This question asks us to identify a set of numbers from the options that shares the same numerical relationship as the two given sets: (25, 150, 3) and (18, 180, 5). We need to find the rule connecting the three numbers within these sets.

Understanding the Given Sets and Finding the Relation

Let's look at the numbers in the first set: (25, 150, 3). We need to find how 25, 150, and 3 are related. Let's call the numbers A, B, and C, so A=25, B=150, C=3.

Now consider the second set: (18, 180, 5). Here, A=18, B=180, C=5.

We are looking for a rule that applies to both (25, 150, 3) and (18, 180, 5). The rule involves operations on the whole numbers, not breaking them down into digits.

Let's try common mathematical operations to find a pattern between A, B, and C.

• Could B be a multiple of A or C? \(150/25 = 6\), \(150/3 = 50\). \(180/18 = 10\), \(180/5 = 36\). The quotients are different, but maybe there's a connection between the quotients and the third number.
• Let's look at the quotient when dividing B by A. For the first set, \(150 \div 25 = 6\). For the second set, \(180 \div 18 = 10\).
• How is 6 related to 3 (from the first set)? \(6 = 3 \times 2\).
• How is 10 related to 5 (from the second set)? \(10 = 5 \times 2\).

It seems the relationship might be that \(B \div A = C \times 2\). Let's rewrite this rule to isolate B: \(B = A \times (C \times 2)\) or simply \(B = A \times C \times 2\).

Let's verify this rule with the given sets:

• For (25, 150, 3): \(25 \times 3 \times 2 = 25 \times 6 = 150\). This matches B.
• For (18, 180, 5): \(18 \times 5 \times 2 = 18 \times 10 = 180\). This matches B.

The rule \(B = A \times C \times 2\) holds for both the given sets. Now we will check this rule against the given options to find the set related in the same way.

Testing the Options with the Relation \(B = A \times C \times 2\)

We will apply the rule \(B = A \times C \times 2\) to each option:

Option 1: (13, 39, 3)

Here, A=13, B=39, C=3.

Calculate \(A \times C \times 2\): \(13 \times 3 \times 2 = 13 \times 6 = 78\).

Is \(B = A \times C \times 2\)? Is \(39 = 78\)? No. This set does not follow the rule.

Option 2: (101, 408, 2)

Here, A=101, B=408, C=2.

Calculate \(A \times C \times 2\): \(101 \times 2 \times 2 = 101 \times 4 = 404\).

Is \(B = A \times C \times 2\)? Is \(408 = 404\)? No. This set does not follow the rule.

Option 3: (52, 728, 7)

Here, A=52, B=728, C=7.

Calculate \(A \times C \times 2\): \(52 \times 7 \times 2 = 52 \times 14\).

Let's calculate \(52 \times 14\): \(52 \times 10 = 520\), \(52 \times 4 = 208\). \(520 + 208 = 728\).

So, \(52 \times 14 = 728\).

Is \(B = A \times C \times 2\)? Is \(728 = 728\)? Yes. This set follows the rule.

Option 4: (61, 601, 5)

Here, A=61, B=601, C=5.

Calculate \(A \times C \times 2\): \(61 \times 5 \times 2 = 61 \times 10 = 610\).

Is \(B = A \times C \times 2\)? Is \(601 = 610\)? No. This set does not follow the rule.

Only option 3 satisfies the relationship \(B = A \times C \times 2\) found in the given sets.

Summary of Option Testing

Based on the analysis, the set (52, 728, 7) is related in the same way as the given sets (25, 150, 3) and (18, 180, 5).

Revision Table: Number Relation Analysis

Additional Information: Numerical Reasoning Tips

When tackling number relation or numerical reasoning questions, consider these strategies:

• Look for relationships between the first and second numbers, first and third, second and third, or a combination of operations involving all three.
• Common relationships include addition, subtraction, multiplication, division, squares, cubes, square roots, cube roots, or combinations of these.
• Consider the position of the numbers (first, middle, last) and how they relate.
• If simple operations don't work, look for patterns involving multiples or factors.
• Always test the potential rule with all the given examples before applying it to the options.
• Pay attention to any specific instructions, such as the one in this question about not breaking down numbers into digits.