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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. 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 тАУ 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.) (15, 55) (12, 43)
(10, 40)
(7, 23)
(9, 30)
(8, 42)
(7, 23)
Look for the relationship x * 3 + constant or x * 4 - constant. Here, the pattern is (First Number * 3) + 10 = Second Number.
Look for the relationship x * 3 + constant or x * 4 - constant. Here, the pattern is (First Number * 3) + 10 = Second Number.
Analyze the pattern
Test the given sets: For (15, 55), 15 * 3 = 45; 45 + 10 = 55. For (12, 43), 12 * 3 = 36; 36 + 7 = 43. Since the constant added (10 and 7) changes, check if the constant is related to the first number. 15 - 5 = 10 and 12 - 5 = 7. Thus, the logic is (First Number * 3) + (First Number - 5) = Second Number, or more simply: 4 * First Number - 5 = Second Number.
Verify the formula 4 * X - 5 = Y
Check (15, 55): 4 * 15 = 60, 60 - 5 = 55. Check (12, 43): 4 * 12 = 48, 48 - 5 = 43. Both match.
Apply formula to options
Test 7: 4 * 7 = 28, 28 - 5 = 23. This matches Option B (7, 23).
A: 4 * 10тИТ5 = 35, not 40. C: 4 * 9 - 5 = 31, not 30. D: 4 * 8 - 5 = 27, not 42.
B is correct because the pair (7, 23) follows the established rule of multiplying the first number by 4 and subtracting 5 to get the second number (4 * 7 - 5 = 23).
When number analogies do not fit a single multiplier, check for linear equations of form Y = mX + c, where m and c are small integers.
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