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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bilv23

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Bunuel

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 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

Since 1/2 is in the set, the so must be:
-x^2 = -1/4;
-x^3 = -1/8.

Since -1/4 is in the set, the so must be:
-x^3 = 1/64;

Since -1/8 is in the set, the so must be:
-x^2 = -1/64.

The only number we cannot get is 1/2^(1/3).

Answer: D.

Lets say if x = 1/2^(1/3), then -x^3 = -1/2

Now since -1/2 is in the set, shouldn't 1/2^(1/3) also be in the set?

Bunuel

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bilv23

Bunuel

Lets say if x = 1/2^(1/3), then -x^3 = -1/2

Now since -1/2 is in the set, shouldn't 1/2^(1/3) also be in the set?

Why is -1/2 necessarily in the set? Also, "x is in the set, then both -x^2 and -x^3 are also in the set" does not necessarily mean that if x is there then -x^(1/3) must also be there: if x then y, does not mean if y then x.

Hope it's clear.

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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

My thought process was quite dumb so putting it here incase any one else is thinking in the same direction:

I was misguided by the mention of 3 ltrs per hour and I ended up thinking additional water in the pool was emptied in the extra 2 hours (additional water due to rain was 3 ltr * 2 hrs=6 ltrs)

It rained for 6 hours in fact and additional water in the pool was 3 ltrs * 6 hours =18 ltrs

In each additional hour 9 ltr water was emptied. 9 ltr/ hour

So, in 4 hours (without rain) emptied water (capacity of the pool) is 9 ltr * 4 hours= 36 ltrs (D)

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Hi Bunuel,
what confused me in the solution is that if -x^2 and -x^3 are -1/4 and -1/8, then how are we again treating them as x individually. The way question is written it seems that the set has 3 numbers, x, -x^2, and -x^3

Please help me out with this, thanks

Bunuel

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. $-\frac{1}{64}$

II. $\frac{1}{64}$

III. $\frac{1}{\sqrt[3]{2}}$

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Since $\frac{1}{2}$ is in the set, the following must also be in the set:

$-x^2 = -\frac{1}{4}$;

$-x^3 = -\frac{1}{8}$.

Since $-\frac{1}{4}$ is in the set, the following must also be in the set:

$-x^3 =\frac{1}{64}$

Since $-\frac{1}{8}$ is in the set, the following must also be in the set:

$-x^2 =-\frac{1}{64}$

The only number we cannot obtain is $\frac{1}{\sqrt[3]{2}}$.

Answer: D.

Bunuel

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saransh2797

Bunuel

$-x^2 = -\frac{1}{4}$;

$-x^3 = -\frac{1}{8}$.

Since $-\frac{1}{4}$ is in the set, the following must also be in the set:

$-x^3 =\frac{1}{64}$

Since $-\frac{1}{8}$ is in the set, the following must also be in the set:

$-x^2 =-\frac{1}{64}$

The only number we cannot obtain is $\frac{1}{\sqrt[3]{2}}$.

Answer: D.

The set's rule means each number generates new elements based on the pattern. Here, -x^2 and -x^3 are treated as elements in the set, not individual variables. They follow the same rule to generate further numbers.

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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

Total arrangements possible: 8!/(5!*3!) = 56

Arrangements with Blue at 7th: 7!(5!*2!) = 21 (Position for 1 Blue Marble is fixed, arrange the remaining marbles)
Arrangements with Blue NOT at 7th: 56-21 = 35

Probability: 35/56 = 5/8

Answer: D

Is this a good approach? Or was it a fluke that I got it right with this method??

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But by the 7th marble, we only have 2 marbles to pick from because it is without replacement. If there's only two left, it means atleast one of the blue marbles have already been picked. Now, the the remaining two could be both blue, 1 blue or no blue. How can we say 5/8? We have to do each cases individually, subtract and then add right?

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 a red marble is $\frac{5}{8}$. Without knowing the other results, the probability of drawing a red marble will not change for ANY successive draw: the second, third, fourth, ..., and seventh. Thus, the probability that the seventh marble is red is $\frac{5}{8}$.

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

Answer: D.

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Sreeveluri

By the 7th draw, the remaining marbles do depend on what happened in the first 6 draws, but we are not given any information about those draws.

Before the drawing starts, the 8 marbles are simply being placed in a random order. Any one of the 8 marbles is equally likely to be in the 7th position, and since 5 of the 8 marbles are red, the probability that the 7th marble is not blue is 5/8.

Consider this: there are 8 cards, 5 spades, and 3 hearts. What is the probability that the first card you pick will be a spade? Clearly 5/8.

Now, the next question: suppose I throw away three cards at random, not telling you which cards I have thrown away. What is the probability NOW that you pick a spade out of the 5 remaining cards? I've just reduced the sample from which you pick, but does the probability change? WHY should it change?

Another question, using the same cards (5 spades and 3 hearts): I say that you can pick one card, but only out of randomly selected 5 cards. What is the probability that the card you pick will be a spade?

There is no difference in ALL the above cases, and the probability will remain 5/8. If it changed, increased (or decreased), it would mean that the probability of picking a heart, on the other hand, decreased (or increased). Why would it?

Similar questions to practice:
https://gmatclub.com/forum/a-box-contai ... 90272.html
https://gmatclub.com/forum/a-bag-contai ... 00023.html
https://gmatclub.com/forum/each-of-four ... 01553.html
https://gmatclub.com/forum/if-40-people ... 97015.html
https://gmatclub.com/forum/a-bag-contai ... 00023.html

Hope this helps.