Set 10

Explanation

We can dissect this logic using the principle of implication. Let Likes Basketball be $P$ and Likes Mathematics be $Q$. The statement "everyone who likes basketball definitely likes mathematics" can be written as $P \rightarrow Q$.

Andi is known to like mathematics ($Q$). In mathematical logic, if the consequent ($Q$) occurs, we cannot guarantee that the antecedent ($P$) is the cause. Andi might like mathematics for other reasons, not necessarily because he likes basketball.

However, there is no information prohibiting Andi from liking basketball. Therefore, the conclusion that "Andi likes basketball" has a chance of being true, but it cannot be confirmed with $100\%$ certainty. Thus, the quality of the conclusion is possibly true.

Explanation

To find the division with the highest acceptance percentage, we need to compare the number of Accepted candidates to the Total Applicants (Accepted + Rejected) in each division. The formula used is:

Let's calculate the acceptance percentage for each division sequentially.

Division A has $30$ accepted candidates out of a total of $20 + 30 = 50$ applicants.

Division B has $20$ accepted candidates out of a total of $30 + 20 = 50$ applicants.

Division C has $50$ accepted candidates out of a total of $10 + 50 = 60$ applicants.

Division D has $90$ accepted candidates out of a total of $30 + 90 = 120$ applicants.

Division E has $50$ accepted candidates out of a total of $25 + 50 = 75$ applicants.

Based on the calculations above, it is clear that Division C has the highest acceptance percentage, which is $83.33\%$.

Explanation

To determine the division with the highest number of applicants, we must sum the Accepted and Rejected candidates for each division. Let's calculate them one by one.

Division A has $20$ rejected candidates and $30$ accepted candidates. The total number of applicants is:

Division B has $30$ rejected candidates and $20$ accepted candidates. The total number of applicants is:

Division C has $10$ rejected candidates and $50$ accepted candidates. The total number of applicants is:

Division D has $30$ rejected candidates and $90$ accepted candidates. The total number of applicants is:

Division E has $25$ rejected candidates and $50$ accepted candidates. The total number of applicants is:

Based on these calculations, it is clear that Division D has the highest number of applicants, which is $120$ people.

Explanation

Our focus is to find the amount of bread obtained by Team D. Let's analyze the available information to determine what is relevant.

Information $(3)$ states that Team D gets one-third of the total bread. However, this information alone is insufficient because we do not yet know the total amount of bread distributed.

Information $(4)$ provides data that one box contains $20$ packs. Since Andi distributes three boxes, we can calculate the total bread:

After knowing the total bread from information $(4)$, we can go back to using information $(3)$ to calculate Team D's share:

Information $(1)$ and $(2)$ discuss the distribution for Teams A, B, and C. This data is not needed as it does not affect the calculation of Team D's share, which is based directly on the total bread.

Therefore, we only need information $(3)$ and $(4)$ to solve this problem.

Explanation

To determine the amount of bread obtained by Team A, we must relate all variables to the total bread availability.

The first step is to find the Total Bread distributed. Information $(4)$ states that one box contains $20$ packs. Since there are $3$ boxes, we can calculate the total:

Next, we need to separate Team D's share to find the remaining bread for Teams A, B, and C. Information $(3)$ mentions Team D gets one-third of the total.

The remaining bread for Teams A, B, and C is $60 - 20 = 40$ packs. Now we need their distribution ratios:

• Information $(1)$ states $A = \frac{1}{2}B$ or $B = 2A$.
• Information $(2)$ states $B = C$, so $C = 2A$.

By substituting these relationships into the remaining bread equation $A + B + C = 40$, we get:

Therefore, we need all information $(1)$, $(2)$, $(3)$, and $(4)$ to determine the amount of bread Team A obtained.

Explanation

To find the pattern of this sequence, we need to look at the difference between consecutive terms. Let's dissect the changes one by one.

Our initial sequence is:

Now, observe the jump in addition from one number to the next:

• From $2$ to $3$, it increases by $1$.
• From $3$ to $5$, it increases by $2$.
• From $5$ to $9$, it increases by $4$.
• From $9$ to $17$, it increases by $8$.

If we write down the addition pattern, we get a new series:

It is clear that each addition is double the previous addition (or powers of 2: $2^0, 2^1, 2^2, 2^3$).

Therefore, the next addition must be double of $8$, which is $16$.

Let's calculate the next term:

So, the correct number to fill the sequence is 33.

Explanation

This sequence actually consists of two different patterns interleaved. Let's separate the terms based on odd and even positions to see the patterns more clearly.

First Pattern (Odd Terms)

We take the 1st, 3rd, 5th, 7th terms, and so on:

It is evident that each term increases by $5$:

• $1 + 5 = 6$
• $6 + 5 = 11$
• $11 + 5 = 16$

So the next term in this pattern is:

We can verify this with the last term: $21 + 5 = 26$. It matches.

Second Pattern (Even Terms)

Now we take the 2nd, 4th, 6th terms, and so on:

It appears that each term increases by $2$:

• $3 + 2 = 5$
• $5 + 2 = 7$

So the next term (filling the first blank) is:

Verify with the next term: $9 + 2 = 11$. It matches.

Conclusion

The first blank corresponds to the continuation of the Second Pattern ($9$), and the second blank corresponds to the continuation of the First Pattern ($21$).

Thus, the correct pair of numbers is $9, 21$.

Explanation

This question tests the ability to draw logical conclusions (syllogism). We can break down the sentences in the text into symbolic logical premises. Let's define three basic statements:

• $P$: It is currently the dry season.
• $Q$: Plants shed their leaves.
• $R$: There is a lot of scattered leaf litter.

Based on the text, we derive two logical implications. The sentence "In the dry season, plants will shed their leaves" can be written as $P \rightarrow Q$. Furthermore, the sentence "when plants shed their leaves, there is a lot of scattered leaf litter" can be written as $Q \rightarrow R$.

Using the principle of Hypothetical Syllogism, we can draw a direct conclusion from $P$ to $R$:

This means that if $P$ occurs, then $R$ must occur. In plain language: "If it is currently the dry season, then there is a lot of scattered leaf litter." Options containing "might be" are incorrect because this deductive logic yields certainty, not mere possibility.

Thus, the correct statement is if it is currently the dry season, then there is a lot of scattered leaf litter.

Explanation

Let's analyze the statements above using mathematical logic by defining the following variables:

• $P$: Increase in fuel (BBM) prices.
• $Q$: Increase in public transportation fares.
• $R$: Increase in the prices of basic needs.

From the text, we derive two main premises:

1. "Every increase in fuel prices is surely followed by an increase in public transportation fares" can be written as $P \rightarrow Q$.
2. "An increase in public transportation fares is always followed by an increase in the prices of basic needs" can be written as $Q \rightarrow R$.

The most appropriate statement can be found using the Modus Tollens principle or Contrapositive equivalence on the first premise. An implication $P \rightarrow Q$ has the same truth value as its contrapositive, $\sim Q \rightarrow \sim P$.

This means that if there is no increase in public transportation fares ($\sim Q$), then it is certain that no increase in fuel prices occurred ($\sim P$). This aligns with the option stating that the absence of an increase in public transportation fares indicates no increase in fuel prices.

Thus, the correct statement is if there is no increase in public transportation fares, then there is no increase in fuel (BBM) prices.

Explanation

To answer this question, we need to compare each statement in the options with the core information presented in the text. The text explicitly states two main mechanisms by which grapes affect blood pressure:

1. High antioxidant content helps lower high blood pressure.
2. High potassium content helps eliminate the effects of sodium, so high blood pressure can be reduced.

The main conclusion is that consuming grapes has a positive impact on lowering blood pressure.

Now let's examine the statement: "The more grapes consumed, the higher the blood pressure will be."

This statement clearly contradicts the information in the passage. The text states that grapes function to lower or reduce high blood pressure, not raise it. Therefore, the claim that grape consumption will make blood pressure higher is false, and this is the answer we are looking for because the question asks for the statement that is NOT TRUE.

The other statements align with the text as they all support the idea that grapes are beneficial for lowering blood pressure or eliminating the effects of sodium.

Explanation

To find the statement that is NOT TRUE, we must compare the claim in the options with the quantitative data presented in the text.

The text explicitly states that deforestation accounts for $15\%$ of the world's greenhouse gas emissions.

Now let's examine the statement: "Deforestation contributes almost all of the world's greenhouse gas emissions."

The phrase "almost all" implies a proportion close to $100\%$ (an absolute majority). Mathematically and linguistically, the figure of $15\%$ is very far from the definition of "almost all". This is a clear data contradiction.

Therefore, the claim is false and does not align with the passage. The other statements (regarding soil erosion, wildlife habitats, and the impact on communities) are all directly supported by sentences in the text.

Explanation

Let's analyze the logical relationship between the three statements in depth.

Statement A focuses on land use. The argument is that the ratio of green areas to built-up areas influences flood potential. This is a general principle regarding soil absorption capacity.

Statement B focuses on meteorological factors. The argument is that high rainfall intensity increases river discharge and triggers flooding. This is a general principle regarding the hydrological cycle.

The Environmental Expert's Statement provides a specific cause for the current flooding in City X: infrastructure failure (a damaged dam).

The cause presented by the expert (dam damage) is an independent factor. The fact that the dam is damaged neither proves the green area theory (A) true or false, nor does it prove the rainfall theory (B) true or false. Dam failure can occur in both green and built-up areas, and it can happen whether there is heavy rain or not.

Therefore, the environmental expert's statement introduces a distinct third variable that has no direct causal link to strengthen or weaken the general arguments of A or B.

Explanation

Let's dissect the logic of each statement to see how it aligns with Andi's situation.

Analysis of Statement A

This statement establishes a tenure requirement (more than 5 years) for entitlement to insurance. Its focus is on "who has the right to own insurance." In Andi's case, we are not given information about how long he has worked. Therefore, Andi's condition cannot be used to directly test the validity of statement A.

Analysis of Statement B

This statement establishes a medical condition (severe illness or injury) as the trigger for activation of the insurance. The logic is:

If an employee suffers a severe injury $\rightarrow$ Insurance is activated.

Analysis of Andi's Condition

The facts show that Andi is experiencing a severe injury (premise fulfilled) and is able to activate his health insurance (conclusion occurred).

Andi's condition serves as empirical evidence that aligns perfectly with the cause-and-effect mechanism described in Statement B. Since the actual event (Andi gets injured, then insurance activates) matches the statement's prediction, this fact supports the validity of argument B.

Thus, Andi's condition stands as evidence that strengthens statement B.

Explanation

Let's dissect the logical flow of the provided information using premises.

We can map the information into three main variables:

• $P$: Rain intensity increases significantly (extreme rain).
• $Q$: Flooding occurs.
• $R$: Green vegetation appears (due to increased soil moisture).

Based on the text, the cause-and-effect relationships formed are:

1. Extreme rain causes flooding ($P \rightarrow Q$).
2. Flooding causes the appearance of green vegetation ($Q \rightarrow R$).

Using the principle of hypothetical syllogism, we can draw a conclusion from these two premises:

The conclusion drawn is "if extreme rain intensity increases significantly again ($P$), it will give rise to green vegetation ($R$)". This statement aligns with the logical deduction $P \rightarrow R$.

Therefore, the conclusion is logically definitely true.

Explanation

Let's analyze the logic of the text using the principle of implication.

The first statement provides a cause-and-effect rule: "A person can catch the flu if they inhale saliva droplets from a patient." We can simplify this to:

If inhale droplets ($P$) $\rightarrow$ Catch the flu ($Q$).

The fact is that Nia accidentally inhaled cough droplets from a person with the flu. This means condition $P$ is met. Based on the logic rule of Modus Ponens, if condition $P$ occurs, then the consequence $Q$ (catching the flu) should occur.

However, the proposed conclusion states the opposite, namely "Nia will not catch the flu". This statement directly contradicts the valid deduction derived from the premises. Since the conclusion denies the logical consequence that should happen, the quality of the conclusion is definitely false.

Explanation

To determine which class has the lowest percentage of students who like mathematics, we need to compare the proportion of students who like the subject to the total number of students in each class. The total number of students is calculated by adding those who like and dislike the subject.

The formula used is:

Here is the detailed percentage calculation for each class:

From the calculation results above, we can compare the percentage values of each class.

It is clear that class $\text{MMM}$ has the smallest percentage, which is approximately $36.5\%$, lower than class $\text{RRR}$ ($37.5\%$) and the other classes.

Explanation

To determine which class has the highest percentage of students who like mathematics, we use the same proportion formula as in the previous question, comparing the number of students who like the subject to the total number of students in that class.

Here are the percentage calculation results for each class:

Based on the comparison above, class $\text{NNN}$ has the highest percentage at $47.3\%$. This indicates that the proportion of students who like mathematics in that class is greater than in the other classes.

Explanation

We will analyze the pattern of visitor increases for each store separately to determine the number of visitors on the eighth day.

Store A Pattern Analysis

The visitor data for store A is $30, 33, 35, 36, 39, 41, 42$. If we observe the differences between consecutive terms, there is a repeating addition pattern as follows:

The addition pattern is a constantly repeating $+3, +2, +1$. Based on this pattern, to find the number of visitors on the eighth day, we must add $3$ to the last term (continuing the pattern sequence after $+1$).

Store B Pattern Analysis

The visitor data for store B is $7, 10, 17, 27, 44, 71, 115$. This pattern follows the Fibonacci sequence rule, where the next term is obtained by summing the two previous terms.

Therefore, the number of visitors on the eighth day is the sum of the last two terms, which are $71$ and $115$.

Thus, the number of visitors to store A and B on the eighth day is $45$ and $186$ people, respectively.

Explanation

The student visitation data forms a number sequence: $7, 10, 12, 15, 17, 20$. We will analyze the difference between terms to find the pattern.

It appears that the addition pattern alternates between $+3$ and $+2$. Since the last term ($20$) was obtained by adding $+3$, the next step to find the 7th day is to add $+2$.

Thus, the number of students visiting on the 7th day is predicted to be $22$ people.

Explanation

The first step is to calculate the total clothes Aryo will donate. It is known to be five dozen.

Next, we analyze the available information to find the number of clothes $\text{D}$ gets.

Based on Statement $(3)$, it is stated that $\text{D}$ gets one-fourth of the total clothes. Since we already know the total clothes from the initial problem description, we can directly calculate $\text{D}$'s share using this statement alone.

The other statements are not needed because Statement $(3)$ is sufficient to answer the question independently without the help of other statements.

Thus, the only information needed is Statement $(3)$.