SAT Digital Practice #23

These questions come from The Princeton Review DIGITAL SAT premium Prep. They are from the first test in the Math section. This section has a wide range of difficulty levels.

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A data set containing only the values 2,2,9,9,9,16,16,16,16,26,26, and 26 is represented by a frequency table. Which on the following is the correct representation of this data set?

• 
• 
• 
• 

Answer explanation

I'd consider this an "easy" question.

The tables have a column for "number" and one for "frequency"

Frequency means how often or "frequent" does the number show up.

Option C and D don't make sense as they dont have the 4 numbers listed in the "number" column. Cross those off.

The number 9 happens 3 times which matches with option B

Answer explanation

I'd call this easy to moderate

Working backward from the answers will be easiest for most people. Remember that the approach is:

(first term) * (first term)

(first term) * (last term)

(last term) *(first term)

(last term) *(Last term

Finally combine any like terms

Look at option C:

(first term) (first term) = x*x or x^2

(first term) * (last term) = (x)(7) or 7x

(last term) (first term) = (-8)(x) or -8x

(last term) *(Last term) = (-7)(8) or -56

Finally combine any like terms

x^2 + 7x -8x - 56 = x^2 -x - 56

A carpenter hammers 10 nails per minute and installs 7 screws per minute during a project. Which of the following equations represents the scenario if the carpenter hammers nails for x minutes, installs screws for y minutes, and uses a combined total of 200 nails and screws?

Answer explanation

I'd call this an easier logic question

1. It seems like the first term is supposed to represent the nails, the second the screws and the number after the equal must mean total of either time or nails and screws.

"10 nails per minute" with "x minutes" would seem to make 10x represent the number of nails in x minutes (i'm not thinking C or D are best options)

if 10x is nails in x minutes and 7y is screws in y minutes the these are total nails and screw which the problem says is 200.

C is the best option

What is the measure of angle F in the triangle DEF, where angle D is 73 degrees and angle E is 35 degrees?

• 38 degrees

• 72 degrees

• 108 degrees

• 126 degrees

Answer explanation

I'd rate this as an "easy" question

You are expected to know that a triangles' angles will add to equal 180.

so 180 - 73 - 35 = 72 so B

The total amount of plastic remaining to be recycled in a facility over x shifts is represented by the graph above. Which of the following represents the y-intercept of the graph

• The total amount of plastic remaining at any given time

• the number of shifts it will take to finish recycling the plastic

• The amount of plastic that is recycled per shift

• The initial amount of plastic to be recycled.

Answer explanation

I'd call this a "moderate" difficulty problem

The question suggests that the two events being represented here are:

how much plastic needs to be recycled

How many shifts have taken place

The graph is also showing the 1st quadrant so I'm only dealing the increases in these events.

I would expect that after each shift the amount of plastic left should go down.

If we put the number of shifts along the x axis each corresponding y number is smaller.

D represents this option

The table shows the condition and subject type for 200 textbooks at a bookstore.

What is the probability that a textbook chosen at random will be a new textbook? (express your answer as a decimal or fraction, not as a percent)

*on SAT you only have 5 boxes for your answer.

Answer explanation

I'd call this an "easy" question in probability that requires reading comprehension

There is a lot of information in the table that we don't really care about. The question only asks for how many NEW books compared to how many TOTAL books.

There are 120 NEW books. There are 200 TOTAL books to choose from. So our Fraction would be: 120/200

The direction say to you can express this as a fraction or a decimal NOT a percent. So there are lots of options:

120/200 OR 12/20 OR 0.6 OR 6/10 OR 3/5

A random sample of 5,000 students out of 60,000 undergraduate students at a university were surveyed about a potential change to the registration system. According to the survey results, 75% of the respondents did not support the existing registration system, with a 4% margin of error. Which of the following represents a reasonable total number of students who did not support the existing registration system?

• 1,250

• 3,750

• 13,800

• 43,800

Answer explanation

I would classify this as a "moderate" difficulty level. There is a phrase you might not be familiar with.

The question asks for "a reasonable number of students that did NOT support" It also states that there are 60,000 students and 75% did NOT support. So 0.75 times 60,000 gives 45,000.

This is NOT an answer choice. "margin of error" means our answer could be off. So the real answer might be as much as 4% higher than we think or 4% lower than we think.

The only choice in that range is D

Note that 5,000 is not used in the work. Sometimes they put extra info in just to throw you off.

Answer explanation

"moderate" Needs a little algebra

Since there is an a in the denominator lets multiply to get rid of that

32/a = a - 4 becomes

a(a-4) = 32 and setting equal to zero gives

a^2 - 4a - 32 = 0 Now we FACTOR

(a - 8) ( a +4) = 0 How did you get that? (-8)*(4) = -32 AND (-8) + (4) = -4

So one of those parentheses gives the answer

a - 8 = 0 makes a = 8 and a + 4 = 0 makes a = -4

so a = -4

After a hot air balloon is launched from a plateau 1,000 meters above sea level, it rises at a constant rate of 750 meters per minute. Which of the following best describes the function used to model the balloon's distance above sea level over time?

• Increasing linear

• Increasing exponential

• Decreasing linear

• Decreasing exponential

Answer explanation

"moderate"

there is no "math" here but you do need to know some terms and be able to visualize the scenerio.

The phrase "at a constant rate" suggests that the balloon is going straight rather than curved so the top 2 graphs make more sense

Since it is going "up" the first one makes sense.

Recognizing this is a LINE so LINEAR and is going UP so INCREASING makes option A logical