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

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

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• 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
  $$\begin{aligned} (a^2 + b^2) = \frac{1}{2}((a+b)^2 + (a-b)^2) \end{aligned}$$

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• 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
  

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• 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.

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• 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

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• 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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