IGDTUW 2025 — Reasoning PYQ

Step 1: Divisibility by 8

A number is divisible by 8 if its last three digits are divisible by 8. Here, the last three digits are $5z6$.

$$5z6=500+10z+6=506+10z$$

For this to be divisible by 8:

• If $z=0$, $506/8=63.25$ (No)

• If $z=1$, $516/8=64.5$ (No)

• If $z=2$, $526/8=65.75$ (No)

• If $z=3$, $536/8=67$ (Yes)

• If $z=7$, $576/8=72$ (Yes)

So, $z$ can be 3 or 7.

Step 2: Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Sum $=4+8+9+y+5+z+6=32+y+z$.

For this to be a multiple of 9, $32+y+z$ could be 36 or 45.

$$y+z=4\text{or}y+z=13$$

Step 3: Finding the possible pairs $(y,z)$

Case 1: $z=3$

• If $y+z=4$, then $y+3=4⟹y=1$. Product $y\times z=1\times 3=3$.

• If $y+z=13$, then $y+3=13⟹y=10$ (Not possible as $y$ is a single digit).

Case 2: $z=7$

• If $y+z=4$, then $y+7=4⟹y=-3$ (Not possible).

• If $y+z=13$, then $y+7=13⟹y=6$. Product $y\times z=6\times 7=42$.

Conclusion:

Comparing the products obtained (3 and 42), the highest possible product is 42. Therefore, the correct option is (c).