10 Most Difficult SAT Questions

Difficult SAT practice questions - magoosh

Here are the 10 toughest SAT questions from our New SAT Prep, as well as the 10 toughest questions from our current “old” SAT Prep. See how many you get right by checking your answers at the end of the post!

(P.S. If you can get these right, then you should check out Harvard SAT scores and Yale SAT scores…)

10 Toughest New (Redesigned) SAT Questions

These are the ten most difficult SAT practice questions you’ll find in our New SAT Prep (which helps students study for the redesigned SAT, which will debut in March 2016). Let us know how you do!

_____

The common setup is researchers will divide subjects into two groups, one of which is allowed to use the Internet after finishing the task, the other of which must finish the task until completion. Yet another common setup allows subjects unfettered use of the Internet when trying to complete the task. Not surprisingly this last group acted 1 worse on tests of productivity. 2 Not so surprisingly the group that used 10 minutes of web access as an incentive, tended not only to finish the task sooner than the group without any web access but also 3 worked with more vigor when their Internet time was up.

1.

A) NO CHANGE

B) the worst

C) badly

D) more poorly

Tip: Carefully read the sentences that come before this question.

2. Within the context of the paragraph, the underlined portion should be changed to which of the following?

A) NO CHANGE

B) Unsurprisingly

C) Less surprisingly

D) What is surprising is that

Tip: The New SAT Writing section will be a lot about context. What I mean by that is to find the answer you’ll have to read the sentences before and after the sentence in which the question appears. Only that way will you have the evidence you need to support your answer.

3.

A) NO CHANGE

B) to work

C) they worked

D) to be working

Tip: Whenever you have the construction “not only VERB A but also VERB B”, the two verbs must always be parallel.

_____
Read the article, The Data-Driven Life, via the New York Times and answer the following questions.

4. The use of Gradgrind (eighth paragraph) as a supporting example is most problematic because it

A) conflates the accumulation of academic facts with the process of quantification.

B) undermines the main thesis of the passage by citing a dated example.

C) accepts without reservation that a trend has intensified with the passing of time.

D) provides an example of a process the author ultimately appreciates.

Tip: Think about the author’s main point. Does it make sense to use Gradgind as an example? Why not? (Your answer to that second question should match the correct answer).

5. In the tenth paragraph, the author would likely view the use of numbers to track intimate aspects of people’s lives as

A) intrusive.

B) inevitable.

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C) ominous.

D) disruptive.

Tip: You will need to understand the thrust of the entire passage to be able to answer this. Don’t just jump to the conclusion that the answer must have a negative connotation.

6. Of the solutions for 3x^3 + 4x^2 - 5x = 0, which has the greatest value?

A) 0

B) (-2 -sqrt{19})/3 

C) (-2 + sqrt{19})/3

D) (-4 + sqrt{19})/3

Tip: Remember to look at the answers accompanying a question. They will sometimes give you an idea of how to approach this question. In this case, the set up of the answer choices should remind you of a certain formula.

7. For x * t ≠ 0, which of the following equations is equivalent to 81x^8 - 16t^8 = 9x^4 + 4t^4?

A) 9x^4 + 4t^4 = 0

B) (3x^2 + 2t^2)^4 = 1

C) (3x^2 - 2t^2)(3x^2 +2t^2) = 1

D) (3x^2 - 2t^2)(3x^2 + 2t^2) (9x^4 + 4t^4) = 0

Tip: Be very careful when factoring out each side. And look at the format of the answer choices. They should show you that you are not combining like terms per se but are using FOIL.

8. The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?

A) 1

B) 29

C) 30

D) 33

Tip: This is a logic question. Setting up an equation for average will only get you so far. Think in terms of what number could be the smallest possible value.

9. Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

A) 250/3

B) 500/3

C) 480

D) 600

Tip: You can solve this question by setting up an equation…or you can think of this problem as a weighted average.

10. If the circle with center O has area 9π, what is area of equilateral triangle ABC?

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A) 9√3

B) 18

C) 12√3

D) 24

Tip: Remember to think of the necessary steps to arrive at the answer. Once you’ve worked those steps at then apply the math. And don’t forget – the fundamental geometry formulas are always in the beginning of each math section.
Answers:

1) B

2) D

3) B

4) A

5) B

6) C

7) C

8) D

9) D

10) C

10 Toughest (Old) SAT Questions

These are the ten most difficult questions you would have found in our Magoosh SAT Prep if you had taken the old version of the SAT exam (the one given until January 23, 2016). You’re still welcome to try them (they’re tricky), but you probably won’t see anything like this on the redesigned SAT. Maybe be glad you’re missing out? 🙂
Directions: Choose the words that best fit the blanks:

1. Cosmologist Martin Rees has cautioned that our present satisfaction with the big bang explanation for the creation of the universe may reflect the ——- of the data rather than the ——- of the theory.

  1. paucity . . validity
  2. genius . . accuracy
  3. relevance . . scope
  4. destruction . . core
  5. persuasiveness . . reality

Tip: Try to come up with your own word(s) for the blank. If you are unable to, it is okay, as a last resort, to plug the answer choices back in the blank. Sometimes meaning emerges this way and the sentence makes sense.

 

2. Apparently the groom was very nervous: one moment he would be ——-, rambling on to his best man about silly, meaningless things, and then abruptly he would turn ——- and could not be prompted to say anything

  1. garrulous . . reticent
  2. grandiose . . taciturn
  3. vociferous . . effusive
  4. melodious . . timorous
  5. munificent . . utilitarian

Tip: Match the clues with the blanks and then find a word that matches. Remember you only need to work one blank at a time, eliminating those answer choices that don’t work. Then, when you move on the other blank, you only have a few possible answers to deal with.

 

Directions: Choose the correct version of the sentence:

3. Regardless of the fact of the ridge-top condominiums’ aesthetics, every investor has enjoyed a high return on their investment.

  1. Regardless of the fact of the ridge-top condominiums’ aesthetics, every investor has enjoyed a high return.
  2. Regardless of the ridge-top condominium aesthetic, every investor has had a high return to enjoy.
  3. Regarding the aesthetics of the ridgetop condominiums, every investor has enjoyed a high return.
  4. Regardless of the fact of the ridge-top condominiums’ aesthetics, a high return by every investor has been enjoyed.
  5. Regardless of the aesthetics of the ridge-top condominiums, every investor has enjoyed a high return

Tip: Remember to retain the original meaning of the sentence – investors are enjoying an investment. If you remove investment than they are enjoying (having a good time) the high return (money). Which, while highly likely, changes the overall meaning of the sentence.

 

4. Included in the cost of many services and products sold in Great Britain, American tourists may not realize that they do not necessarily have to pay the value added tax (VAT).

  1. Included in the cost of many services and products sold in Great Britain, American tourists may not realize that they do not necessarily have to pay the value added tax (VAT).
  2. Included in the cost of many services and products which are sold in Great Britain, tourists from America may not realize that they do not necessarily have to pay the value added tax (VAT).
  3. American tourists may not realize that they do not necessarily have to pay the value added tax (VAT) that are included in the cost of many services and products sold in Great Britain.
  4. In addition to the cost of many services and products sold in Great Britain, American tourists may not realize that they do not necessarily have to pay the value added tax (VAT).
  5. American tourists may not realize that they do not necessarily have to pay the value added tax (VAT) that is included in the cost of many products and services sold in Great Britain.

Tip: Remember to make sure that the nouns in the sentence are being modified correctly. American tourists are not included in the cost of many services.

 

Select the answer that best answers the question:

5. The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?

  1. 1
  2. 19
  3. 29
  4. 30
  5. 33

Tip: This is a logic question. Setting up an equation for average will only get you so far. Think in terms of what number could be the smallest possible value.

 

6. If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?

Note: Figure not drawn to scale

  1.  3/4
  2. 5/4
  3. 6/5
  4. 4/3
  5. 5/3

 Tip: If you are not sure how to set up the question algebraically you can also solve using the given information. In this case you can assume the answer is (C). So if the side of the small square is 6/5 do we end up with 25 as the area of the big square? Remember the big square has an area that is twice as big as that of the small square (in this question the algebraic approach is better).

 

7. Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

  1. 250/3
  2. 500/3
  3. 400
  4. 480
  5. 600

Tip: You can solve this question by setting up an equation…or you can think of this problem as a weighted average.

 

8. On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?

  1. Cannot be determined
  2. 16
  3. 19
  4. 21
  5. 24

Tip: This is a question based more on logic. Do not try to set up an equation but think in terms of how many 7-point questions you need and how many 9-point questions you need for the two to cancel out.

 

9. A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform k calculations?

  1. 60ks/c
  2. ks/c
  3. ks/60c
  4. 60c/ks
  5. k/60cs

Tip: Assign values to k, s, and c if you have difficulty thinking through this question algebraically.

 

10. If the circle with center O has area 9π, what is area of equilateral triangle ABC?

  1.  
  2. 18
  3. 24

Tip: Remember to think of the necessary steps to arrive at the answer. Once you’ve worked those steps at then apply the math. And don’t forget – the fundamental geometry formulas are always in the beginning of each math section.

For this last question, try it out in Magoosh SAT to see the answer and video explanation!

 

 

Answers:

1. A

2. A

3. E

4. E

5. E

6. B

7. E

8. B

9. C

10. C

 

Which exam do you think is more difficult – the current or new SAT? 🙂

 

Looking for answers to the most challenging Official SAT Study Guide math questions? Use our Official SAT Study Guide Question Explanations and watch test prep expert Chris Lele explain the smartest way to solve new SAT math questions.

 

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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