Mutipication Tricks : Unit digit, Digital root, Zeros in, Digital root ..........

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Q. 713 × 896 × 232

Option : a) 148212736 b) 148212746 c) 148212756 d) 148212766

Solⁿ

713 = 7 +1+ 3 = 11 = 2 

896 = 8 + 9 + 6 = 2+3 = 5

232 = 2 + 3 + 2 = 7

Multiply digital roots: 2 * 5 * 7 = 70 = 7 (cancel 0), answer should be the Multiply digital roots "7" useing the given tricks.

Options (cancel 9, 0-pairs): use casting out 9s (digital root) to quickly eliminate wrong options without full multiplication.

(a)148212736 → 1 + 4 + 2 = 7,Short Trick(6+3=9,7+2=9,1+8=9 cancel left
1+4+2=7, Multiply digital roots "7", answer shold be (a).

(b)148212746 → 4 + 4 =
8

(c)148212756 → 4 + 5 = 9 → 0

(d)  148212766 → 6 + 6 = 10 → 1

Ans: (a)

1.  Find the correct value of 248×375×64

Options: a) 5952000   b) 5952100   c) 5952200    d) 5952300

Solⁿ:

Digital roots:
248 → 2+4+8=14 → 5
375 → 3+7+5=15 → 6
64 → 6+4=10 → 1

• Multiply digital roots: 5×6×1=30 → 3


• Check options: (a) sum digits 5+9+5+2+0+0+0 = 21 → 2+1=3

Ans: a) 5952000

2.  Unit digit of  9¹⁰³×7²⁰²

Options: a) 1   b) 3   c) 7   d) 9

Solⁿ:

• Powers of  9 → cycle 9, 1 → 103 ÷ 2 remainder 1 → last digit = 9


• Powers of  7 → cycle 7,9,3, 1 → 202 ÷ 4 remainder 2 → last digit = 9 (7¹ = 7, 7² = 49 , 7³ = 343 , 7⁴ = 2401  ,,,  7,9,3,1 respectively)


• Multiply:  9×9 = 81 → unit digit = 1

Ans: a) 1

3.  Find the correct value of 512×243×125

Options: a) 15552000  b) 15553000  c) 15554000  d) 15555000

Solⁿ:

• Digital roots: 512 → 5+1+2 = 8, 243 → 2+4+3 = 9 → 0, 125 → 1+2+5 = 8


• Multiply: 8×0×8=0


• Option (a) → sum digits 1+5+5+5+2+0+0+0 = 18 → 1+8 = 9

Ans: a) 15552000

4.  Digital root of 36×48×125

     Options: a) 3  b) 6  c) 9  d) 0

Solⁿ:

• 36 → 3 + 6 = 9 → 0


• Anything × 0 = 0

Ans: d) 0

5.  Zeros in 20×25×40×125

Options: a) 3  b) 4  c) 5  d) 6

Solⁿ:

·         Factorize: 20 = 2² × 5¹, 25 = 5², 40 = 2³ × 5¹, 125 = 5³

·         Count 5s = 1 + 2 + 1 + 3 = 7

·         Count 2s = 2 + 3 = 5 → enough

·         Zeros = min(2s,5s) = 5

Ans: c) 5

5.  Find the correct value of 729×64

Options: a) 46656  b) 46646  c) 46636  d) 46626

Solⁿ:

• Digital roots: 729 → 7+2+9=18 → 9, 64 → 6+4=10 →1


• Multiply: 9×1 = 9


• Option (a) → sum digits 4+6+6+5+6=27 → 2+7=9

Ans: a) 46656

6.  Digital root of 111 × 222 × 333

Options: a) 3  b) 6  c) 9  d) 0

Solⁿ:

• 111 → 3, 222 → 6, 333 → 9 → 0


• Multiply: 3×6×0=0

Ans: d) 0

8. Unit digit of 13⁴⁷

Options: a) 1  b) 3  c) 7  d) 9

Solⁿ:

• Powers of 3 cycle: 3,9,7,1 (cycle 4)


• 47 ÷ 4 = 11 remainder 3 → third number = 7

Ans: c) 7

9. Find the correct value of 88 × 99 × 111

Options: a) 967032  b) 967042  c) 967052  d) 967062

Solⁿ:

• Digital roots: 88 → 16 → 7, 99 → 18 → 9 → 0, 111 → 3


• Multiply: 7×0×3=0


• Option (a) → sum digits 9 + 6 + 7 + 0 + 3 + 2 = 27 → 2 + 7 = 9 → 0

Ans: a) 967032

10. Zeros in 5×10×15×20×25

Options: a) 3  b) 4  c) 5  d) 6

Solⁿ:

• Count 5s: 5(1), 10(1), 15(1), 20(1), 25(2) → total 6


• 2s are enough → zeros

Ans: d) 6

Exam Tips

• Digital root → quick option check


• 2 × 5 → one zero


• Powers → use cycle tables


• Count zeros → min(2s,5s)