(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)
(40, 10, 150)
(65, 35, 150)
Number Set Relation: Finding the Pattern
The question asks us to identify a relationship between the three numbers in a given set and find the option that follows the same relationship.
Identifying the Pattern
Let's denote the numbers in a set as $(A, B, C)$. We need to find a mathematical operation involving $A$ and $B$ that results in $C$. The constraint is to operate on whole numbers.
Consider the first given set $(40, 10, 150)$. We test possible operations:
- $(A + B) \times K = C \implies (40 + 10) \times K = 150 \implies 50 \times K = 150 \implies K=3$.
- $(A - B) \times K = C \implies (40 - 10) \times K = 150 \implies 30 \times K = 150 \implies K=5$.
Now let's check the second set $(65, 35, 150)$ with the second potential pattern, $(A - B) \times 5 = C$.
- $(65 - 35) \times 5 = 30 \times 5 = 150$.
The pattern $(A - B) \times 5 = C$ holds true for both given sets.
Checking the Options
We apply the identified pattern $(A - B) \times 5 = C$ to each option:
| Option | Set (A, B, C) | Calculation | Result | Matches C? |
|---|---|---|---|---|
| 1 | (75, 40, 225) | $(75 - 40) \times 5$ | $35 \times 5 = 175$ | No |
| 2 | (30, 12, 120) | $(30 - 12) \times 5$ | $18 \times 5 = 90$ | No |
| 3 (C) | (55, 10, 225) | $(55 - 10) \times 5$ | $45 \times 5 = 225$ | Yes |
| 4 | (70, 30, 270) | $(70 - 30) \times 5$ | $40 \times 5 = 200$ | No |
Option 3 (C) is the only set where the numbers follow the pattern $(A - B) \times 5 = C$.
Important Questions from Analogy
Select the option that is related to the third number in the same way as the second number is related to the first number.
12 : 60 :: 16 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
16 : 144 :: 28 : ?
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)
(42, 18, 3)
(36, 14, 4)
Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
ABILITY : LIBAYTI : : CHRONIC : ORHCCIN : : HEAVILY : ?
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
(4, 50, 6)
(13, 128, 3)
