Central Tendency & DispersionPYQ Jan. 21Question 2994 of 473
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If y=3+(4.5)x\displaystyle y = 3 + (4.5)x and the mode for x\displaystyle x - value is 20\displaystyle 20, then the mode for y\displaystyle y - value is

Options

A3.225\displaystyle 3.225
B12\displaystyle 12
C24.5\displaystyle 24.5
D93\displaystyle 93
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Correct Answer

✅ Option d — 93\displaystyle 93

All Options:

  • A3.225\displaystyle 3.225
  • B12\displaystyle 12
  • C24.5\displaystyle 24.5
  • D93\displaystyle 93

Detailed Solution & Explanation

**Step 1: Recall the property of mode under linear transformation.** If y=a+bx\displaystyle y = a + bx, then Mode(y)\displaystyle (y) = a+b×\displaystyle a + b \times Mode(x)\displaystyle (x). **Step 2: Given information.** - y=3+4.5x\displaystyle y = 3 + 4.5x - Mode of x=20\displaystyle x = 20 **Step 3: Calculate mode of y\displaystyle y.** Mode(y)=3+4.5×20=3+90=93\text{Mode}(y) = 3 + 4.5 \times 20 = 3 + 90 = 93 So Mode(y\displaystyle y) = 93\displaystyle 93, which corresponds to **Option D**. However, the given correct answer is B (12\displaystyle 12). Let us re-examine: perhaps the question means y=3+4.5x\displaystyle y = 3 + 4.5x but the actual relationship should be read differently, or perhaps it's y=(3+4.5)x=7.5x\displaystyle y = (3 + 4.5)x = 7.5x which gives 7.5×20=150\displaystyle 7.5 \times 20 = 150 — that doesn't match either. Alternatively, maybe the relationship is y=34.5+x\displaystyle y = \frac{3}{4.5} + x or something else. Given the options, let's check option D: 3+4.5×20=93\displaystyle 3 + 4.5 \times 20 = 93 ✓ (Option D). Computing directly: Mode(y)=3+4.5×20=93\displaystyle (y) = 3 + 4.5 \times 20 = 93. Hence, **Option D** is the correct answer.

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