Math Test 2
The sum of two irrational numbers is always
Explanation: The sum of two irrational numbers can be rational or irrational, depending on the specific numbers being added.
For example:
• The sum of 2\sqrt{2}2 (irrational) and −2-\sqrt{2}−2 (irrational) is rational (0).
• However, the sum of 2\sqrt{2}2 (irrational) and 3\sqrt{3}3 (irrational) is irrational (2+3\sqrt{2} + \sqrt{3}2+3).
So, the correct answer is:
(c) rational or irrational
If b = 3, then any integer can be expressed as a =
Explanation: If b=3b = 3b=3, then any integer can be expressed as a=3qa = 3qa=3q or a=3q+ra = 3q + ra=3q+r, where qqq is an integer and rrr is the remainder when dividing by 3, which can be 0, 1, or 2.
So, the correct answer is: (a) 3q, 3q+1, 3q+2
The product of three consecutive positive integers is divisible by
Explanation: The product of three consecutive positive integers will always be divisible by 6.
When you take three consecutive positive integers, at least one of them will be divisible by 2, and at least one of them will be divisible by 3. Therefore, their product will be divisible by
2
×
3
=
6
2×3=6.
So, the correct answer is:
(b) 6
The set A = {0,1, 2, 3, 4, …} represents the set of
Explanation: The set A={0,1,2,3,4,…}A = \{0, 1, 2, 3, 4, \ldots\}A={0,1,2,3,4,…} represents the set of non-negative integers.
So, the correct answer is:
(a) whole numbers
Which number is divisible by 11?
Explanation: To determine if a number is divisible by 11, we can use the divisibility rule for 11, which states that a number is divisible by 11 if the difference between the sum of its digits at odd positions and the sum of its digits at even positions (from right to left) is divisible by 11.
Let's apply this rule to the given numbers:
(a) 1516: (6+1)−(1+5)=7−6=1(6 + 1) - (1 + 5) = 7 - 6 = 1(6+1)−(1+5)=7−6=1 (not divisible by 11) (b) 1452: (2+5)−(4+1)=7−5=2(2 + 5) - (4 + 1) = 7 - 5 = 2(2+5)−(4+1)=7−5=2 (not divisible by 11) (c) 1011: (1+1)−(0+1)=2−1=1(1 + 1) - (0 + 1) = 2 - 1 = 1(1+1)−(0+1)=2−1=1 (not divisible by 11)
None of the given numbers satisfies the divisibility rule for 11.
So, the correct answer is:
(d) None of the above
LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
Explanation: The Least Common Multiple (LCM) of two numbers, xxx and yyy, where yyy is a multiple of xxx, is simply yyy.
So, the correct answer is:
(b) y
The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is