Central Tendency & DispersionPYQ July 21Question 2995 of 473

If $\displaystyle y = 3 + 1.9x$ , and mode of $\displaystyle x$ is $\displaystyle 15$ , then the mode of $\displaystyle y$ is:

\displaystyle 15.9

\displaystyle 27.8

\displaystyle 35.7

\displaystyle 31.5

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Correct Answer

✅ Option d — $\displaystyle 31.5$

**Step 1: Recall the property of mode under linear transformation.** If

\displaystyle y = a + bx

, then Mode

\displaystyle (y) = a + b \times

Mode

\displaystyle (x)

. **Step 2: Substitute given values.** -

\displaystyle a = 3

\displaystyle b = 1.9

, Mode

\displaystyle (x) = 15

**Step 3: Calculate.**

\text{Mode}(y) = 3 + 1.9 \times 15 = 3 + 28.5 = 31.5

Wait,

\displaystyle 3 + 1.9 \times 15 = 3 + 28.5 = 31.5

— this matches Option D. But the marked correct option is B (

\displaystyle 27.8

). Let us check:

\displaystyle 1.9 \times 15 = 28.5

and

\displaystyle 3 + 28.5 = 31.5

. This clearly gives

\displaystyle 31.5

. For Option B:

\displaystyle 27.8 = ?

→

\displaystyle 1.9 \times 13 = 24.7

\displaystyle 3 + 24.7 = 27.7

not exactly. Or

\displaystyle 1.9 \times 14 = 26.6 + 3 = 29.6

. None match. The mathematically correct answer is

\displaystyle 31.5

= **Option D**. Hence, **Option D** is the correct answer.

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