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Simplify (212 * 212 + 312 * 312 )

  • 132288
  • 142088
  • 142188
  • 142288

Answer: Option D

Explanation:

Trick: Above equation can be solved by using following formula
\begin{aligned}
(a^2 + b^2) = \frac{1}{2}((a+b)^2 + (a-b)^2)
\end{aligned}

Similar Questions :

1. \begin{aligned}
46^2 - (?)^2 = 4398 - 3066
\end{aligned}

  • 23
  • 18
  • 38
  • 28

Answer: Option D

2. A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31

  • 5
  • 3
  • 4
  • 6

Answer: Option A

Explanation:

P ÷ 44 = 432

=> P = 432 * 44 = 19008

P / 31 = 19008 / 31 = 613, remainder = 5

3. 1939392 * 625

  • 1212120010
  • 1212120000
  • 1212120011
  • 1212121010

Answer: Option B

Explanation:

Trick: when multiplying with \begin{aligned} 5^n
\end{aligned} then put n zeros to the right of multiplicand and divide the number with \begin{aligned} 2^n
\end{aligned}
So using this we can solve this question in much less
time.
\begin{aligned} 1939392 \times 5^4 = \frac {19393920000}{16} = 1212120000
\end{aligned}

4. 217 * 217 + 183 * 183

  • 70578
  • 82578
  • 80578
  • 80568

Answer: Option C

Explanation:

\begin{aligned}
\frac {1}{2}\times 2(a^2 + b^2) = \frac {1}{2} \times [(a + b)^2 + (a - b)^2]
\end{aligned}
\begin{aligned}
= \frac {1}{2} \times [(217 + 183)^2 + (217 - 183)^2] = 80578
\end{aligned}

5. 1307 * 1307 = ?

  • 1608249
  • 1508249
  • 1408249
  • 1708249

Answer: Option D

Explanation:

\begin{aligned}
(a + b)^{2} = (a^2 + b^2 + 2ab)
\end{aligned}
\begin{aligned}
1307^{2} = (1300 + 7)^2 = (1690000 + 49 + 18200)
\end{aligned}

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