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Test: Fractions/Ratios/Decimals - GMAT MCQ


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10 Questions MCQ Test - Test: Fractions/Ratios/Decimals

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Test: Fractions/Ratios/Decimals - Question 1

The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 1

Let's assume the number of women at the party is 2x and the number of children is 5x. According to the given ratio, the number of men would be (5x * 4/3) = (20x/3).

We know that there are more than 13 and less than 20 women at the party. Let's check the range of possible values for x:

For more than 13 women: 2x > 13 x > 6.5

For less than 20 women: 2x < 20 x < 10

The only integer value of x that satisfies both conditions is x = 7.

So, the number of men at the party would be (20x/3) = (20 * 7/3) = 140/3 = 46.67 (approximately).

Since the number of men must be an integer, the closest integer to 46.67 is 47. Therefore, the number of men at the party is 47.

Hence, the correct answer is option C.

Test: Fractions/Ratios/Decimals - Question 2

The ratio of cars to trucks in your toy box is 5 to 2. After you lose two cars, you buy a pack of eight trucks. The ratio of cars to trucks in the toy box after these changes is 3 to 2. How many trucks did you have originally ?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 2

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.

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Test: Fractions/Ratios/Decimals - Question 3

Which of the following fractions is equal to the decimal 0.0625 ?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 3

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.

Test: Fractions/Ratios/Decimals - Question 4

In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?

Test: Fractions/Ratios/Decimals - Question 5

Two libraries are planning to combine a portion of their collections in one new space. The new space will house 1/3 of the books from Library A, along with 1/4 of the books from Library B. If there are twice as many books in Library B as in Library A, what proportion of the books in the new space will have come from Library A?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 5

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.

Test: Fractions/Ratios/Decimals - Question 6

A pool which was 2/3 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 6

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.

Test: Fractions/Ratios/Decimals - Question 7

A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4th of the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 7

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.

Test: Fractions/Ratios/Decimals - Question 8

An assembly line produces 500 vehicle parts daily. The line produces only car parts and truck parts in a ratio of 2 : 3 and the ratio of defective car parts to defective truck parts is 1 : 2. If 6 parts on a certain day are defective, how many non-defective car parts are produced on that day?

Detailed Solution for Test: Fractions/Ratios/Decimals - Question 8

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.

Test: Fractions/Ratios/Decimals - Question 9

A bag contains blue, red and green marbles only. If the ratio of blue marbles to red marbles is 4 to 5, and the ratio of green marbles to blue marbles is 4 to 3, what is the minimum number of marbles in the bag?

Test: Fractions/Ratios/Decimals - Question 10

A photographer purchases 30 rolls of black and white film and 25 rolls of color film. If the cost of each roll of color film is twice of the cost of each roll of black and white film, what percent of the total cost of the film is the price of a roll of color film?

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