Get ready to enhance your GMAT score with these challenging GMAT practice questions designed to help you excel! 1. The distance from the Y-axis to point K is 1/3 of the distance from the X-axis to point K. If the coordinates of K are (-3, y), what is the distance between point K and X-axis? A. 1/2 B. 1 C. 3 D. 4.5 E. 9. 2. What is the area of a region enclosed by |x/3|+|y/9|=10? A. 675 B. 1350 C. 2700 D. 5400 E. 10800 3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x? A. 1 B. 1.25 C. 2 D. 2.5 E. 4 4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool? A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters 5. For a certain set of numbers, if x is in the set, then both -x^2 and -x^3 are also in the set. If the number \frac{1}{2} is in the set, which of the following must also be in the set? I. -1/64 II. 1/64 III. 1/2^(1/3) A. I only, B. II only, C. III only, D. I and II only E. I, II and III 6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have? A. 37 B. 38 C. 39 D. 40 E. 41 7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? A. 16% B. 25% C. 32% D. 48% E. 75% 8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school? A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes 9. If x and y are integers and x + y = -12, which of the following must be true? A. Both x and y are negative B. xy > 0 C. If y 0 D. If y > 0, then x 0 10. If n is a non-negative integer and the remainder when 3^n is divided by 4 is a multiple of 3, then which of the following must be true? I. n^2 divided by 4 yields the reminder of 1 II. (-2)^n is less than 0 III. n is a prime number A. I only B. II only C. III only D. I and II only E. II and III only BONUS QUESTION: 11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue? A. 7/8 B. 3/4 C. 2/3 D. 5/8 E. 3/8 The solutions can be found below on this page.

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oss198

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22 Nov 2014, 08:01

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Bunuel

I. n^2 divided by 4 yields the reminder of 1 --> odd^2 divided by 4 always yields the reminder of 1. So, this statement must be true.

Can someone explain that rule please?

Bunuel

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22 Nov 2014, 08:06

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oss198

Bunuel

I. n^2 divided by 4 yields the reminder of 1 --> odd^2 divided by 4 always yields the reminder of 1. So, this statement must be true.

Can someone explain that rule please?

Not much there to explain...

Odd^2 divided by 4 always yields the reminder of 1:
1^2 = 1 divided by 4 yields the reminder of 1;
3^2 = 9 divided by 4 yields the reminder of 1;
5^2 = 25 divided by 4 yields the reminder of 1;
7^2 = 49 divided by 4 yields the reminder of 1;
...

Or: odd^2 = (2x + 1)^2 = 4x^2 + 4x + 1 --> divided by 4 yields the reminder of 1

Hope it's clear.

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18 Jan 2015, 06:51

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Bunuel

9. If x and y are integers and x + y = -12, which of the following must be true?
A. Both x and y are negative
B. xy > 0
C. If y < 0, then x > 0
D. If y > 0, then x < 0
E. x - y > 0

Look at option D: if y is positive, then x must be negative in order the sum of x and y to be negative.

Answer: D.

Hi,

By this logic, then shouldn't even Answer C be ok? Can you please explain why D satisfies the "must" rule and C does not?

Thank you,

TO

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18 Jan 2015, 07:33

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thorinoakenshield

Bunuel

Hi,

By this logic, then shouldn't even Answer C be ok? Can you please explain why D satisfies the "must" rule and C does not?

Thank you,

TO

Given x + y = -12: the sum of two numbers is negative.

(C) says if y is negative, then x is positive. Well, that's not necessarily true: if y is negative, x can be positive, negative, or 0. For example:
y = -20, x = 8.
y = -10, x = -2.
y = -12, x = 0.

(D) says if y is positive, then x is negative. Now, if y is positive, then for the sum of x and y to be negative (-12), x must be negative. If it's not, the sum of x and y would be positive, not negative -12.

Does this make sense?

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01 Feb 2017, 20:16

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Bunuel

Dear Bunuel, What if C. If $y < 0$, then $x > 0$, $x = 12$, $y = -24$, $x + y = 12 - 24 = -12$?

Bunuel

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02 Feb 2017, 06:14

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ziyuenlau

Bunuel

Dear Bunuel, What if C. If $y < 0$, then $x > 0$, $x = 12$, $y = -24$, $x + y = 12 - 24 = -12$?

C is not always true. y < 0 does not necessarily mean that x > 0. For example, consider y = -1 and x = -11.

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Bunuel

8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?
A. 15 minutes
B. 20 minutes
C. 25 minutes
D. 30 minutes
E. 210 minutes

Let the usual speed be $s$ and usual time $t$ minutes, then as the distance covered is the same we will have: $st=1.2s*(t-20+15)$ --> $t=30$ minutes.

Answer: D.

Hi Bunuel,
Can you please explain why the time when the speed is 1.2s is (t-20+15)? Should it not be (t+20-15) since she starts 20 minutes later and arrives 15 minutes earlier?

Thanks!

Bunuel

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Bunuel

Hi Bunuel,
Can you please explain why the time when the speed is 1.2s is (t-20+15)? Should it not be (t+20-15) since she starts 20 minutes later and arrives 15 minutes earlier?

Thanks!

So, usually Holly needs 30 minutes to get to the school (so if she leaves usually at 9, she's at school at 9:30). She left home 20 minutes later (at 9:20), so she are left with 30 - 20 = 10 minutes to be on time. But she's still 15 minutes late (so she's there at 9:45) so she spent 10 + 15 =25 minutes to get to the school (9:20 + 25 minutes = 9:45).

Hope it's clear.

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Bunuel

11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?
A. 7/8
B. 3/4
C. 2/3
D. 5/8
E. 3/8

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is 5/8. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is 5/8.

The same for blue marble: the probability of drawing blue marble is 3/8, the probability that for instance the 8th marble drawn is blue is still 3/8. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Answer: D.

MentorTutoring

In this question we have to draw w/o replacement, so wouldn't the probability of drawing balls be different - 1st ball red 5/8, 2nd ball red 4/7...

Pls explain how to do this

Thanks in advance!

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20 May 2020, 15:47

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GDT

Bunuel

I know it may be counterintuitive, GDT, but the answer should be (D). Picture eight slots in the following manner:

___ ___ ___ ___ ___ ___ ___ ___

Now, if I told you I had drawn all eight marbles and asked specifically about any given slot, would you not agree that the answer would be 5/8 for any particular draw that was NOT blue? That is, all you can say here is that for any given slot, there would be only two options, red or blue, and there happen to be 5 red and 3 blue marbles. If you knew what had been selected first, second, third, and so on, the probability would change on a sliding scale, as you have indicated. A specific designation per selection is the more typical variant of this concept. This problem comes to mind, for example. In the slots above, however, there is no way to distinguish one selection from another without more information.

Out of curiosity, what answer would you propose from the choices above if you did attempt to solve the problem in the manner you have outlined?

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GDT

Bunuel

Thank you for the clarification!

I was trying to make cases-1. when 2 left in the end would be red, 2.when out of 2 left in end one would be red and other blue
But that was not working out

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21 May 2020, 14:17

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GDT

Bunuel

Thank you for the clarification!

I was trying to make cases-1. when 2 left in the end would be red, 2.when out of 2 left in end one would be red and other blue
But that was not working out

Glad to help out. I was picturing a different way to arrange the eight slots for emphasis of the point that any slot is the same as another if the results of a selection are not known, something along the lines of a ring of slots instead. In such a case, how could anyone tell which selection would be made first, seventh, or whatever? But I can see that such a diagram is not necessary. In the end, a simple approach typically leads to the correct answer. When you find yourself really laboring over a problem, there is almost assuredly a more efficient way to solve it. (I have spent countless hours, it seems, refining my own approach to all GMAT™ questions.)

Thank you for bringing the question to my attention.

- Andrew

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Bunuel

Hello @Banuel,

Could you please explain why cant the answer be C in this case? If we consider two values -14,+2 the sum is -12. In this case x and y can be used interchangeably. So if x is negative y may or may not be negative.
I don't see a difference between option C and option D.

Thanks in advance

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Bunuel

The question asks which of the following must be true, not could be true. Only D must be true (only D is always true). If y is positive (2 in your example), then x must be negative (-14 in your case) in order the sum of x and y to be negative. So, D MUST be true.

As for C: if y = -1 and x = -11, then C is not true, so C is NOT always true.

Hope it's clear.

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Bunuel

4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?
A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

Let the rate of the draining pipe be $x$ liters per hour. Then the capacity of the tank will be $C=time*rate=4x$;

Now, when raining, the net outflow is x-3 liters per hour, and we are told that at this new rate the pool is emptied in 6 hours. So, the capacity of the pool also equals to $C=time*rate=6(x-3)$;

Thus we have: $4x=6(x-3)$ --> $x=9$ --> $C=4x=36$.

Answer: D.

Little confused with equation x - 3 , other pipe is filling up the tank then why we are consider x - 3 instead of 3 - x

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14 Dec 2020, 22:51

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abhinavsodha800

Bunuel

Little confused with equation x - 3 , other pipe is filling up the tank then why we are consider x - 3 instead of 3 - x

We have a draining pipe, which empties the tank at the rate of $x$ liters per hour and rain inflow into the pool, which fills the tanks at the rate of 3 liters per hour. When the draining pipe is open and it's raining the pool is still emptied, so x > 3 and the net outflow is x-3 liters per hour.

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Bunuel

7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat?
A. 16%
B. 25%
C. 32%
D. 48%
E. 75%

64% of her salary on food;
16% of her salary on mea

64%-16%=48% on food but not on meat --> 48/64=3/4=75% of the salary spent on food were not spent on meat.

Answer: E.

Hi Bunnuel , i assumed the total salary as $100 n my answer was coming as 48% . From question my assumption was that we are asked to calculate the amount spent on Food ? But when i saw you solution you are calculating F/ F + M . which is calculation percent on amount spend on food and meet but we are asked to calculate from salary which i have assumed as 100 why so ?

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abhinavsodha800

Bunuel

The question asks: What percent of the salary spent on food were not spent on meat?

Salary = 100.
On food (including meat) = 64.
On meat = 16.
On food but not on meat = 48.

The percent of the salary spent on food that were not spent on meat = 48/64.

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Bunuel

Hey Bunuel, can you please help me understand why only option D works?
As per my understanding, there can be couple of scenarios..

A. x=-7, y=-5 => both are negative works
B. clearly doesn't work, as anyone has to be definitely negative for sum to be negative
C. if say y=-16 and x=4, x+y=-12.. this should satisfy too right?
D. if say y=4 and x=-16.. this works just the same way option (C) works
E. works when
(i) x>0 and y<0 and x > y (x=4,y=-16)
(ii) x<0 and y<0, but y > x (x=-5,y=-7)

How come, out of all these options, only option (D) is must true?
Can you help me understand where I am going wrong

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Bunuel

The question asks which of the following must be true, not could be true. Only D must be true (only D is always true).

For example:

A. Both x and y are negative. This is not always true: x = -20 and y = 8.

B. xy > 0. This is not always true: x = -20 and y = 8.

C. If y < 0, then x > 0. This is not always true: y = -2 and x = -10.

E. x - y > 0. This is not always true: x = -20 and y = 8.

Only D is ALWAYS true: if y is positive, then x must be negative in order the sum of x and y to be negative.