If p is an integer, which of the following must be true about 4p+7?
a) it is odd
b) it is even
c) it is greater than 7
d) it is greater than p
e) it is divisible by 11
Seven added to any number that has
been multiplied by 4 equals an odd
number. ans. = a.
4P = EVEN number, 7 = ODD number.
EVEN + ODD = ODD.
4P + 7 = ODD number. ans. = a.
To determine which of the given options must be true about the expression 4p + 7, let's analyze each option one by one:
a) it is odd:
If p is an integer, then 4p is always even since it is a multiple of 4. Adding an odd number (7) to an even number will always result in an odd number. Therefore, option a) is correct: it is odd.
b) it is even:
As mentioned above, 4p is always even. Adding an odd number (7) to an even number will always result in an odd number. Therefore, option b) is incorrect: it is not even.
c) it is greater than 7:
Since we don't have information about the specific value of p, we cannot guarantee that 4p + 7 will always be greater than 7. Therefore, option c) is incorrect: it is not necessarily greater than 7.
d) it is greater than p:
Comparing 4p + 7 to p is not possible without knowing the specific value of p. Therefore, option d) cannot be determined, as it depends on the value of p.
e) it is divisible by 11:
To determine if 4p + 7 is divisible by 11, we need to analyze the divisibility rules of 11. However, since we don't have information about the specific value of p, we cannot guarantee that 4p + 7 will always be divisible by 11. Therefore, option e) is incorrect: it is not necessarily divisible by 11.
In summary, the correct answer is option a) it is odd.
To determine which of the given options must be true about 4p + 7, we can analyze the expression step by step.
First, let's consider the constant term, which is 7. It is already evident that 7 is an odd number.
Now, let's focus on the coefficient of p, which is 4. To determine whether the expression 4p is even or odd, we need to consider whether p itself is even or odd.
If p is even, then 4p will also be even, since multiplying an even number by any other number results in an even number.
If p is odd, then 4p will be even, since multiplying an odd number by an even number also results in an even number.
Therefore, regardless of whether p is even or odd, the expression 4p will always be even.
Taking this into consideration, we can now analyze the sum of 4p + 7.
Since an even number added to an odd number always results in an odd number, we can conclude that the expression 4p + 7 will be odd, satisfying option a).
To summarize, the correct answer is:
a) it is odd