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Chris Lele

10 Most Difficult SAT Questions

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 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!
 
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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.
 
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Humans make errors. We make errors of fact and errors of judgment. We have blind spots in our field of vision and gaps in our stream of attention. Sometimes we can’t even answer the simplest questions. Where was I last week at this time? How long have I had this pain in my knee? How much money do I typically spend in a day? These weaknesses put us at a disadvantage. We make decisions with partial information. We are forced to steer by guesswork. We go with our gut.

That is, some of us do. Others use data. A timer running on Robin Barooah’s computer tells him that he has been living in the United States for 8 years, 2 months and 10 days. At various times in his life, Barooah — a 38-year-old self-employed software designer — has also made careful records of his work, his sleep and his diet.

A few months ago, Barooah began to wean himself from coffee. His method was precise. He made a large cup of coffee and removed 20 milliliters weekly. This went on for more than four months, until barely a sip remained in the cup. He drank it and called himself cured. Unlike his previous attempts to quit, this time there were no headaches, no extreme cravings. Still, he was tempted, and on Oct. 12 last year, while distracted at his desk, he told himself that he could probably concentrate better if he had a cup Coffee may have been bad for his health, he thought, but perhaps it was good for his concentration.

Barooah wasn’t about to try to answer a question like this with guesswork. He had a good data set that showed how many minutes he spent each day in focused work. With this, he could do an objective analysis. Barooah made a chart with dates on the bottom and his work time along the side. Running down the middle was a big black line labeled “Stopped drinking coffee.” On the left side of the line, low spikes and narrow columns. On the right side, high spikes and thick columns. The data had delivered their verdict, and coffee lost.

He was sad but also thrilled. Instead of a stimulating cup of coffee, he got a bracing dose of truth. “People have such very poor sense of time,” Barooah says, and without good time calibration, it is much harder to see the consequences of your actions. If you want to replace the vagaries of intuition with something more reliable, you first need to gather data. Once you know the facts, you can live by them.

Barooah knows that this behavior is abnormal. He is an outlier. But why does what he does seem so strange? In other contexts, it is normal to seek data. A fetish for numbers is the defining trait of the modern manager. Corporate executives facing down hostile shareholders load their pockets full of numbers. So do politicians on the hustings, doctors counseling patients, and fans abusing their local sports franchise on talk radio. Charles Dickens was already making fun of this obsession in 1854, with his sketch of the fact-mad schoolmaster Gradgrind, who blasted his students with memorized trivia. But Dickens’s great caricature only proved the durability of the type. For another century and a half, it got worse.

Or, by another standard, you could say it got better. We tolerate the pathologies of quantification — a dry, abstract, mechanical type of knowledge — because the results are so powerful. Numbering things allows tests, comparisons, experiments. Numbers make problems less resonant emotionally but more tractable intellectually. In science, in business and in the more reasonable sectors of government, numbers have won fair and square.

For a long time, only one area of human activity appeared to be immune. In the cozy confines of personal life, we rarely used the power of numbers. The techniques of analysis that had proved so effective were left behind at the office at the end of the day and picked up again the next morning. The imposition, on oneself or one’s family, of a regime of objective record keeping seemed ridiculous. A journal was respectable. A spreadsheet was creepy. And yet, almost imperceptibly, numbers are infiltrating the last redoubts of the personal. Sleep, exercise, food, mood, location, alertness, productivity, even spiritual well-being are being tracked and measured, shared and displayed.
 

4. The use of Gradgrind (sixth 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 last paragraph, the author would likely view the use of numbers to track intimate aspects of people’s lives as

A) intrusive.

B) inevitable.

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. 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?

10mdnsq_img1

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.

 

Improve your SAT or ACT score, guaranteed. Start your 1 Week Free Trial of Magoosh SAT Prep or your 1 Week Free Trial of Magoosh ACT Prep today!

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About Chris Lele

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 8 million views.

You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog!

You can follow him on Twitter and Facebook!


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