Find the last two digits of the following-101 - 102 - 103 - 197 - 198 - 199

The correct option is C 64(101 × 102 × 103 × 197 × 198 × 199)/100→[1 × 2 × 3 × ( 3)× ( 2)× ( 1)]/100→ 36 as remainder → remainder is 64. ...

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Quantitative Aptitude

Last Two Digits of a Number

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Question

Find the last two digits of the following:
$101 \times 102 \times 103 \times 197 \times 198 \times 199$

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Solution

The correct option is C 64
$\frac{(101 \times 102 \times 103 \times 197 \times 198 \times 199)}{100} \to \frac{[1 \times 2 \times 3 \times (- 3) \times (- 2) \times (- 1)]}{100} \to - 36$ as remainder $\to$ remainder is 64.

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Similar questions

Q. Sum the series:

199 \cdot 1 + 197 \cdot 3 + 195 \cdot 5 + . . . . . + 103 \cdot 197 + 101 \cdot 99

Find the values of
(i) $(82)^{2} - (18)^{2}$
(ii) $(128)^{2} - (72)^{2}$
(iii) $197 \times 203$
(iv) $\frac{198 \times 198 - 102 \times 102}{96}$
(v) $(14.7 \times 15.3)$
(vi) $(8.63)^{2} - (1.37)^{2}$

Q. Find the value of:
(i) (82)² − (18)²
(ii) (128)² − (72)²
(iii) 197 × 203
(iv)

\frac{198 \times 198 - 102 \times 102}{96}

(v) (14.7 × 15.3)
(vi) (8.63)² − (1.37)²

Q. Find the value of :
(i)

(82)^{2} - (18)^{2}

(ii)

(128)^{2} - (72)^{2}

(iii)

197 \times 203

(iv)

\frac{198 \times 198 - 102 \times 102}{96}

(v)

(14.5 \times 15.3)

(vi)

(8.63)^{2} - (1.37)^{2}

Find the number from each of the following expanded forms:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵+ 5 × 10³+ 3 × 10²+ 2 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

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Find the last two digits of the following: 101×102×103×197×198×199

The correct option is C 64(101×102×103×197×198×199)100→[1×2×3×(−3)×(−2)×(−1)]100→−36 as remainder → remainder is 64.

Find the last two digits of the following:
$101 \times 102 \times 103 \times 197 \times 198 \times 199$

The correct option is C 64
$\frac{(101 \times 102 \times 103 \times 197 \times 198 \times 199)}{100} \to \frac{[1 \times 2 \times 3 \times (- 3) \times (- 2) \times (- 1)]}{100} \to - 36$ as remainder $\to$ remainder is 64.