Q8. Q is the successor and R is the additive inverse of an integer P, respectively.
Which of the following values of P makes P Q * R a non-negative integer?
A. 2
B.-1
C.3
D. 1
ANS: B
Q9. Four consecutive integers were taken and their product was calculated. Among the
following, which value of the greatest integer among them will NOT make the product
positive?
A. 6.
B. 3
C. -2
D. -5
ANS: B
Q10.In an exam, 3 marks were awarded for every correct answer, -1 marks for every
wrong answer and no marks for unattempted questions
Answers
Given : Q is the successor and R is the additive inverse of an integer P, respectively.
To find : Which of the given values of P makes P Q * R a non-negative integer
Solution:
Q = P + 1
R = - P
P Q R = P (P + 1)(-P)
= -P²(P + 1)
P + 1 ≤ 0
=> P = - 1
option B is correct
Let say 4 integers in decending order
a , a - 1 , a - 2 , a - 3
a (a - 1) (a - 2)(a - 3) ≤ 0
=> (a² - 3a)(a² - 3a + 2) ≤ 0
=> (a² - 3a)² + 2(a² - 3a) ≤ 0
(a² - 3a)² can not be less than 0
=> 2(a² - 3a) ≤ 0
=>a² - 3a ≤ 0
=> a(a - 3) ≤ 0
=> a ∈ [ 0 , 3]
3 is the greatest integer
option B is correct
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