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Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 тАУ Operations on 13 such as adding / subtracting /multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 19-57-114-134; 21-63-126-146
18-54-108-118
17-51-102-112
20-60-120-180
16-48-96-116
16-48-96-116
Identify the multiplier triplet (x3, x2, +20). The pattern is (First ├Ч 3 = Second), (Second ├Ч 2 = Third), (Third + 20 = Fourth).
Identify the multiplier triplet (x3, x2, +20). The pattern is (First ├Ч 3 = Second), (Second ├Ч 2 = Third), (Third + 20 = Fourth).
Analyze the given sets
Set 1: 19 тЖТ 57 (19├Ч3=57) тЖТ 114 (57├Ч2=114) тЖТ 134 (114+20=134). Set 2: 21 тЖТ 63 (21├Ч3=63) тЖТ 126 (63├Ч2=126) тЖТ 146 (126+20=146).
Establish the pattern
The mathematical operations are consistently: First to Second (├Ч3), Second to Third (├Ч2), Third to Fourth (+20).
Verify Option D
Apply the rule to 16: 16 ├Ч 3 = 48; 48 ├Ч 2 = 96; 96 + 20 = 116. This perfectly matches the identified sequence pattern.
A: 18-54-108-118 fails because 108+20 should be 128, not 118. B: 17-51-102-112 fails because 102+20 should be 122, not 112. C: 20-60-120-180 fails because 120+20 should be 140, not 180.
D is correct because 16-48-96-116 satisfies the established logic of multiplying by 3, then 2, then adding 20.
When faced with numeric triplets or quadruplets, always check for multiplication factors (├Ч2, ├Ч3) first before looking for additive differences.
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