation 1 to solve for X, In which we get 3X=1500.

Solving for X, we get X = 500.

Thus, the weight of the empty jug is 500 grams, making option E the correct answer.

Question 10

We can infer that the triangle occupies ¼ of the square’s area. Consequently, the square’s area is 16, and the triangle’s area is 4. If we sum up the areas of the square and the triangle, considering there are two of each, the total becomes 48. Therefore, B is the correct answer.

Question 11

To solve this problem we can use our basic arithmetic operations, namely addition, subtraction, multiplication, and division

Given:
– There are 25 planks of wood.
– Each plank measures 30 cm in length.
– The total length of all the planks is \(25 \times 30 = 750\) cm.

We’re also given that 6.9 meters is equal to 690 cm.

To find the length of the overlap between any pair of adjacent planks, we first calculate the total length of the overlap. We can do this by subtracting the length of 6.9 meters (690 cm) from the total length of the planks (750 cm):

750 cm – 690 cm=60cm

Now, we need to distribute this 60 cm of overlap among the 24 seams between adjacent planks. Since there are 25 planks but only 24 seams between them, we divide the total overlap length by 24:

60/24 = 2.5

Therefore, the length in cm of the overlap between any pair of adjacent planks is indeed 2.5 cm. So, the answer is B.

Question 12

To solve this problem we can use basic principles of geometry and arithmetic operations

Given that there are 5 identical right-angled triangles, we can calculate the measure of the larger acute angle by dividing the total angle measure of 360 degrees by the number of triangles, which gives us 72 degrees.

Subtracting 72 degrees from the right angle (90 degrees), we find that the smaller acute angle measures 18 degrees.

Now, to find out how many times the smaller acute angle fits into a full circle (360 degrees), we divide 360 by 18, which equals 20.

Therefore, option D is the correct answer.

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