Dear Reader,
Below are three problems dealing with calculations on positive and negative numbers.
Question 1
If P is a positive prime number, then which of the following is the greatest?
a) -P b) 0 c) -(P2) d) (-3)(-P)2
Answer : b) 0
Solution :
If P is a positive number, then P > 0 => -P < 0.
(P2) > 0 and -(P2) < 0
(-P)2 = (P)2 > 0
3(P)2 > 0 => -3(-P)2 < 0.
Therefore, -P, -(P2), (-3)(-P)2 < 0
So the greatest of them is 0.
Question 2
If -5 < = p < = 6 and 5 < = q < = 8, then which of the following is the least value of 5q-8p?
a) 65 b) -23 c)-8 d) 12.
Answer : b) -23.
Solution :
Given that, 5 < = q < = 8.
i.e., q > = 5 then 5q > = 25.
Now, -5 < = p < = 6
We have to find least value of -8p. (in negative term).
So, we take p < = 6 => -8p > = -48.
i.e., least value of -8p is -48.
Required least value = 5q-8p = 25-48 = -23.
Question 3
If 0 < p < 800 and -500 < q < -5, then which of the following is the greatest value of p+q?
a) 795 b) 793 c) -499 d) -500
Answer : b) 793
Solution :
Given that, 0 < p < 800.
The possible values of p are { 1, 2, 3,...,799}
And, the greatest value of p = 799
Now, -500 < q < -5
The possible values of q are {-499, -498, -497,....,-8, -7, -6}
And, the greatest value of p = -6.
Hence, the required value = p+q = 799-6 = 793.
Below are three problems dealing with calculations on positive and negative numbers.
Question 1
If P is a positive prime number, then which of the following is the greatest?
a) -P b) 0 c) -(P2) d) (-3)(-P)2
Answer : b) 0
Solution :
If P is a positive number, then P > 0 => -P < 0.
(P2) > 0 and -(P2) < 0
(-P)2 = (P)2 > 0
3(P)2 > 0 => -3(-P)2 < 0.
Therefore, -P, -(P2), (-3)(-P)2 < 0
So the greatest of them is 0.
Question 2
If -5 < = p < = 6 and 5 < = q < = 8, then which of the following is the least value of 5q-8p?
a) 65 b) -23 c)-8 d) 12.
Answer : b) -23.
Solution :
Given that, 5 < = q < = 8.
i.e., q > = 5 then 5q > = 25.
Now, -5 < = p < = 6
We have to find least value of -8p. (in negative term).
So, we take p < = 6 => -8p > = -48.
i.e., least value of -8p is -48.
Required least value = 5q-8p = 25-48 = -23.
Question 3
If 0 < p < 800 and -500 < q < -5, then which of the following is the greatest value of p+q?
a) 795 b) 793 c) -499 d) -500
Answer : b) 793
Solution :
Given that, 0 < p < 800.
The possible values of p are { 1, 2, 3,...,799}
And, the greatest value of p = 799
Now, -500 < q < -5
The possible values of q are {-499, -498, -497,....,-8, -7, -6}
And, the greatest value of p = -6.
Hence, the required value = p+q = 799-6 = 793.
