Please help me with these SAT math questions

Test Preparation
1

The table above(in this case below since I can’t copy and paste the image) shows some values for the function f. If f is a linear function,what is the value of a +b?
X f(x)
0 a
1 24
2 b

Here are the answer choices
(A) 24
(B) 36
© 48
(D) 72
(E) It cannot be determined from the
information given.

And her is another question I struggled with:
The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set.
(A) 25
(B) 26
© 50
(D) 51
(E) 52

And this one:
At a bottling company, machine A fills a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between 11 7/8 and 12 1/8. If machine B accepts a bottle containing n fluid ounces, which of the following describes all possible values of n?
(A) I n-12 I = 1/8
(B) I n+12 I=1/8
© I n-12 I<1/8
(D) I n+12 I<1/8
(E) I n-12 I> 1/8
In case it looks weird I= absolute value signs.
Please include clear and concise explanations on how you answered the question
Anyways thanks! :slight_smile:

2

Also, if you only feel like helping me with only one problem that’s fine.

3

@Tookme10mins Based on the info given:
For the first problem, the answer is E. We are only given one complete point, and we need to know the slope (or at least one other point) to figure out the values of a and b.

For the second problem: the set of integers is -25 to 26 inclusive. The reason why the sum is 26 is because each positive integer has a negative integer to cancel it out except for 26. Therefore, there are 52 integers in the set.

4

Thank you soo much. I thought no one was going to answer and I was kind of freaking out. Thanks again

5

@Tookme10mins Also, to answer your last question:
The answer is C. All I did was plug in values between the two numbers. Since floz. “n” must be between 95/8 and 97/8, all you have to do is take two or three values between them. I used 11.9 and 12 for simplicity sake. The absolute value of the difference is always less than .125: abs(11.9-12)=.1 and abs(12-12)=0.

6

Thank you so much! :smiley:

7

on the answer key it said the first problem is C I honestly don’t know why… maybe if I spend a long time trying to figure out the answer itshall be revealed…hopefully…

8

@michelle426 the first problem is solvable.

@Tookme10mins For the first one, note that 1 is halfway between 0 and 2, and because f is linear (and hopefully with a defined slope), 24 will be halfway between a and b. So a+b = 2*24 = 48.

9

@Tookme10mins Oh sorry, I misread the information you provided me. I was eating at the time. @MITer94 provided the correct answer and explanation.

10

Oh no it’s fine.

11

@ MITer94 thank you so much. I don’t know why but that one really confused me, but you helped so thanks

12

For this one:
And her is another question I struggled with:
The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set.
(A) 25
(B) 26
© 50
(D) 51
(E) 52

It will take you 51 integers to get a sum of 0 (from -25 to -1 must be cancelled out with 1-25, and you’ll need the 0 to make them consecutive.)

Then you’ll need to add in one more (26) to get you the sum of 26.

13

Here are the answersin case anyone was wondering. For the first one the answer was C. For the second one the answer was E. For the last one the answer was C. Thanks for your help everyone! : )