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Quantitative Comparison Pacing Drill

The very first problem you will see test day will be a Quantitative Comparison one (QC). Indeed, the first seven problems will be QC, unless you decide to skip them (which in the case of the last couple may, for some, be a wise strategy).

Therefore, while prepping, you should make sure not to neglect QC, as it makes up over a 1/3 of the questions (remember, each question is worth the same points). To assess your ability on QC tackle the seven questions below. I’ve tried to make them similar in difficulty to what you’ll see test day.


The first question is the easiest, and the last the most difficult. That is, theoretically, the higher the number the more difficult the problem. I say theoretically because sometimes a question #6 turns out to be more difficult then question #7. Though, a question #3 will never be more difficult than a question #7.

What this means in terms of pacing is that you should not spend too much time at the beginning of the QC section. Yet, many do just that, thinking that they want to make sure to get the first few questions correct. So instead of checking your work several times on the first QC question, try to go through these questions quickly–but accurately–so you can spend more time focusing on the medium level questions.

That said, if you are struggling on the last couple QC (the difficult ones), then you should skip to other parts of the section and spend your time answering easier and medium level questions. With the questions below, you only have seven QC–as I didn’t want to write an entire GRE math section! So do you best, and see how many you can answer correctly in 12 minutes.


1. The average price of a home County X is 250,000. The average price of a home in County Y is 300,000. The average price of a home in both County X and Y is 265,000.

The number homes in County X

The number homes in County Y


2. x^2 - 7 = 0




3. x + 1 = |x – 1|




4. Event X and event Y are independent. The probability of event X is 40%. The probability of events X and Y both occurring is 16%.

The probability of X occurring

The probability of Y occurring


5. A
The number of factors of 3^5

The number of factors of 5^3


6. The area of a square is doubled.

The percent increase in one side of the resulting square



7. 13^x + 12^x = n, where x is a positive integer

The number of distinct numbers that can be the units digit of n



1. A

2. B

3. C

4. C

5. A

6. B

7. B



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53 Responses to Quantitative Comparison Pacing Drill

  1. sonali August 7, 2016 at 1:49 pm #

    can u please confirm for #3,
    If a equation results in no solution then the ans is 0???

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert August 14, 2016 at 1:35 pm #

      Hi Sonali,

      Happy to help! 🙂 The equation does have a solution–the only possible value for x is 0, which is why the answer ends up being C. I hope that makes sense!

  2. Shankar October 9, 2012 at 7:43 am #

    Got them all except for the first. Maybe it’s quite simple. But it didn’t strike me. 😐
    Help pls.

    • Chris Lele
      Chris October 9, 2012 at 1:24 pm #

      Hi Shankar,

      An easy way to look at it is if we had an equal number of homes in County X and County Y, then the average price would be 275,000. Since the average price of a home, when we combine both counties, is less than 275,000, we know that there have to be more homes from County X than from County Y (County X homes average 250,000 so this will pull the average below 275,000).

      Hope that makes sense!

    • JohnKeen October 17, 2012 at 7:28 am #

      Hi Chris,

      Just bombed the GRE (295) but I feel it was due mostly to test anxiety. You mention that the QC questions go from easiest to hardest.
      Are you referring to the exercise or the actual GRE. This knowledge would calm my nerves when I test next time lol.


      • Chris Lele
        Chris October 17, 2012 at 12:21 pm #

        Hi John,

        Yes, on the GRE the QC goes from easy to difficult. It is not always an exact linear curve, as #3 may be harder than #4. That said, #2 will never be more difficult than #6.

        Hope that helps next time around :). Good luck!

  3. Sib October 7, 2012 at 2:08 am #

    Could you please explain the 3rd one completely?

    • Chris Lele
      Chris October 8, 2012 at 3:31 pm #

      If we solve this algebraically we get two equations (keep in mind the rules for absolute values).

      Eq. 1) x + 1 = x – 1
      Eq. 2) x + 1 = -x + 1

      For eq. 1) the two ‘x’s cancel out. So we are left with no solution.
      For eq. 2) we get 2x = 0, x = 0.

      Just like that (C). The reason this question is tricky is it lulls us into thinking that there must be two values for x, therefore the answer could be anything but (C).

      Hope that helps!

  4. kumar September 26, 2012 at 10:59 am #

    hey Chris,

    in question # 7 nothing has been said about the value of x what if x = 0, -1, … ???

    • Chris Lele
      Chris September 27, 2012 at 9:21 am #

      Hi Kumar,

      I must have just made the changes as you were answering the question. As you noted, x can be all sorts of numbers, which really makes everything confusing. Therefore, I added: “x is a positive integer.”

  5. Satish September 25, 2012 at 10:58 am #

    For #4, since X and Y are independent events,
    P(Both X and Y occur)= P(X) P(Y)
    0.16 = 0.4 P(Y)
    P(Y) = 0.4
    Ans: C

    For #7,
    for 13 ^ x, possible units digits are 3, 9, 7, 1 for x=1,2,3,4 resp.(after this the pattern repeats) , for 12 ^ x possible units digits are 2, 4,8,6 for x=1,2,3,4 resp. (after this pattern repeats . so possible units digits for n are 3+2= 5, 9+4=13 i.e 3, 7+8= 15 i.e 5 and 1+ 6= 7. So possible distinct numbers in units digits of n are 3. So the answer is B.

    I hope these are the correct solutions.

    • Chris Lele
      Chris September 25, 2012 at 4:13 pm #


      Those are the answers! And good explanations, to boot :).

      • Petar September 26, 2012 at 7:21 am #

        But he did not account for the possibility that x could be zero. In that case 13^0 +12^0 would equal 1+1, which would give 2 for n. Therefore, 2 is also an answer and the answer should be C.

        • Chris Lele
          Chris September 26, 2012 at 11:59 am #

          Yes, the answer should definitely be C. I’ve re-written the question so as to make ‘B’ the right answer, but thanks for spotting that :). My mistake.

  6. Yasir September 24, 2012 at 6:29 pm #

    Hello all 🙂

    Can someone please give how to solve the last question? I’m totally don’t know how to solve it 😛

    Please help and highly appreciated 🙂

    • Chris Lele
      Chris September 25, 2012 at 4:20 pm #

      Hi Yasir,

      Satish (comment above) provides a good explanation. I’m also posting one below.

  7. Lindsey September 24, 2012 at 5:49 pm #

    I don’t get the answer to 7, I am getting 5 different n digits. x=0, n =2; x=1 n=5; x=2, n=3; x=4 n=7. That’s four different n’s so the answer should be C – correct?

    • Petar September 25, 2012 at 7:11 am #

      Yes, I am getting the same. I think the answer should be C.

      • Chris Lele
        Chris September 25, 2012 at 4:27 pm #

        Hi Peter,

        I’ve posted an explanation below. Hope that helps!

        • jubaer September 26, 2012 at 7:13 am #

          hi chris,

          what if x=0,then we got is not define that x can not be 0.
          sorry,if iam getting something wrong.
          thanks in advance.

          • Chris Lele
            Chris October 8, 2012 at 3:32 pm #

            Hi Jubaer,

            I’ve changed that question as it was a little ambiguous. I did not want n to be a single digit number because it is strange saying that the units digit of a single-digit number. Hopefully it makes sense now!

    • Chris Lele
      Chris September 25, 2012 at 4:26 pm #

      Hi guys,

      This is a tricky one! We only want to look at the last digits of 12^x and 13^x and then sum those two digits. A quick way is to ignore the ‘1’ in front of the ‘2’ and the ‘3’, so essentially we are comparing 2^x + 3^x.

      For x = 1,

      2 + 3 = 5

      x = 2, 4 + 9 = 3

      x = 3, 8 + 7 = 5

      x = 4, 6 + 1 = 7.

      Notice how the ‘5’ repeats, even though ‘2’ and ‘3’, when taken individually, repeat units digit numbers every fourth number. That’s why it is tempting to think the answer is (C). But as the quick math above shows, the answer is (B), because there are only three different units value for ‘n’.

      Hope that helps!

      • Florian September 26, 2012 at 12:04 am #

        Hi Chris,

        what about the option that x = 0 and therefore n would be 2?

        • Chris Lele
          Chris September 26, 2012 at 11:53 am #

          Yes, that is correct. I had intended to write x equals a positive integer–as I’ve done now. Thanks for spotting that. My mistake :).

      • elena September 26, 2012 at 6:00 am #

        Hi, Chris!

        Sorry to bother you once more with this question but I still can’t understand why the answer is B. The problem doesn’t state that x cannot be 0, so we should take x=0 into account which gives us 4 possible units digits for n and the answer is C in that case.

        Thanks in advance!

        • Chris Lele
          Chris September 26, 2012 at 11:53 am #

          Yes, that is my mistake. I’ve corrected the problem :).

          • elena September 26, 2012 at 10:37 pm #

            Thank you Chris! ))

  8. Katie September 24, 2012 at 4:58 pm #

    Can anyone show me how to solve 7?

    • Chris Lele
      Chris September 25, 2012 at 4:27 pm #

      I’ve posted an explanation above!

  9. Tawsif September 24, 2012 at 1:28 pm #

    Would you please explain the answer for number 7 since I am getting these 4 distinct numbers: 0-0=0, 3-2=1, 9-4=5, 27-8=19. It repeats from this point.

    • Tawsif September 24, 2012 at 1:30 pm #

      Okay the question has been changed now.

  10. vaidehi September 24, 2012 at 1:28 pm #

    hi Chris,
    I think 2 nd one will have answer B not A as plus or minus root 7 will have values plus or minus 2.6 which are less than 3.In 3 rd one I have doubt because when we open the absolute value will get 2 solutions one is that there is no solution as x gets cancelled both sides if the expression in absolute value is positive but if expression is negative then x is zero.Can you please provide the explanation??

    • Chris Lele
      Chris September 24, 2012 at 1:36 pm #

      Yes, I just caught that mistake! Thanks for pointing that out :).

  11. Azfar September 24, 2012 at 11:52 am #

    Hi Mag team,

    Its really a fantastic thing that you are putting up questions like this.
    Almost most of us have different answers.
    It would be really nice if you could provide the answers to above questions as well

    • Chris Lele
      Chris September 24, 2012 at 1:29 pm #

      Hi Azfar,

      Now that I believe there are no glitches in the questions, I propose that the Magoosh community provides explanations. If there are still questions afterwards, I’d be happy to provide explanations. I’ll wait to see if there is any traction :).

      • Azfar September 25, 2012 at 11:19 am #

        Hi Chris,
        If you get a chance, can you please explain #4 and #3?

        • Chris Lele
          Chris October 8, 2012 at 3:24 pm #

          #3, the only possible value in which the equation holds true is when x = 0. Therefore the answer has to be (C).

          For #4, if the probability of A is 40% and the probability of both A and B is 16%, then the probability of B must also be 40%. The way we arrive at this is because to get probability of both A and B, we have to multiply them. So (2/5)(Prob B) = 4/25. (Remember 40% = 2/5, and 16% = 4/25). Solving for Prob B we get 40%, thus the answer is (C).

          Hope that makes sense!

  12. Craig September 24, 2012 at 11:14 am #

    Hey guys, I think the 4th is D, because we don’t have a total of outcomes…..

    • Chris Lele
      Chris September 24, 2012 at 1:27 pm #

      Hi Craig,

      I’ve changed #4, as I think it was too confusing a question and not necessarily fair or indicative of what you’d see on the GRE. I’ve changed it to make more sense, hopefully :).

  13. Craig September 24, 2012 at 11:06 am #

    how come number 4 is d? Is it because we don’t know what total of the 40 percent we are taking?

    • Chris Lele
      Chris October 8, 2012 at 3:28 pm #

      I’ve changed this question. Hopefully it makes more sense now :).

  14. Asish September 24, 2012 at 10:43 am #


    Can you please provide explanations for Question Number 2,4 and 7.

    For Question 7 i am only getting 4 different digits 1,5,9 and 0.

    For Question 2 how can the answer be A.


    • Petar September 24, 2012 at 1:07 pm #

      For 2, i also got confused, but that is because we are not careful. The answer is either 7^1/2 or -(7^1/2). Quick calc with the calculator will tell you that 7^1/2 is about 2.6. The other solution is -2.6. Both are less than 3. I think what confused you, was that when you immediately saw 2 solutions with different signs you assumed that the answer has to be D. At least that is what I did. I did not pay attention that B says 3, which is greater than both solutions. Stupid mistake.

      For, 4 you can’t really determine. There is no way to know. If we had the probability of A or B occurring, then we would be able to determine the probability of A and B occurring together.

      • Petar September 24, 2012 at 1:23 pm #

        And i just saw that for 2 the answer is A, when my explanation was that the answer is B. I don’t see how the answer could be A for number 2. I think that is a mistake.

        • Chris Lele
          Chris September 24, 2012 at 1:32 pm #

          Yes, that is definitely a mistake :). The answer should be (B).

          • Muhammad August 7, 2013 at 6:29 pm #

            Hello Chris. How is the answer for the 2nd problem B and not D?

            X^2 – 7 = 0. Can’t that convert to (x+ 7)(x – 7) = 0, where x = -7 or +7?

            A B
            —- —–
            7 > 3


            A B
            ——- ——
            -7 < 3


            • Chris Lele
              Chris Lele August 8, 2013 at 2:20 pm #

              Hmm…I seem to have made a mistake in responding to the student above. Sorry for any confusion! The answer is definitely (D).

    • Chris Lele
      Chris September 24, 2012 at 1:28 pm #

      I’ve changed the questions that you mentioned (#2, 4, and 7) for various reasons (basically they were faulty, etc.). Hopefully, everything should make more sense now.

      • Petar September 24, 2012 at 1:41 pm #

        Hi Chris

        I think there are 4 possible units digits for #7: 2,3,5 and 7.

        • Chris Lele
          Chris October 8, 2012 at 3:16 pm #

          It actually ends up being: 12^1 + 13^1 = 5, 12^2 + 13^2 = 3, 12^3 + 13^3 = 5, 12^4 + 13^4 = 7. Notice how ‘5’ repeats as a units digit. Therefore, there are only three possible units digits.

  15. Nitish September 24, 2012 at 9:25 am #

    Got all of them except 4th. :/
    Would love to see an explanation from someone who got it right.

    • Craig September 24, 2012 at 11:19 am #

      I think it is because we don’t have a total number of outcomes.

      • Chris Lele
        Chris October 8, 2012 at 3:27 pm #

        I’ve changed #4. Hopefully it makes sense now!

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