(NOTE – A two/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
7 - 21 - 31 - 62; 9 - 27 - 37 - 74
Identifying the Number Series Pattern
This question requires identifying a consistent set of mathematical operations applied across two given number sequences. The goal is to find the option that uses the same operations.
Analyzing Number Set Patterns
Let's break down the operations in the provided sets:
Set 1: 7 - 21 - 31 - 62
- From 7 to 21: The operation is multiplication. Calculation: $7 \times 3 = 21$.
- From 21 to 31: The operation is addition. Calculation: $21 + 10 = 31$.
- From 31 to 62: The operation is multiplication. Calculation: $31 \times 2 = 62$.
Set 2: 9 - 27 - 37 - 74
- From 9 to 27: The operation is multiplication. Calculation: $9 \times 3 = 27$.
- From 27 to 37: The operation is addition. Calculation: $27 + 10 = 37$.
- From 37 to 74: The operation is multiplication. Calculation: $37 \times 2 = 74$.
Determining the Consistent Operations
Both sets demonstrate a clear pattern comprising three sequential operations:
- Multiply the number by 3.
- Add 10 to the result.
- Multiply the result by 2.
Checking Options Against the Pattern
We will now apply this pattern (x3, +10, x2) to each option:
Option 1: 11-33-43-86
- Step 1: $11 \times 3 = 33$. (Correct)
- Step 2: $33 + 10 = 43$. (Correct)
- Step 3: $43 \times 2 = 86$. (Correct)
This sequence perfectly matches the identified operations.
Checking Other Options
- Option 2 (12-36-46-82): $12 \times 3 = 36$; $36 + 10 = 46$; $46 \times 2 = 92$. The last number (92) does not match 82.
- Option 3 (8-32-42-84): $8 \times 3 = 24$. The second number (24) does not match 32.
- Option 4 (6-18-28-76): $6 \times 3 = 18$; $18 + 10 = 28$; $28 \times 2 = 56$. The last number (56) does not match 76.
Therefore, Option 1 is the only sequence that follows the established mathematical operations.
Important Questions from Analogy (Notes)
- If 15: 225:: 35: x, then what is the value of $\sqrt{x + 100}$ ?
- In the following question, find out the alternative which will replace the question mark.
84:9:: 124: ? :: 292:17 - EGDH is related to FIFI in a certain way based on the English alphabetical order. In the same way, JMHL is related to KOJM. To which of the following is NPRS related, following the same logic?
- VASE is related to ZEOA in a certain way based on the English alphabetical order. In the same way, DIKW is related to HMGS. To which of the following is LQCO related, following the same logic?
- 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 their 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, 46, 2)
(32, 136, 24)
