If the relationship between x and y is given by 2x + 3y = 10 and the range of y is 10, then what is the range of x?

Option d: 15. Solution: Step 1: Express x in terms of y. From 2x + 3y = 10: x = 10 - 3y/2 = 5 - 3/2y Step 2: Apply the range transformation rule. If x = a + by, then Range(x) = |b| x Range(y). Here b = -3/2. Step 3: Calculate Range of x. text{Range}(x) = <=ft|-3/2right| x 10 = 3/2 x 10 = 15 Hence, Option D is the correct answer.

If the relationship between $x$ and $y$ is given by $2x + 3y = 10$ and the range of $y$ is $10$, then what is the range of $x$?

The correct answer is Option d: 15. **Step 1: Express $x$ in terms of $y$.** From $2x + 3y = 10$: $$x = \frac{10 - 3y}{2} = 5 - \frac{3}{2}y$$ **Step 2: Apply the range transformation rule.** If $x = a + by$, then Range$(x) = |b| \times$ Range$(y)$. Here $b = -\frac{3}{2}$. **Step 3: Calculate Range of $x$.** $$\text{Range}(x) = \left|-\frac{3}{2}\right| \times 10 = \frac{3}{2} \times 10 = 15$$ Hence, **Option D** is the correct answer.

Central Tendency & DispersionPYQ July 21Question 3077 of 473

All Questions

If the relationship between $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 2x + 3y = 10$ and the range of $\displaystyle y$ is $\displaystyle 10$ , then what is the range of $\displaystyle x$ ?

Options

A10

B18

D15

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 15

All Options:

Detailed Solution & Explanation

**Step 1: Express

\displaystyle x

in terms of

\displaystyle y

.** From

\displaystyle 2x + 3y = 10

x = \frac{10 - 3y}{2} = 5 - \frac{3}{2}y

**Step 2: Apply the range transformation rule.** If

\displaystyle x = a + by

, then Range

\displaystyle (x) = |b| \times

Range

\displaystyle (y)

. Here

\displaystyle b = -\frac{3}{2}

. **Step 3: Calculate Range of

\displaystyle x

.**

\text{Range}(x) = \left|-\frac{3}{2}\right| \times 10 = \frac{3}{2} \times 10 = 15

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

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If the relationship between x\displaystyle xx and y\displaystyle yy is given by 2x+3y=10\displaystyle 2x + 3y = 102x+3y=10 and the range of y\displaystyle yy is 10\displaystyle 1010, then what is the range of x\displaystyle xx?