Test: Quantitative Reasoning (Level 500) - GMAT MCQ

If each machine works at a rate of "x" days to complete the job individually, the equation representing the work rate of six machines becomes:

1/x + 1/x + 1/x + 1/x + 1/x + 1/x = 1/12

Simplifying this equation, we find:

6/x = 1/12

Solving for "x", we get:

x = 72

Now, let "y" represent the number of machines needed to complete the job in 8 days. The equation representing the work rate of all machines becomes:

y/72 = 1/8

Simplifying this equation, we find:

y = 9

To determine the additional number of machines required, we subtract the initial number of machines (6) from the required number of machines (9):

required = y - x = 3

Therefore, the answer is B. 3.

Let's analyze the time it takes for Jan to walk down the steps and the time it takes for her to ride the elevator.

Walking down the steps: Jan takes 30 seconds per floor, so if she lives x floors above the ground floor, it will take her 30x seconds to walk down the steps.

Riding the elevator: Jan takes 2 seconds per floor, so it will take her 2x seconds to ride the elevator down.

According to the problem, the time it takes Jan to walk down the steps is the same as the time it takes for her to wait for the elevator for 7 minutes (which is 7 * 60 = 420 seconds) and ride down.

Therefore, we have the equation:

30x = 420 + 2x

Simplifying the equation:

28x = 420

Dividing both sides by 28:

x = 15

Therefore, the answer is D. 15.

Given: y = x + 2 z = y + 2

We need to find the value of the largest number, which is represented by z.

To find the median of x, y, and z, we need to arrange the numbers in ascending order:

The smallest number is x. The middle number is y. The largest number is z.

From the given relationships, we can substitute the values of y and z:

y = x + 2 z = (x + 2) + 2 = x + 4

The median is the middle number, y.

The product of the smallest number and the median is x * y.

The difference between the median and the product is y - (x * y).

According to the problem, this difference is 0:

y - (x * y) = 0

Substituting the value of y:

(x + 2) - (x * (x + 2)) = 0

Expanding and simplifying:

x + 2 - (x² + 2x) = 0 x + 2 - x² - 2x = 0 -x² - x + 2 = 0

To solve this quadratic equation, we can factor it:

-(x - 1)(x + 2) = 0

Setting each factor equal to zero:

x - 1 = 0 or x + 2 = 0

Solving for x:

x = 1 or x = -2

Since the problem states that x, y, and z are positive numbers, we discard the negative solution x = -2.

Therefore, the value of x is 1.

Using the relationship y = x + 2:

y = 1 + 2 y = 3

Using the relationship z = y + 2:

z = 3 + 2 z = 5

The largest number is z, which is equal to 5.

Therefore, the answer is (C) 5.

To find the value of n, we can use the remainder formula. According to the formula, when a positive integer m is divided by a positive integer n, the division can be expressed as m/n = Q + r/n, where Q is the quotient and r is the remainder.

In this problem, we are given that the remainder when m is divided by n is 12. Therefore, we can write the equation as m/n = Q + 12/n.

We are also given that m/n = 24.2. By rewriting 24.2 as a mixed fraction, we have m/n = 24 + 2/10, which can be simplified to m/n = 24 + 1/5.

Since the quotient Q must be an integer, we can determine that Q is 24. Thus, the remainder 12/n must be equivalent to 1/5.

Setting up the equation 12/n = 1/5, we can solve for n:

Cross-multiplying, we get 12 * 5 = n * 1, which simplifies to 60 = n.

Therefore, the value of n is 60, which corresponds to option B.

To find the number of valid votes received by the candidate other than the one who got 52% of the valid votes, we first calculate the total number of valid votes. Since 25% of the total votes were invalid, we subtract that percentage from 100% to get the percentage of valid votes, which is 75%.

Next, we calculate 75% of the total number of votes, which is (75/100) * 8400 = 6300. Therefore, the total number of valid votes is 6300.

Since the candidate who won received 52% of the valid votes, the candidate who was defeated received the remaining percentage, which is 48%. To find the number of valid votes received by the defeated candidate, we calculate (48/100) * 6300 = 3024.

Hence, the defeated candidate received 3024 valid votes, which corresponds to option C.

The minimum value of the product occurs when:

• The result has a negative sign (if possible)
• The absolute value of the product is maximized

From the integers between -5 and +5 {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}, we can select {-5, -4, +5, +4} to maximize the absolute values.

To achieve a negative sign and maximize the absolute value, we choose the negative value with the greatest absolute value, which is -3.

Therefore, the product becomes -5 * -4 * -3 * 4 * 5 = -1200.

To solve this problem, we can set up an equation based on the principle of conservation of salt.

Let's assume the number of liters of the 25% saline solution to be added is x.

The amount of salt in the 25% solution is 0.25x (since it is 25% saline) and the amount of salt in the 15% solution is 0.15(10 - x) (since the total volume is 10 liters).

When we mix these two solutions, the total amount of salt in the final solution should be 0.20(10) = 2 liters.

Now we can set up the equation:

0.25x + 0.15(10 - x) = 2

Simplifying the equation:

0.25x + 1.5 - 0.15x = 2

0.10x + 1.5 = 2

0.10x = 0.5

x = 0.5 / 0.10

x = 5

Therefore, approximately 5 liters of the 25% saline solution must be added to the 15% saline solution to make 10 liters of a solution that's 20% saline.

The correct answer is C) 5.0 liters.

To determine the solution set for the inequality |x| > x, we can consider the possible cases based on the properties of absolute value.

Case 1: x > 0 In this case, |x| is equal to x since x is already positive. However, if |x| is greater than x, it implies that x must be negative, which contradicts our assumption. Therefore, x > 0 is not a valid solution.

Case 2: x < 0 In this case, |x| is equal to -x since x is negative. If |x| is greater than x, it means that -x is greater than x, which is true for all negative values of x. Thus, x < 0 satisfies the inequality.

Therefore, the correct answer is D) x < 0, which represents the entire solution set for the inequality |x| > x.

To find the total length of the wire, we need to determine the length of all the edges of the cube.

Let's assume that each edge of the cube has a length of "a."

A cube has 6 faces, and each face is a square. The surface area of a cube is given by the formula:

Surface Area = 6 * (side length)²

We are given that the surface area of the cube is 24, so we can set up the equation:

24 = 6 * a²

Dividing both sides by 6:

4 = a²

Taking the square root of both sides:

√4 = √(a²)

2 = a

Now that we know the length of each edge (a = 2), we can find the total length of the wire by multiplying the length of one edge by the number of edges.

The number of edges in a cube is 12.

Total length of wire = Length of one edge * Number of edges Total length of wire = 2 * 12 Total length of wire = 24

Therefore, the correct answer is B) 24, which represents the total length of the wire.

Let's break down the information given in the problem:

Total number of cadets in the graduating class = 400

Percentage of women cadets = 30% Number of women cadets = (30/100) * 400 = 120

Of these women cadets, 1/5 became instructors: Number of women who became instructors = (1/5) * 120 = 24

The number of men who became instructors was twice the number of women who became instructors: Number of men who became instructors = 2 * 24 = 48

Therefore, the correct answer is (B) 48, which represents the number of men who became instructors.

Let's assume that there are 3x boys and 2x girls in the college, based on the given ratio.

Given that 20% of the boys are adults, the number of adult boys would be 20% of 3x, which is (20/100) * 3x = 0.6x.

Similarly, 25% of the girls are adults, so the number of adult girls would be 25% of 2x, which is (25/100) * 2x = 0.5x.

The total number of adult students would be the sum of adult boys and adult girls: 0.6x + 0.5x = 1.1x.

The total number of students in the college is 3x (boys) + 2x (girls) = 5x.

The percentage of students who are not adults can be calculated as:

(1 - (total number of adult students / total number of students)) * 100

(1 - (1.1x / 5x)) * 100

(1 - 0.22) * 100

0.78 * 100

78%

Therefore, the correct answer is C) 78, which represents the percentage of students who are not adults.

Let's denote the average speed of the slower car as x miles per hour. Since the faster car traveled, on average, 10 miles per hour faster than the slower car, the average speed of the faster car can be represented as (x + 10) miles per hour.

The total distance covered by the slower car in 3 hours is 3x miles, and the total distance covered by the faster car in 3 hours is 3(x + 10) miles.

Since they started from the same point and traveled in opposite directions, the total distance between them after 3 hours is the sum of the distances covered by both cars:

3x + 3(x + 10) = 300

Simplifying the equation:

3x + 3x + 30 = 300 6x + 30 = 300 6x = 300 - 30 6x = 270 x = 270 / 6 x = 45

Therefore, the average speed of the slower car for the 3-hour trip is 45 miles per hour.

The correct answer is (B) 45 miles per hour.

To find the sum of the even integers between 200 and 400, inclusive, we need to determine the first even number within this range and the last even number within this range, and then calculate the sum.

The first even number within the range is 200, and the last even number within the range is 400. We can calculate the number of even numbers within this range by subtracting the first even number from the last even number and adding 2 (since both 200 and 400 are inclusive).

Number of even numbers = (400 - 200) / 2 + 1 = 101

To find the sum of the even numbers, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

where n is the number of terms.

Sum = (101/2)(200 + 400) = 50.5(600) = 30,300

Therefore, the sum of the even integers between 200 and 400, inclusive, is 30,300. Thus, the correct answer is option C.

Since we know Leo pays 7% of the amount that is in excess of $1000
We can assume 'x' to be the excess amount. Then 7 percent of x = 87.50 => x = 1250.
Hence total value = 1000 + 1250 = 2250. Hence (C)

Use the group formula:
Total = Group 1 + Group 2 - Both + Neither.
Using the formula above and the information we are given:
100% = 78% + 65% - 52% + Neither
100% = 91% + Neither or
Neither = 100% - 91% = 9%
The total here is 500 so we can multiply 9% with 500 to get the amount of business people who do no use their laptops at home or in hotels.

(9/100) * 500 = 45 Answer.

In ONE hour, the boat will travel 32 miles and will use 24 gallons of fuel
So, the fuel consumption rate is 32 miles per 24 gallons
Or we can write: fuel consumption rate = 32/24 miles/gallon
32/24 = 4/3
So, the fuel consumption rate = 4/3 miles per gallon
Answer: D

To minimize |-5x + 7| when x is an integer:

• Evaluate the expression for each answer choice:
• For x = 0, |-5(0) + 7| = 7
• For x = 1, |-5(1) + 7| = 2
• For x = 2, |-5(2) + 7| = 3
• For x = 3, |-5(3) + 7| = 8
• For x = 4, |-5(4) + 7| = 3

The minimum value occurs when x = 1, making the correct answer B: 1.

Let the total production order be of 60 units
1^st machine can fill the production order at 6 units per minute
2^nd machine can fill the production order at 5 units per minute
So, 1^st  and 2^nd machine working togather can fill the production order at 11 units per minute.
The total production order is of 60 units so the time taken to complete the order is  minutes

Hence answer is (C) ,

Total there are 10 players.
Each player will play with another 9 players. But in this process, the play between 2 players will be counted twice and hence needs to be divided by 2.

So (10*9)/2=45. Option C.

Stage 1: Select an entree
There are four different entrees from which to choose.
So, we can complete stage 1 in 4 ways

Stage 2: Select 2 different side dishes
Since the order in which we select the 2 side dishes does not matter, we can use combinations.
We can select 2 side dishes from 5 side dishes in 5C2 ways = (5)(4)/(2)(1) = 10
So we can complete stage 2 in 10 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a meal) in (4)(10) ways (= 40 ways)

Answer: C