Question

If 36: 84 :: 42: X, then the value of X, is:

• A. 18
• B. 98
• C. 72
• D. 48

Hint:

In proportion problems, you can also simplify the first ratio before solving. \(36:84\) can be simplified by dividing both numbers by their greatest common divisor, which is 12. \(36 \div 12 = 3\) and \(84 \div 12 = 7\). So the proportion becomes \(3:7 :: 42:X\). Now, \(3 \times X = 7 \times 42\), which gives \(X = (7 \times 42) / 3 = 7 \times 14 = 98\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The given expression is a proportion. In a proportion a: b :: c: d, the product of the extremes (a and d) is equal to the product of the means (b and c).
So, \(a \times d = b \times c\).
Step 2: Key Formula or Approach:
Given proportion: \(36: 84 :: 42: X\).
Here, a = 36, b = 84, c = 42, and d = X.
Using the rule of proportion:
\[ 36 \times X = 84 \times 42 \]
Step 3: Detailed Explanation:
To find the value of X, we need to solve the equation from Step 2.
\[ 36 \times X = 84 \times 42 \]
Isolating X:
\[ X = \frac{84 \times 42}{36} \]
We can simplify the fraction. We know that \(42 = 6 \times 7\) and \(36 = 6 \times 6\).
\[ X = \frac{84 \times (6 \times 7)}{6 \times 6} \]
Cancel out a 6 from the numerator and denominator:
\[ X = \frac{84 \times 7}{6} \]
Now, we can divide 84 by 6. \(84 \div 6 = 14\).
\[ X = 14 \times 7 \]
\[ X = 98 \]
Step 4: Final Answer:
The value of X is 98.