Select the option that is related to the sixth number in the same way as the first number is related to the second number and the third number is related to the fourth number. 1444 ∶ 38 ∶∶ 1225 ∶ 35 ∶∶ ? ∶ 47
2209
Understanding the Number Analogy Pattern
The question presents a number analogy in the format A : B :: C : D :: E : F. This means that the relationship between A and B is the same as the relationship between C and D, and this same relationship should also exist between E and F.
We are given the following pairs:
- 1444 ∶ 38
- 1225 ∶ 35
- ? ∶ 47
Our goal is to identify the relationship between the numbers in the first two pairs and then apply it to the third pair to find the missing number.
Analyzing the Relationship in the Pairs
Let's examine the first pair: 1444 and 38.
We can try to find a mathematical relationship between these two numbers. If we consider squaring the second number, we get:
\(\text{38}^2 = 38 \times 38\)
Let's calculate this:
\(\text{38}^2 = (40 - 2)^2 = 40^2 - 2 \times 40 \times 2 + 2^2 = 1600 - 160 + 4 = 1440 + 4 = 1444\)
So, the first number (1444) is the square of the second number (38). Alternatively, the second number (38) is the square root of the first number (1444), i.e., \(\sqrt{1444} = 38\).
Now, let's check if this relationship holds true for the second pair: 1225 and 35.
Let's square the second number (35):
\(\text{35}^2 = 35 \times 35\)
We can calculate this:
\(\text{35}^2 = (30 + 5)^2 = 30^2 + 2 \times 30 \times 5 + 5^2 = 900 + 300 + 25 = 1200 + 25 = 1225\)
Indeed, the third number (1225) is the square of the fourth number (35). This confirms that the relationship is that the first number in each pair is the square of the second number, or the second number is the square root of the first.
Step-by-Step Solution for the Analogy
Based on the pattern found, the missing number (?) should be the square of the number 47.
We need to calculate \(47^2\).
- Identify the pattern: The first number is the square of the second number in each pair.
- Apply the pattern to the third pair: The missing number (?) must be the square of 47.
- Calculate the square of 47:
\(\text{47}^2 = 47 \times 47\)
Calculation:
\(\text{47}^2 = (50 - 3)^2 = 50^2 - 2 \times 50 \times 3 + 3^2 = 2500 - 300 + 9 = 2200 + 9 = 2209\)
So, the missing number is 2209.
Checking the Options and Final Answer
Now let's look at the given options to see which one matches our calculated missing number:
- 2162
- 1369
- 1024
- 2209
Our calculated missing number is 2209, which matches option 4.
Final Answer Determination
The missing number in the analogy is 2209, following the established pattern where the first number is the square of the second number in each pair.
Revision Table: Key Analogy Concepts
| Concept | Description | How it applies here |
|---|---|---|
| Analogy | A comparison between two things for clarification or explanation. In number analogies, it's about finding a mathematical relationship. | The relationship between 1444 & 38 is analogous to the relationship between 1225 & 35. |
| Pattern Recognition | The ability to identify repeating sequences or rules in data. | We identified the pattern: First number = (Second number)2. |
| Squares and Square Roots | A number multiplied by itself is its square (n2). The number that, when multiplied by itself, equals a given number is its square root (\(\sqrt{n}\)). | The core pattern involves square numbers and their square roots. |
Additional Information: Perfect Squares
A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a perfect square because \(9 = 3 \times 3 = 3^2\).
In this analogy, 1444, 1225, and 2209 are perfect squares. Knowing common perfect squares or being able to quickly calculate squares helps in solving such analogy problems.
- \(35^2 = 1225\)
- \(38^2 = 1444\)
- \(47^2 = 2209\)
Recognizing these numbers as squares can quickly reveal the underlying pattern in the analogy.
Similar Questions
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
(52, 34, 43)
(61, 33, 47)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(221, 144, 73)
(222, 153, 75)
Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(111, 117, 123)
(169, 200, 231)
Select the set in which the number are related in the same way as the numbers of the given sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
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(20, 102, 122)
Select the set in which the number are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(9, 7, 189)
(4, 13, 156)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13- Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(4, 60, 5)
(5, 90, 6)
Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(20, 16, 8)
(10, 13, 12)
Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(12, 9, 4)
(18, 9, 6)
Select the set in which the number are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(8, 8, 128)
(11, 7, 162)
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
16 : 50 :: 49 : ? :: 144 : 338
Important Questions from Letter and Number Based
Select the related number from the given alternatives that will complete the series:
Y 2 : 4 : : V 2 : ?Select the related number from the given alternatives:
F : 216 : : L : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
Three of the following four number-pairs ale alike in a certain way and one is different. Find the odd one out.
In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?
