217 * 217 + 183 * 183

Answer: Option D

Explanation:

Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944

Answer: Option A

Explanation:

Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
586645 * (10000 - 1) = 5866450000 - 586645 = 5865863355

Answer: Option C

Explanation:

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

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.
$$\begin{aligned} 1939392 \times 5^4 = \frac {19393920000}{16} = 1212120000 \end{aligned}$$

Answer: Option B

Explanation:

(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030