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10 Most Difficult SAT Questions

Here are the 10 toughest SAT questions from Magoosh SAT: 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…)


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?

  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!




1. A

2. A

3. E

4. E

5. E

6. B

7. E

8. B

9. C

10. C

About the Author

Chris Lele has been helping students excel on the GRE, GMAT, and SAT for the last 10 years. He is the Lead Content Developer and Tutor for Magoosh. His favorite food is wasabi-flavored almonds. Follow him on Google+!

44 Responses to 10 Most Difficult SAT Questions

  1. Ayush M Agrawal April 13, 2014 at 8:49 am #

    Got 8 of them correct. Thank you for the questions Chris. And i will give my SAT exam this June. :)

    • Chris Lele
      Chris Lele April 15, 2014 at 6:26 pm #

      Good luck, Ayush :)

  2. John February 15, 2014 at 5:11 pm #

    I didn’t understand how to solve out 6,7, and 9. Also any general tips for the sat because I’m a really hard worker and still did poorly. Thanks!

  3. DS February 14, 2014 at 2:53 am #

    Do you know of a book that has groups of questions that are ONLY the hard ones from or like the SAT or ACT? Thx.

  4. Sepheroth January 18, 2014 at 2:08 am #

    Hey man i was wondering about the 5th question
    there are no restrictions about the other 3 intgers so couldnt the other 2 numbers also be 90 and 90 as 90 is the largest integer so in retrospect only one of the numbers need to be smaller than 90

    • Lucas
      Lucas January 18, 2014 at 2:41 am #

      You have great instincts! The SAT could definitely trap you with something like that. But in this case, the question does specify “four different integers,” so we know there can’t be three 90s. We instead have to use 90, 89, and 88 for the three large numbers, since those are the three largest different integers allowed. Notice how one word in the question can totally change the answer—this is a perfect example of the SAT being tricky and teaches an important lesson!

  5. Shubham Mathur December 17, 2013 at 3:03 am #

    got a 2380 on the SAT, these questions were really helpful, thx for posting them

    • Chris Lele
      Chris Lele January 6, 2014 at 11:29 pm #

      You are welcome :) — I’m happy you enjoyed the questions.

      And great score!

  6. Danah December 6, 2013 at 11:06 pm #

    I got 7/10 correct (yay), although, my SAT scores suck (except in math) ( ;__; )

    Anyway, I don’t understand question 1. The sentence doesn’t make sense to me with those answers.

    • Chris Lele
      Chris Lele December 9, 2013 at 7:44 pm #

      Good job! Your SAT scores can’t suck too much if you did that well :).

      For #1, what the question is saying is that scientists are happy with the Big Bang theory because they simply don’t have enough data–data that could indicate the theory is not valid.

      Hope that helps!

  7. Ahmed Alshamy December 3, 2013 at 2:30 pm #

    Hey there,

    Thank you very much for these very helpful questions.

    I need to understand number 10 and 7, I am stuck in 7 for not knowing how many millimeters contain what percentage.

    in 10 it’s because I did 9^2÷π=25.78310078, and that’s close to the correct answer but I need to understand the idea!

    Thank you in advance, have a beautiful day :D

    • Chris Lele
      Chris Lele December 3, 2013 at 6:39 pm #

      On number 10, the key is to solve for the radius. Another important thing is on the SAT never change π to 3.14. Just keep it as π. If we know the circle has an area of 9π, then its radius must equal 3 (9π = πr^2, r = 3).

      Each length of the equi. triangle is therefore 6. Using the area for equi. formula (s^2√3)/4, where s corresponds to the side of the equi. triangle, we get 9√3.

      For number 7, think of the problem has a weighted average. If equal parts of each solution were put in a new container, then the resulting mixture would contain 20% alcohol. The resulting mixture, however, contains 25% alcohol. Therefore, more of solution Y has to be in the mix? How much more?

      Quick way to figure this is out is find the ratio between solution Y – resulting mixture (30 – 25) = 5, and resulting mixture and solution X (25 – 10) = 15. That gives us 1:3. Therefore there is three times as much solution Y as X: 3 x 200 = 600.

      Hope that makes sense!

      • Nikita Jivrajani January 1, 2014 at 5:40 pm #

        Hey Chris,

        For number 10 the answer is 12 root 3 not 9 root 3. Yes, there is a 6 however that is the diameter of circle O. Once one has the diameter, he/she could simply use the 30-60-90 triangle as a reference and find the base of the triangle, segment CB. CB comes out to be 4 root 3. Using the formula A=(1/2)base times height : [(1/2)(4 root 3)(6)] the area comes out to be 12 root 3.

        Hope this helped =)

        • Chris Lele
          Chris Lele January 6, 2014 at 9:27 pm #

          Oops, it looks like I made a very basic error there. Clearly the diameter is not the same as the length of a leg of the equilateral triangle. Morale of the story: don’t rush :).

          • Hmm April 11, 2014 at 9:21 am #

            So .. trigonometry is in the syllabus of SAT ?

            • Chris Lele
              Chris Lele April 15, 2014 at 6:25 pm #

              Actually, it’s not. You’ll just have questions that use basic geometry. For instance, you won’t have to know how to derive the length ratio of a 30:60:90 triangle. That’s given to you at the beginning of the section.

              The new SAT, the one set to debut in 2016, will have trigonometry, or so it’s rumored :).

  8. Anzie December 2, 2013 at 11:11 pm #

    Hi Chris,

    I don’t understand number 5 at all whatsoever. Could you please explain it to me? Also, regarding number 5, why is the answer not 1? The question doesn’t ask for the highest possible smallest integer that could result in the mean? It merely asks for the smallest, so 1 should be applicable, shouldn’t it?

    Thank you!

    • Chris Lele
      Chris Lele December 3, 2013 at 6:27 pm #

      Hi Anzie,

      It does seem that way, that ’1′ should be the answer. But this is a tricky one. If we actually add up the four integers, x + 88 + 89 + 90 = 300 we get 33 for x. x cannot equal ’1′ because the two integers in the middle have to be less than 90, and the greatest possible numbers they can equal are 88 and 89 respectively.

      Hope that helps shed some light :).

      • Viraj December 23, 2013 at 2:58 pm #

        I do not get number 9 at all because I tried to plug in 60 for all the values, and only choice B. worked using that method. The only way that I could see choice C. working is if there was a fraction bar between the ks and 60c like this:

        ks —–

        Is this how it was intended to be written? I tried to follow the choices given to me using order of operations.

        Thanks and Happy Holidays!

        • Viraj December 23, 2013 at 2:59 pm #

          #9 was the only one I got wrong and I am in 7th grade. :P

        • Chris Lele
          Chris Lele January 6, 2014 at 11:28 pm #

          Hi Viraj,

          Good job on getting most of the questions correct!

          Yes, on question #9, it should be written as ks/60 (that mark is the same as the horizontal line dividing the numerator and the denominator).

          Hope that helps!

  9. Rose November 11, 2013 at 12:44 am #

    Im stuck on number 5 could you please explain? I was thinking that if there are no restrictions on what the other possible integers could be then couldn’t 1 be one of them and then the other two would add up to the rest? That was my thinking but I guess I was wrong. Could you please explain, thank you so much!!

    • Chris Lele
      Chris Lele November 18, 2013 at 10:48 pm #

      Hi Rose,

      So we know that the sum of the average has to be 300 (75×4) = 300. If the largest number is 90, then the next largest numbers could be 89 and 88. Remember, we want to maximize these two numbers so that the remaining number can be as small possible. This gives us 90+89+88+x = 33 (E).

      Hope that makes sense :)

  10. mAdCap October 23, 2013 at 5:12 pm #

    Well, tell me if I am wrong , but there is something off about question 8. Even I came up with 16(b) at first but then I considered this situation …

    Suppose Sally is as bad as a student as myself and managed to get 4/16 questions correct , earning her 4*9=36 marks .

    However she skipped or got wrong 12/16 questions , losing a total of 12*7=84 marks .

    So, her total score is = ta ta ra ra … negative 48.
    You see my point?

    • Chris Lele
      Chris Lele November 5, 2013 at 6:50 pm #

      Hi Madcap,

      It seems that we already have a given piece of information: the student scored zero points on the test. The only way this is possible, given the test has fewer than 30 questions, is if there are 16 questions on the test. The question is not saying, if the test had 16 questions, then how many points must Sally have gotten? She could have gotten a bunch of different points, including, as you mentioned, -48.

      Hopefully that makes sense :)

  11. Ash October 17, 2013 at 7:17 pm #

    I’ve been studying for a few weeks and could only get 5 right (barely)…I am so gonna to bomb the SAT…

    • Chris Lele
      Chris Lele November 5, 2013 at 6:53 pm #

      Hi Ash,

      Not at all — these are all difficult questions. Only about 25% of the questions on the SAT are this difficult. So if you are getting half of the difficult ones correct, you are probably do even better on the medium and easy questions.

      Good luck–and don’t get discouraged :)!

  12. Student August 21, 2013 at 12:37 am #

    Could you please explain how to do number 10? I keep getting the answer 27 times the square root of three. Thank you.

    • Student August 21, 2013 at 12:43 am #

      I just answered my question, sorry ^^.

      • Margarette
        Margarette August 23, 2013 at 11:40 pm #

        No problem! :) Glad you figured it out!

  13. Ned August 4, 2013 at 6:38 pm #

    I got 9/10 correct and I have a 1960 SAT Score. These questions were helpful though

    • Chris Lele
      Chris Lele August 27, 2013 at 5:59 pm #

      Hi Ned,

      These questions are very tough — so you did well. I’m guessing you do pretty well on the quant, maybe close to 700. Even then, on the SAT, those “easy” and “medium” questions can get you to go :).

      Good luck!

  14. Dkgladr July 30, 2013 at 2:55 pm #

    Hi there I’m 13 and in 8th grade in this test I got 4/10 ….I’m feeling bad

    • Chris Lele
      Chris Lele August 27, 2013 at 6:43 pm #


      Wow, that’s actually a great score, for someone who isn’t even required to take the PSAT. Some of the questions above are taken from GMAT and GRE tests, which are for those looking to go to graduate school (some of the smartest people around :)). So, I’d say you are doing pretty well :).

  15. Ankush November 1, 2012 at 4:09 am #

    sat exam math is so easy as compared to iits math,its almost like nothing

    • Chris Lele
      Chris November 2, 2012 at 7:05 pm #

      Hi Ankush,

      The general SAT math portion is meant more to test one’s thinking/problem solving skills. It is definitely not too difficult, and sometimes getting a perfect score for us seasoned tutors, is making sure we don’t make a careless error. The SAT math subject tests, on the other hand, are much more difficult, and are targeted towards those who want to study in math/science fields.

    • Akshita Bhalla November 20, 2012 at 11:49 am #

      Are you Ankush Sharma from FIITJEE Chandigarh?????

  16. julie October 6, 2012 at 10:50 am #

    Nice Dude It was pretty helpful but got just 6 so sad :(

    • Margarette
      Margarette October 8, 2012 at 5:49 pm #

      Hi, Julie! 6/10 certainly isn’t bad to start out with– I’m sure that after studying for a few weeks, you could score even higher :)

  17. mayank May 25, 2012 at 5:15 pm #

    thanx dude got 9 of dem correct and i hav got 2300 in SAT

    • Chris Lele
      Chris May 26, 2012 at 4:15 am #

      Great! That shows that the questions are pretty tough, and that you are very good at the SAT :).

    • Scott January 8, 2014 at 11:32 pm #

      Whoa…I got the exact same stats. THere’s really is a correlation.

  18. Antaryirreree January 24, 2012 at 3:41 am #

    Hello! Just want to say thank you for this interesting article! =) Peace, Joy.

    • Chris Lele
      Chris January 25, 2012 at 11:05 pm #

      Thanks for the kudos!

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