how many integers are there from -25 to 45
Answers
Step-by-step explanation:
x = the total number of positive, odd 2 digit numbers less than 100
Column A
x
Column B
45
Possible Answers:
The two quantities are equal
The relationship cannot be determined from the given information
The quantity in column A is greater
The quantity in column B is greater
Correct answer:
The two quantities are equal
Explanation:
There are 50 positive, odd numbers less than 100, and 45 of them are 2 digit numbers.
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Find The Number Of Integers Between Two Other Integers : Example Question #2
0 < x < y < z < 10
x, y, and z are integers.
Quantity A: –7
Quantity B: x + y – z
Possible Answers:
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined from the information given.
Correct answer:
Quantity B is greater.
Explanation:
Since:
There are only 9 integers between 0 and 10
x, y, and z must all be unique
They must be specifically ordered such that x < y < z
There are actually not too many ways in which these numbers can be chosen. So what we can do is find a range of answers for Quantity B, and see if 6 falls a) below b) above or c) in between the range.
For the maximum:
Note that the term (x + y) is maximized when x and y are maximum. The (–z) term is maximized when z is minimized. However, there are 2 terms in (x + y) and one term in (–z); thus intuitively it seems we should prioritize (x+y). To make x and y maximum:
0 < 7 < 8 < 9 < 10 since x, y, and z must be unique.
Thus maximum: (x + y – z) = 7 + 8 – 9 = 6
For the minimum:
Note that (x + y) is minimum when (x) and (y) are minimum, and (–z) is minimum when (z) itself is maximimized. However since there are 2 terms in (x+y) and1 of (–z) , again intuititively you should prioritize (x+y) over (-z). Then in order to make this the least number possible, x and y would be:
min(x + y – z) = 1 + 2 – 9 = –6
Thus, the range of possible answers is:
(x + y – z): [–6, 6]
and –7 is always less than this amount.
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Find The Number Of Integers Between Two Other Integers : Example Question #3
Quantity A: The number of positive even integers less than 1000
Quantity B: The number of positive odd integers less than 1000
Possible Answers:
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
Correct answer:
Quantity B is greater.
Explanation:
The question asks for the number of positive even and odd integers less than 1000. Because 1000 is not included, the numbers to consider are 1 through 999. Every positive odd integer will have a corresponding even integer (1 and 2, 3 and 4, 5 and 6, etc.) until you get to 999. This gives the positive odd integers one more number than the number of positive even integers.
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Find The Number Of Integers Between Two Other Integers : Example Question #4
Miles is 3 years older than Ashley. Ashley is 5 years younger than Bill. How old is Ashley if together the three of their ages sum to 44?
Possible Answers:
16
10
14
12
8
Correct answer:
12
Explanation:
Miles is 3 years older than Ashley, so M = A + 3. Also, Bill is 5 years older than Ashley, so B = A + 5. Together the three of their ages sum to 44, thus:
A + A + 3 + A + 5 = 44
3A + 8 = 44
3A = 36
A = 12
Answer:
70
Step-by-step explanation:
The difference between will be the number of integers from -25 to 45
Difference = 45 - (-25) = 45 + 25 = 70
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