Question

Select the set in which the numbers are related in the same way as the following sets.

(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers info its

constituent digits. E.g. 13 — Operations on 13 such as adding /deleting/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)

(12,15,18)

(45,35,25)

• A. (13, 10, 17)
• B. (19,18, 1)
• C. (14, 28, 14)
• D. (15,20, 25)

Answer 1

Answer:

D. (15,20, 25)

2nd number =(1st number +3rd number)/2

Pattern Analysis

The underlying logic is that the second number is the average of the first and third numbers:
$\frac{\text{First Number} + \text{Third Number}}{2} = \text{Second Number}$

Alternatively, this means the three numbers form an arithmetic progression (AP), where the difference between the numbers within the set remains constant.

Set 1: $(12, 15, 18)$

• Applying the formula:
  $\frac{12 + 18}{2} = \frac{30}{2} = 15$

• The difference between consecutive terms is constant: $+3$ ($15 - 12 = 3$ and $18 - 15 = 3$).

Set 2: $(45, 35, 25)$

• Applying the formula:
  $\frac{45 + 25}{2} = \frac{70}{2} = 35$

• The difference between consecutive terms is constant: $-10$ ($35 - 45 = -10$ and $25 - 35 = -10$).

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Checking the Options

Based on this question's standard choices in competitive examinations, the correct option will maintain a constant difference (or have the middle number as the precise average):

• (A) $(13, 10, 17)$ $\rightarrow \frac{13 + 17}{2} = 15 \neq 10$

• (B) $(19, 18, 1)$ $\rightarrow \frac{19 + 1}{2} = 10 \neq 18$

• (C) $(14, 28, 14)$ $\rightarrow \frac{14 + 14}{2} = 14 \neq 28$

• (D) $(15, 20, 25)$ $\rightarrow \frac{15 + 25}{2} = \frac{40}{2} = 20$ (Constant difference of $+5$)

Correct Answer

(15, 20, 25)