Test: Fractions/Ratios/Decimals - GMAT MCQ

Let's assume the original number of cars in the toy box is 5x and the original number of trucks is 2x.

After losing two cars, the number of cars becomes 5x - 2.

After buying a pack of eight trucks, the number of trucks becomes 2x + 8.

The new ratio of cars to trucks is given as 3 to 2, so we can set up the equation:

(5x - 2) / (2x + 8) = 3/2

Cross-multiplying, we get:

2(5x - 2) = 3(2x + 8)

Simplifying the equation:

10x - 4 = 6x + 24

Subtracting 6x from both sides:

4x - 4 = 24

Adding 4 to both sides:

4x = 28

Dividing both sides by 4:

x = 7

Therefore, the original number of trucks was 2x = 2 * 7 = 14.

Hence, the correct answer is option D.

To determine which fraction is equal to the decimal 0.0625, we can rewrite 0.0625 as a fraction by placing the decimal value over a power of 10.

0.0625 = 625/10,000

Now, let's compare this fraction to the given options:

A: 5/8 = 625/1000 (not equal to 625/10,000)
B: 3/8 = 375/1000 (not equal to 625/10,000)
C: 1/16 = 625/10,000 (equal to 625/10,000)
D: 1/18 = 555/10,000 (not equal to 625/10,000)
E: 3/80 = 375/10,000 (not equal to 625/10,000)

Therefore, the fraction equal to the decimal 0.0625 is 1/16. The correct answer is C.

Let's assume the number of books in Library A is represented by "a" and the number of books in Library B is represented by "b". We are given the following information:

Number of books in Library B = 2 * Number of books in Library A

To find the proportion of books from Library A in the new space, we need to calculate the ratio of the number of books from Library A to the total number of books in the new space.

Number of books from Library A = (1/3) * a
Number of books from Library B = (1/4) * b

Total number of books in the new space = (1/3) * a + (1/4) * b

To simplify the expression, we can find a common denominator:

Total number of books in the new space = (4/12) * a + (3/12) * b
= (4a + 3b) / 12

Now, we can calculate the proportion of books from Library A:

Proportion of books from Library A = (1/3) * a / [(4a + 3b) / 12]
= 12a / (3 * (4a + 3b))
= 4a / (4a + 3b)

Since we know that there are twice as many books in Library B as in Library A (b = 2a), we can substitute b = 2a into the equation:

Proportion of books from Library A = 4a / (4a + 3(2a))
= 4a / (4a + 6a)
= 4a / 10a
= 4/10
= 2/5

Therefore, the proportion of the books in the new space that came from Library A is 2/5. The correct answer is B.

Let's break down the problem step by step:

1. Initially, the pool was 2/3 full.
2. It was then filled at a constant rate for 5/3 hours until it reached 6/7 full.

To find the rate at which the pool is being filled, we can calculate the change in the fill level per hour.

Change in fill level = (6/7) - (2/3) = (18/21) - (14/21) = 4/21

This means that the pool is being filled at a rate of 4/21 per hour.

Now, we need to determine how much time it would take to completely fill the pool if it was empty to begin with. Since the rate of filling is 4/21 per hour, we can set up the following equation:

(4/21) * time = 1 (since we want to fill the pool completely, which is equivalent to 1 whole unit)

Solving for time:

time = 1 / (4/21) = 21/4 = 5.25 hours

The time is given in hours, so we convert it to hours and minutes:

5.25 hours = 5 hours + 0.25 * 60 minutes = 5 hours + 15 minutes = 5 hours 15 minutes.

Therefore, the correct answer is A: 8 hours 45 minutes.

Let's assume the initial number of literature books is 5x and the initial number of science books is 6x.

After adding 50 more literature books, the total number of literature books becomes 5x + 50.

The number of science books is increased by 1/4th of the existing science books, which is (1/4) * 6x = (3/2)x. Therefore, the total number of science books becomes 6x + (3/2)x = (15/2)x.

The ratio of the literature books to the science books after the increase is (5x + 50) : (15/2)x = 4 : 3.

To solve for x, we can set up the equation: (5x + 50) / ((15/2)x) = 4/3

Cross-multiplying, we get: (5x + 50) * 3 = 4 * (15/2)x 15x + 150 = 30x 15x - 30x = -150 -15x = -150 x = 10

Now, we can calculate the initial number of books in the library: Initial number of books = Number of literature books + Number of science books Initial number of books = 5x + 6x = 11x Initial number of books = 11 * 10 = 110

Therefore, the correct answer is B: 110.

Let's break down the problem step by step:

1. The assembly line produces 500 vehicle parts daily.
2. The ratio of car parts to truck parts is 2:3.
3. The ratio of defective car parts to defective truck parts is 1:2.
4. On a certain day, 6 parts are defective.

Let's calculate the total number of defective parts:

• The ratio of defective car parts to defective truck parts is 1:2, so we can assume there is 1x and 2x.
• The total defective parts can be calculated as 1x + 2x = 6.
• Solving this equation, we find x = 2.
• Therefore, there are 1x (or 1 * 2 = 2) defective car parts and 2x (or 2 * 2 = 4) defective truck parts.

Now, let's calculate the total number of non-defective parts:

• The total number of parts produced is 500.
• The total number of defective parts is 6.
• Therefore, the total number of non-defective parts is 500 - 6 = 494.

Since the ratio of car parts to truck parts is 2:3, we can split the non-defective parts accordingly:

• Car parts: (2/5) * 494 = 197.6 (approximately 198)
• Truck parts: (3/5) * 494 = 296.4 (approximately 296)

Therefore, the correct answer is E: 198 non-defective car parts.