Question

10 is related to 75 following a certain logic. Following the same logic, 6 is related to 47. To which of the following is 15 related following the same logic? (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.

• A. 164
• B. 110
• C. 123
• D. 156

Answer 1

Answer:

B. 110

Let’s look for a whole-number operation rule.

Given:

• (10 \rightarrow 75)

• (6 \rightarrow 47)

Assume a linear relation of the form:
$f(n) = an + b$
From the given pairs:
$10a + b = 75$
$6a + b = 47$
Subtract the second equation from the first:
$4a = 28 \Rightarrow a = 7$

Substitute back:
$6(7) + b = 47 \Rightarrow 42 + b = 47 \Rightarrow b = 5$

So the rule is:
$f(n) = 7n + 5$

Now apply it to 15:
$15 \rightarrow 7 \times 15 + 5 = 105 + 5 = \boxed{110}$

Answer: 110