The number 4,29,714 is divisible by:
- (a)6 and 5
- (b)3 and 6
- (c)4 and 6
- (d)3 and 5
Answer
Why
Correct — B. Test the rules against 4,29,714 rather than dividing.
Digit sum = 4 + 2 + 9 + 7 + 1 + 4 = 27, a multiple of 3, so the number is divisible by 3.
The last digit is 4, so the number is even and divisible by 2.
Divisible by 2 and by 3 together means divisible by 6.
Last digit 4 is neither 0 nor 5, so it is not divisible by 5.
Last two digits are 14, not a multiple of 4, so it is not divisible by 4.
3 and 6 are the pair that survives → option (b).
Why the others are wrong
- (a)6 and 5 — The 6 does hold, but a multiple of 5 must end in 0 or 5, and this number ends in 4. One failed divisor kills the whole pair.
- (c)4 and 6 — The 6 holds. For 4 you check only the last two digits: 14 is not a multiple of 4, so 4,29,714 is not divisible by 4.
- (d)3 and 5 — The 3 holds, since the digits add to 27. The 5 fails on the last digit 4, exactly as it does in option (a).
Concept
Divisibility items are answered by rules, not by long division.
3: digit sum is a multiple of 3. 9: digit sum is a multiple of 9.
2: last digit is even. 5: last digit is 0 or 5.
4: last two digits form a multiple of 4. 8: last three digits do.
6 is composite, so it needs 2 and 3 together. Never test 6 on its own — test its two coprime factors and combine them.
Here the digit sum 27 is also a multiple of 9, so 4,29,714 is divisible by 9 as well, and being even it is divisible by 18 too.
Each option pairs two divisors, so a single failure kills the option outright.
Start with the cheapest test. The last digit alone rules out both options containing 5, which leaves only two pairs to separate.
Key facts
- 4,29,714 has digit sum 27, so it is divisible by 3 and also by 9.
- Its last digit 4 makes it even, and even together with divisible-by-3 gives divisible by 6.
- Its last two digits are 14, which is not a multiple of 4, so the number is not divisible by 4.
- A number is divisible by 5 only when its last digit is 0 or 5.
Study next
Common traps
- Testing 6 by halving and guessing instead of checking 2 and 3.
- Applying the digit-sum rule to 4 or 8, where only the trailing digits matter.
- Stopping at the first rule that passes without checking the second divisor in the pair.
SSC also turns this into a missing-digit item.
9 Sep 2024, 09:00, Quant Q.11 asks which value of k makes 217924k divisible by 6, 17 Sep 2024, 09:00, Quant Q.20 asks for the least k in 249k876, and 25 Sep 2024, 16:00, Quant Q.18 simply asks which of four given numbers is divisible by 6.
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