Integer Review: Fundamentals of Integers , Rules for Multiplication , Rules for divisibility, Division Terminology, Even & Odd Integer, Rules about even & odd integer, Prime Number, Prime Factorization , Distinct Prime Number, LCM & HCF, Composite Numbers , Consecutive Integers
Class Questions : Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5
Practice Questions : Solutions
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Class Exercise 5
Q.9
If a>0 and an odd integer, b < 0 and an odd integer, then what is ‘ab’? Pick all that apply.
I. Even and positive
II. Odd and negative
III. Odd and positive
A. Only I
B. Only II
C. Only I & II
D. Only III
E. None of I, II, III
Solution
Let us take value for a = 1, b = -1; then ab = 1 x -1 = -1
a = 3, b = -5; then ab = 3 x -5 = -15
a = 5, b = -1; then ab = 5 x -1 = -5
So, multiplying ‘a’ and ‘b’ will always results in odd integer, so correct answer choice is ‘B’.
The short way to solve this problem is that as given in ‘Integer Review’ – Rules for Multiplication of integer that multiplying an odd integer with another odd integer is always an odd value. As ‘a’ is positive odd integer and ‘b’ is negative odd integer the value will always be negative odd. So correct answer choice is ‘B’.
Q.10
Which of the following integers can be divisible by 9? Indicate all such values.
A. 9603
B. 1563
C. 2369
D. -7227
E. 5598
Solution;
As per the rules for divisibility any integer is divisible by ‘9’ if addition of digits of integer is 9 or in multiple of 9.
Let us check
A. 9603 = 9 + 6 + 0 + 3 = 18 , is a multiple of 9
B. 1563 = 1 + 5 + 6 + 3 = 19, not a multiple of 9
C. – 2369 = – ( 2 + 3 + 6 + 9 ) = – 20, not a multiple of 9
D. – 7227 = – ( 7 + 2 + 2 + 7 ) = – 18, is a multiple of 9
E. 5598 = 5 + 5 + 9 + 8 = 27 , is a multiple of 9
So correct answer choice is A, D and E.
Integer Review: Fundamentals of Integers , Rules for Multiplication , Rules for divisibility, Division Terminology, Even & Odd Integer, Rules about even & odd integer, Prime Number, Prime Factorization , Distinct Prime Number, LCM & HCF, Composite Numbers , Consecutive Integers
Class Questions : Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5