IGDTUW 2025 — Reasoning PYQ

Step 1: Understand the relationship between H.C.F. and numbers

If the H.C.F. of two numbers is $h$, then the numbers can always be represented as $hx$ and $hy$, where $x$ and $y$ are coprime numbers (numbers with no common factor other than 1).

Given:

• H.C.F. ($h$) = 21

• Ratio of the numbers = $1:4$

Therefore, we can let the two numbers be $21\times 1$ and $21\times 4$.

Step 2: Identify the numbers

• First number = $21\times 1=21$

• Second number = $21\times 4=84$

Step 3: Verification (Optional)

We can verify this using the L.C.M. property. For two numbers $a$ and $b$:

$$\text{Product of numbers}=\text{H.C.F.}\times \text{L.C.M.}$$

$$21\times 84=21\times 84$$

$$1764=1764$$

The verification holds true.

Step 4: Find the larger number

Comparing the two numbers, 21 and 84, it is clear that 84 is the larger value.

Conclusion:

The larger of the two numbers is 84. Therefore, the correct option is (a).