Q.10 The numeral in the units position of 211870 + 146127 × 3424 is _____.
Concept Used
To find the units digit of large powers, we use the
cyclicity of unit digits.
Only the last digit of the base affects the units digit of its power.
Step-by-Step Solution
Step 1: Units digit of 211870
The units digit of 211 is 1.
Powers of 1 always end in 1.
211870 ⇒ units digit = 1
Step 2: Units digit of 146127
The units digit of 146 is 6.
Powers of 6 always end in 6.
146127 ⇒ units digit = 6
Step 3: Units digit of 3424
Powers of 3 follow a cycle of 4:
| Power | Units Digit |
|---|---|
| 31 | 3 |
| 32 | 9 |
| 33 | 7 |
| 34 | 1 |
Reduce the exponent:
424 mod 4 = 0
3424 ⇒ units digit = 1
Step 4: Units digit of the product
146127 × 3424
Units digit = 6 × 1 = 6
Step 5: Units digit of the final expression
211870 + (146127 × 3424)
Units digit = 1 + 6 = 7
Correct Answer
Correct Answer: 7
Options Analysis
| Option | Value | Correct? | Explanation |
|---|---|---|---|
| (A) | 1 | ❌ | Ignores the contribution of the product term. |
| (B) | 6 | ❌ | Only the product’s units digit is considered. |
| (C) | 7 | ✅ | Correct sum of the individual units digits. |
| (D) | 9 | ❌ | Incorrect application of cyclic patterns. |
Final Conclusion
By applying unit digit cyclic patterns, the numeral in the units
position of
211870 + 146127 × 3424
is 7.
