Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 25 : 125 :: 32 : 160 :: 73 : ?
365
Solving Number Analogy Problems
This question asks us to find a relationship between pairs of numbers and apply that same relationship to a third number to find a missing value. This type of problem is known as a number analogy.
The given analogy is:
\(25 : 125 :: 32 : 160 :: 73 : ?\)
We need to determine how 125 is related to 25, and how 160 is related to 32. Once we find this rule, we apply it to 73 to find the missing number.
Analyzing the Relationship between the First Pair
Let's look at the first pair of numbers: 25 and 125.
We can try different basic arithmetic operations or relationships:
- Addition: \(25 + X = 125 \implies X = 125 - 25 = 100\). Adding 100.
- Subtraction: \(25 - X = 125\) (not applicable as 125 is larger).
- Multiplication: \(25 \times X = 125\). To find X, we divide 125 by 25. \(125 \div 25 = 5\). So, \(25 \times 5 = 125\). Multiplying by 5.
- Division: \(25 \div X = 125\) (not applicable as 125 is larger).
The relationship seems to be multiplication by 5 or addition of 100. Let's check the second pair to confirm the rule.
Verifying the Relationship with the Second Pair
Now, let's examine the second pair: 32 and 160.
Let's test the potential rules found from the first pair:
- Applying Addition of 100: \(32 + 100 = 132\). This is not 160. So, adding 100 is not the rule.
- Applying Multiplication by 5: \(32 \times 5\). Let's calculate this:
Yes, \(32 \times 5 = 160\). This matches the second pair. Therefore, the relationship between the numbers in each pair is that the second number is obtained by multiplying the first number by 5.
Applying the Rule to the Third Pair
The established rule is to multiply the first number by 5 to get the second number in the pair.
Now, we apply this rule to the third pair: 73 and ?
The missing number is \(73 \times 5\).
Calculating the Missing Number
Let's perform the multiplication:
\[ 73 \times 5 \]We can calculate this as:
\[ 73 \times 5 = (70 + 3) \times 5 = (70 \times 5) + (3 \times 5) = 350 + 15 = 365 \]So, the missing number is 365.
Conclusion
The relationship observed in the given number analogy is that the second number is five times the first number. Applying this rule to the third pair (73 : ?) gives us \(73 \times 5 = 365\). Thus, the missing number is 365.
Revision Table: Number Relationships
| First Number | Second Number | Relationship |
|---|---|---|
| 25 | 125 | \(25 \times 5 = 125\) |
| 32 | 160 | \(32 \times 5 = 160\) |
| 73 | ? | \(73 \times 5 = 365\) |
Additional Information on Number Analogies
Number analogies are common in reasoning tests and quantitative aptitude sections. They require you to identify patterns or relationships between numbers. These relationships can be based on various mathematical operations or properties.
Common types of relationships found in number analogies include:
- Basic arithmetic operations (addition, subtraction, multiplication, division).
- Squares, cubes, or other powers.
- Square roots or cube roots.
- Operations involving the digits of the number (sum of digits, product of digits, reversing digits).
- Combinations of operations.
- Prime numbers, composite numbers, or other number properties.
- Patterns related to sequences or series.
To solve number analogies, it's helpful to systematically test common relationships between the given pairs to find a consistent rule.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
