Exercises in reason and proportion

Test your knowledge of reason and proportion with the 10 questions Next. Check out the comments after the feedback to get your questions answered.

question 1

A ratio can be defined as the comparison between two quantities. if The and B are magnitudes, being B other than 0, then the split a/b or a: b is a ratio.

These are examples of reasons we use, EXCEPT:

a) Average speed
b) Density
c) Pressure
d) Temperature

See Answer

Correct alternative: d) Temperature.

Temperature measures the degree of agitation of the molecules.

The quantities that are given by the quotient between two numbers are:

Average speed = distance/time

Density = mass/volume

Pressure = force/area

question 2

A contest to fill 200 vacancies received 1600 entries. How many candidates are there for each vacancy?

a) 4
b) 6
c) 8
d) 12

See Answer

Correct alternative: c) 8.

Comparing the number of candidates with the number of vacancies in a division, we have:

Therefore, the ratio between the numbers is 8 to 1, that is, there are 8 candidates for 1 vacancy in the competition.

Since a number divided by 1 results in itself, so the correct alternative is the letter c) 8.

question 3

Gustavo was training penalties in case he needed it in the final of the school football games. Knowing that from 14 shots on goal he hit 6, what is the ratio of the number of hits to the total of shots?

a) 3/5
b) 3/7
c) 7/3
d) 5/3

See Answer

Correct alternative: b) 3/7.

For one thing, the first number is called the antecedent and the second the consequent. So we have the case of The for B, which, according to the data in the statement, is the number of hits for the total number of kicks.

We write in as reason as follows:

Thus, for every 7 kicks Gustavo hit 3 and, therefore, the ratio it represents is 3/7, as per letter b).

question 4

Determine the value of x in the following proportions.

a) 2/6 = 9/x
b) 1/3 = y/12
c) z/10 = 6/5
d) 8/t = 2/15

See Answer

Answers: a) 27, b) 4, c) 12 and d) 60.

Proportion is an equality between two ratios. By the fundamental rule of proportion, the product of the means is equal to the product of the extremes and vice versa.

Therefore,

question 5

In a selection, the ratio between the number of men and women candidates for a vacancy is 4/7. Knowing that 32 candidates are male, the total number of participants in the selection is:

a) 56
b) 72
c) 88
d) 94

See Answer

Correct alternative: c) 88.

First, we calculate, through the fundamental rule of proportion, the number of women in the selection.

Now, we add up the number of men and women to find the total number of participants.

56 + 32 = 88

Therefore, alternative c) 88 is correct.

question 6

(IFSP/2013) In a model of a condominium, one of its 80 meter high buildings is only 48 centimeters tall. The height of another building of 110 meters in this model, maintaining the proper proportions, in centimeters, will be:

a) 56
b) 60
c) 66
d) 72
e) 78

See Answer

Correct alternative: c) 66.

The height of another 110 meter building in this model, with the proper proportions, in centimeters, will be 66 cm.

question 7

(UEPB/2014) The ratio between a person's weight on Earth and their weight on Neptune is 5/7. Thus, the weight of a person who on earth weighs 60 kg, in Neptune, is in the range

a) [40 kg; 45 kg]
b) 45 kg; 50 kg]
c) [55 kg; 60 kg]
d) 75 kg; 80 kg[
e) [80 kg; 85 kg]

See Answer

Correct alternative: e) [80 kg; 85 kg]

Thus, 84 kg corresponds to a person's weight in Neptune and is in the range [80 kg; 85 kg], as per letter e.

question 8

(OMRP/2011) A mixture is made up of 90 kg of water and 10 kg of salt. Putting it to evaporate, a new mixture is obtained of which 24 kg contains 3 kg of salt. Determine the amount of water evaporated.

a) 60
b) 50
c) 30
d) 40
e) 20

See Answer

Correct alternative: e) 20.

The initial mixture contains 100 kg (90 kg of water and 10 kg of salt). What will vary is the amount of water, since the salt does not evaporate, that is, 10 kg of salt will remain.

Through the proportion, we find the mass of the new mixture.

Therefore, the mass of the mixture must not exceed 80 kg. By subtracting the initial mass from the calculated one, we will find the amount of water evaporated.

100 - 80 = 20 kg

Another way of thinking is that if at the beginning it had 90 kg of water and the new mixture contains 80 kg, keeping the 10 kg of salt, then the mass of water became 70 kg

90 - 70 = 20 kg

Therefore, alternative e) 20 is correct.

question 9

(Enem/2016) Five brands of wholegrain bread have the following fiber concentrations (fiber dough per bread dough):

- Brand A: 2 g of fiber for every 50 g of bread;
- Brand B: 5 g of fiber for every 40 g of bread;
- Brand C: 5 g of fiber for every 100 g of bread;
- Brand D: 6 g of fiber for every 90 g of bread;
- E brand: 7 g of fiber for every 70 g of bread.

It is recommended to eat the bread that has the highest concentration of fiber.
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The brand to be chosen is

a) A.
b) B.
c) C.
d) D.
and is.

See Answer

Correct alternative: b) B.

a) For brand A the reason is:

That is, every 25 g of bread contains 1 g of fiber

b) For brand B the reason is:

That is, every 8 g of bread contains 1 g of fiber

c) For brand C the reason is:

That is, every 20 g of bread contains 1 g of fiber

d) For brand D the reason is:

That is, every 15 g of bread contains 1 g of fiber

e) For the E brand the reason is:

That is, every 10 g of bread contains 1 g of fiber

Therefore, the greatest amount of fiber can be seen in brand B bread.

question 10

(Enem/2011) It is known that the real distance, in a straight line, from a city A, located in the state of São Paulo, to a city B, located in the state of Alagoas, is equal to 2 000 km. A student, when analyzing a map, verified with his ruler that the distance between these two cities, A and B, was 8 cm.

The data indicate that the map observed by the student is on the scale of

a) 1: 250.
b) 1: 2,500.
c) 1: 25,000.
d) 1: 250,000.
e) 1: 25,000,000.

See Answer

Correct answer: e) 1: 25 000 000.

Using the cartographic scale, the distance between two locations is represented by a ratio, which compares the distance on the map (d) with the real distance (D).

To be able to relate the measurements it is necessary that the two are in the same unit. So, first, we need to convert kilometers into centimeters.

If 1 m is 100 cm and 1 km is 1000 m, then 1 km is equal to 100,000 cm.

2000 km → cm
2 000 x 100 000 = 200 000 000 cm

Therefore, the scale can be calculated by substituting the utterance values.

Simplifying the terms of the scale by 8, we have:

Therefore, alternative e) 1: 25 000 000 is correct.

If you still have questions, these texts will help you:

• Ratio and Proportion
• Proportionality
• Magnitudes directly and inversely proportional