If , where A is a positive integer lesser than or equal to 20, B is a non-zero integer between -10 and 10, inclusive, and m and n are non-negative single-digit numbers, which of the following expressions is true?a)0 andlt; P andlt; (0.2)9b)-10-9 andlt; P andlt; (0.2)9c)10-18 andlt; P andlt; 209d)-20-9andlt;Pandlt;209e)-10-18 andlt; P andlt; 209Correct answer is option 'C'. Can you explain this answer?

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, where A is a positive integer lesser than or equal to 20, B is a non-zero integer between -10 and 10, inclusive, and m and n are non-negative single-digit numbers, which of the following expressions is true?

a)
0 < P < (0.2)⁹
b)
-10^-9 < P < (0.2)⁹
c)
10^-18 < P < 20⁹
d)
-20^-9<P<20⁹
e)
-10^-18 < P < 20⁹

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

If , where A is a positive integer lesser than or equal to 20, B is ...

Given:

Possible values of Integer A = {1, 2, 3 . . . 19, 20}
Possible values of Integer B = { -10, -9, -8 . . . -1, 1, 2, 3 . . . 9, 10}
- B ≠ 0
Possible values of m, n = {0, 1, 2, 3 . . . 8, 9}

To Find: Out of the given options on the range of P, which is correct?

Approach:

To answer this question, we need to find the maximum possible value of P and the minimum possible value of P
- P is maximum when Aⁿ is maximum and B^2m is minimum
  - Since both A and n are non-negative integers, Aⁿ will be maximum when A is maximum and n is maximum
  - Since both B and m are non-negative integers, B^2m will be minimum when both B and m are at their minimum possible values
- P is minimum when Aⁿ is minimum and B^2m is maximum
  - Since both A and n are non-negative integers, A will be minimum when Aⁿ is minimum and n is minimum
- Since both B and m are non-negative integers, B^2m will be maximum when both B and m are at their maximum possible values.
The option that lies between the calculated maximum and minimum values of P will be the correct answer

Working out:

Calculating the maximum possible value of P
- Finding maximum value of Aⁿ
  - Maximum possible value of A = 20
  - And, maximum possible value of n = 9
  - So, maximum A = 20
Finding minimum value of B^2m
- Since this term is the perfect square of integer B, it’s least value can be 1 (happens when m = 0)
- Note that the minimum possible value of B did not depend on the value of B here only because the minimum possible value of m here is 0. Had m been a positive integer, then the minimum possible value of B would have depended on the minimum possible value of both m and B.
So, P maximum =

Calculating the minimum possible value of P
- Finding minimum value of Aⁿ
  - Minimum possible value of A = 1
  - For this value of A, the value of n will not matter
    - Note that the minimum possible value of A here didn’t depend on the value of n only because the minimum possible value of A was 1 (and 1 raised to the power of anything is equal to1). If however A had been a positive integer greater than 1, then to find the minimum possible value of A , you would have needed to consider the minimum values of both A and n.
  - So, minimum A = 1
Finding maximum value of B^2m
- Maximum possible value of B = 10
- And, maximum possible value of m = 9
- So, maximum B^2m = 10¹⁸
- So, P minimum =

Choosing the answer
- We’ve calculated that: 10^-18 < P < 20⁹

Looking at the answer choices, we see that the correct answer is Option C

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If , where A is a positive integer lesser than or equal to 20, B is a non-zero integer between -10 and 10, inclusive, and m and n are non-negative single-digit numbers, which of the following expressions is true?a)0 < P < (0.2)9b)-10-9 < P < (0.2)9c)10-18 < P < 209d)-20-9<P<209e)-10-18 < P < 209Correct answer is option 'C'. Can you explain this answer?

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