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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.) (105,35,7)(135,45,9)
(150,50,10)
(90,25,5)
(115,30,6)
(120,40,12)
(150,50,10)
In the given triplets (A, B, C), the pattern is A = B multiplied by C, or simply A / B = C. Check the division relationship for all provided sets.
In the given triplets (A, B, C), the pattern is A = B multiplied by C, or simply A / B = C. Check the division relationship for all provided sets.
Analyze the given sets
Given sets are (105, 35, 7) and (135, 45, 9). For (105, 35, 7): 35 multiplied by 3 equals 105, and 105 / 35 equals 3. Wait, check the divisor: 105 / 35 = 3 (not 7). Let's re-examine: 35 / 7 = 5. The relation is (B / C) * something? No, let's try 105 / 7 = 15, 15 * 2.33? No. Let's try 105 / 35 = 3. 35 / 7 = 5. Let's try 105 / 7 = 15. The pattern is (First number / Third number) = Constant. 105 / 7 = 15. 135 / 9 = 15. The constant is 15.
Verify the constant ratio
In (105, 35, 7), 105 / 7 = 15. In (135, 45, 9), 135 / 9 = 15. Also, note the middle number relationship: 105 / 35 = 3, and 35 / 7 = 5. Actually, 3 * 5 = 15. Alternatively: 35 * 3 = 105 and 9 * 5 = 45? No. The simplest rule is: First number = Third number * 15 and Middle number = Third number * (some factor). Let's check options: A) (150, 50, 10). 150 / 10 = 15. This matches the ratio.
B: 90 / 5 = 18 (does not match 15). C: 115 / 6 is not 15. D: 120 / 12 = 10 (does not match 15).
A is correct because the ratio of the first number to the third number is 15 in the given sets (105/7 = 15 and 135/9 = 15), and 150/10 = 15 in option A.
When dealing with sets of three numbers, always test the relationship between the first and third numbers first, as it often reveals a constant multiplier or divisor.
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