# Numbers Questions Answers

• #### 1. Simplify 586645 * 9999

1. 5865863355
2. 5665863355
3. 4865863355
4. 4665863355
##### Answer And Explanation

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

• #### 2. 1939392 * 625

1. 1212120010
2. 1212120000
3. 1212120011
4. 1212121010
##### Answer And Explanation

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}

• #### 3. Simplify (212 * 212 + 312 * 312 )

1. 132288
2. 142088
3. 142188
4. 142288
##### Answer And Explanation

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}

• #### 4. Find the unit digit in \begin{aligned} (544)^{102} + (544)^{103} \end{aligned}

1. 2
2. 4
3. 0
4. 1
##### Answer And Explanation

Answer: Option C

Explanation:

Required digit is = \begin{aligned}
(4)^{102} + (4)^{103} \end{aligned}
as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0

• #### 5. What least value should be replaced by * in 223*431 so the number become divisible by 9

1. 3
2. 4
3. 5
4. 6
##### Answer And Explanation

Answer: Option A

Explanation:

Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9,
15+3 will be divisible by 9,
so that least number is 3.

• #### 6. How many terms are there in 2,4,8,16,....,1024

1. 7
2. 8
3. 9
4. 10
##### Answer And Explanation

Answer: Option D

Explanation:

It is a GP. with r = 2, ie \begin{aligned} 2^1, 2^2, 2^3... \end{aligned}
If number of terms is n. Then,
\begin{aligned} 2 \times 2^{n-1} = 1024 \end{aligned} =>
\begin{aligned} 2^{n-1} = 512 \end{aligned}
or \begin{aligned} 2 \times 2^{n-1} = 2^9 \end{aligned}
so n-1 = 9 => n = 10

• #### 7. Which of the following is a prime number

1. 9
2. 2
3. 4
4. 8
##### Answer And Explanation

Answer: Option B

Explanation:

A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number

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