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.

A The number homes in County X

B The number homes in County Y

2.

A X

B 3

3. x + 1 = |x – 1|

A x

B 0

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%.

A The probability of X occurring

B The probability of Y occurring

5. A The number of factors of

B The number of factors of

6. The area of a square is doubled.

A The percent increase in one side of the resulting square

B 50%

7.

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

What should be the time spacing based on timing by splitting the the 20 questions into 4 sections of comprising of 5 questions each To simplify 5 questions in how many minutes, 10 questions in how many minutes I keep loosing out usually in the Data interpretation(DI) part and end up not completing the paper. So, usually the DI comes in around 15-16, with how many mintues before I should reach there so that, I can complete the test

Magoosh Test Prep ExpertAugust 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!

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).

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.

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.

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).

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.”

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.

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.

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?

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!

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’.

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.

Hey, 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.

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??

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

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 :).

#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).

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 :).

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.

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.

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.

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.

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What should be the time spacing based on timing by splitting the the 20 questions into 4 sections of comprising of 5 questions each

To simplify 5 questions in how many minutes, 10 questions in how many minutes

I keep loosing out usually in the Data interpretation(DI) part and end up not completing the paper. So, usually the DI comes in around 15-16, with how many mintues before I should reach there so that, I can complete the test

Hi Sabarish,

Have you seen our blog on GRE Quant pacing? I think it will answer many of your questions 🙂

can u please confirm for #3,

If a equation results in no solution then the ans is 0???

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!

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

Help pls.

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!

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.

Thanks

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!

Chris,

Could you please explain the 3rd one completely?

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!

hey Chris,

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

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.”

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.

Satish,

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

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.

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.

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 🙂

Hi Yasir,

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

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?

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

Hi Peter,

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

hi chris,

what if x=0,then we got 1+1=2.it is not define that x can not be 0.

sorry,if iam getting something wrong.

thanks in advance.

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!

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!

Hi Chris,

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

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 :).

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!

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

Thank you Chris! ))

Can anyone show me how to solve 7?

I’ve posted an explanation above!

Hey,

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.

Okay the question has been changed now.

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??

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

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

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 :).

Hi Chris,

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

#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!

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

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 :).

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

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

Chris,

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.

Thanks

Asish

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.

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.

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

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

while,

A B

——- ——

-7 < 3

?

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

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.

Hi Chris

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

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.

Got all of them except 4th. :/

Would love to see an explanation from someone who got it right.

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

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