Set 4

Explanation

To determine the number of possible password arrangements, we can use the multiplication rule (filling slots). The password consists of $5$ digits with the pattern: Number - Number - Letter - Number - Letter.

Let's analyze the number of possibilities for each position using the following table:

Position Analysis

Total Calculation

Based on the multiplication rule, the total number of password arrangements is the product of the possibilities at each position:

Thus, the number of password arrangements that can be formed is $72$.

Explanation

To determine which combination is most likely to be obtained, we need to calculate the probability of each option.

First, let's calculate the total number of toys in each box:

The probability of taking a specific toy is the number of those toys divided by the total number of toys in that box. Since taking from Box $1$ and Box $2$ are independent events, we multiply their probabilities.

Let's analyze each option:

Probability Analysis

For combinations of two different types of toys (e.g., Ball and Barbie), there are two possibilities: Ball from Box 1 & Barbie from Box 2, OR Barbie from Box 1 & Ball from Box 2.

Conclusion

From the calculations above, we compare the numerators since the denominators are the same ($240$):

The largest probability is $\frac{32}{240}$, which corresponds to the combination of 1 teddy bear and 1 ball.

Explanation

To draw a valid conclusion, we need to logically analyze the given premises.

Analysis of Premises

We have two main statements:

1. Premise 1: All West Javanese dishes have a sour and spicy taste.
2. Premise 2: Generally, West Javanese dishes use raw vegetables.

The word "Generally" in Premise 2 indicates that most West Javanese dishes use raw vegetables, but not all. This implies that there is a small portion of West Javanese dishes that do not use raw vegetables.

Logical Deduction

Let's connect the implication from Premise 2 with Premise 1:

• We know there are West Javanese dishes that do not use raw vegetables (from Premise 2).
• Since all West Javanese dishes have a sour and spicy taste (from Premise 1), those dishes that do not use raw vegetables must also have a sour and spicy taste.

Evaluation of Options

Let's examine each option:

• There are West Javanese dishes that are not sour and spicy: Incorrect. This contradicts Premise 1 which states "All" West Javanese dishes are sour and spicy.
• Some West Javanese dishes are neither sour nor spicy: Incorrect. Contradicts Premise 1.
• All West Javanese dishes use raw vegetables: Incorrect. Contradicts the word "Generally" in Premise 2.
• There are West Javanese dishes that do not use raw vegetables: Correct, but incomplete as it does not include information about the taste (Premise 1).
• There are West Javanese dishes that do not use raw vegetables but have a sour and spicy taste: Correct and complete. This combines the fact of the exception in using raw vegetables with the universal property of the dishes' taste.

The most appropriate conclusion is a combination of both premises: There are dishes (the subset of West Javanese dishes that don't use raw vegetables) that still possess the main property (sour and spicy taste).

Therefore, the correct answer is There are West Javanese dishes that do not use raw vegetables but have a sour and spicy taste.

Explanation

We can calculate the nutrient content in $350$ gr of pear by using a direct proportion relative to the $100$ gr baseline.

Given:

• Pear weight = $350$ gr.
• Baseline = $100$ gr.
• Multiplier factor = $\frac{350}{100} = 3.5$.

Calculating Carbohydrate

The carbohydrate content per $100$ gr is $15.2$ gr. So, for $350$ gr:

Calculating Fiber

The fiber content per $100$ gr is $3.1$ gr. So, for $350$ gr:

Conclusion

Therefore, the carbohydrate and fiber content are respectively $53.2$ gr and $10.85$ gr.

Explanation

To solve this problem, we first need to calculate the calorie content of watermelon per $100$ grams, and then calculate the total calories for a weight of $250$ grams.

Calculating Watermelon Calories per 100 grams

It is known that the calorie content of pears per $100$ grams is $57$ cal. The calorie content of watermelon is half that of a pear:

Calculating Watermelon Calories for 250 grams

We use direct proportion. If $100$ grams of watermelon contains $28.5$ calories, then for $250$ grams:

Conclusion

Therefore, the calorie content of $250$ gr of watermelon is $71.25$ cal.

Explanation

This question asks us to find a statement that weakens the Minister of Finance's argument.

Identifying the Argument

The Minister of Finance put forward two main reasons for the formation of LPDP:

1. The education fund allocation of $20\%$ from the State Budget is often not fully absorbed.
2. The fact that there is a lack (scarcity) of Indonesia's best students who can study at the best universities abroad.

Analyzing the Options

To weaken the argument, we must find a statement that refutes one of the premises or reasons above. The second argument states that the number of Indonesian students abroad is low (minimal/scarcity).

Let's check the options:

• Education fund allocation increases: This actually supports the background of the first reason (funds are getting bigger but not absorbed).
• Many best students can study at the best universities within the country: Irrelevant to the argument about studying abroad.
• Some of Indonesia's best students can study at the best universities abroad: The word "some" can still be consistent with "minimal" (few), so it is not strong enough to weaken.
• Education fund allocation is not fully absorbed: This repeats the first reason, so it supports rather than weakens.
• Many of Indonesia's best students can study at the best universities abroad: This statement directly contradicts the second reason. If in fact "many" can study abroad, then the claim that the number is "minimal" becomes invalid, making the reason for creating the endowment fund based on that premise weak.

The statement "Many of Indonesia's best students can study at the best universities abroad" is a direct negation of the premise "lack of Indonesia's best students who can study abroad".

Therefore, the correct answer is Many of Indonesia's best students can study at the best universities abroad.

Explanation

We can simplify the statements into mathematical logic forms.

Variable Definitions

Let:

• $p$: $A = B$
• $q$: $C \neq D$
• $r$: $E = F$
• $s$: $G = H$

Translating Statements

1. Statement 1: $A = B$ or $C \neq D$

   $$p \lor q$$

   This form is equivalent to the implication: $\sim p \to q$.

2. Statement 2: If $E = F$ then $G = H$

   $$r \to s$$

   This form is equivalent to the contrapositive: $\sim s \to \sim r$.

3. Statement 3: $C = D$ or $G \neq H$

   Note that $C = D$ is the negation of $q$ ($\sim q$), and $G \neq H$ is the negation of $s$ ($\sim s$).

   $$\sim q \lor \sim s$$

   This form is equivalent to the implication: $q \to \sim s$.

Drawing Conclusion

We have the following logical chain:

1. From Statement 1: $\sim p \to q$
2. From Statement 3: $q \to \sim s$
3. From Statement 2: $\sim s \to \sim r$

Using syllogism, we can combine all three:

The final result is $\sim p \to \sim r$. This implication form is equivalent to a disjunction (or):

Translating Back to Sentences

• $p$ is $A = B$
• $\sim r$ is $E \neq F$

So the conclusion is: $A = B$ or $E \neq F$.

Explanation

Let's analyze each option based on the data in the table. The data provided is per $100$ grams, so the gram value is equal to the percentage ($x$ grams in $100$ grams is equal to $x\%$).

Option Analysis

1. Statement: Tempeh has higher energy content compared to beef.

   • Tempeh Energy: $201$ kcal.
   • Beef Energy: $273$ kcal.
   • Since $201 < 273$, this statement is false.

2. Statement: Tempeh has little nutritional content compared to beef.

   This statement is subjective and not fully supported by the data. Tempeh has advantages in protein, carbohydrates, and fiber. This statement is incorrect.

3. Statement: Beef has many nutritional advantages compared to tempeh.

   Similar to before, beef only excels in energy and fat, while tempeh excels in protein, carbohydrates, and fiber. This statement is incorrect.

4. Statement: Protein content in tempeh is $3.3\%$ greater than protein content in beef.

   • Tempeh Protein: $20.8$ gr ($20.8\%$).

   • Beef Protein: $17.5$ gr ($17.5\%$).

   • Difference:

     $$20.8 - 17.5 = 3.3 \text{ gr}$$

   • Since the basis is $100$ grams, a difference of $3.3$ grams is equivalent to a percentage difference of $3.3\%$. This statement is true.

5. Statement: Fat content in beef is $12.2\%$ greater than fat content in tempeh.

   • Beef Fat: $22$ gr.

   • Tempeh Fat: $8.8$ gr.

   • Difference:

     $$22 - 8.8 = 13.2 \text{ gr}$$

   • The difference is $13.2$ grams (or $13.2\%$), not $12.2\%$. This statement is false.

Therefore, the most appropriate conclusion is that the protein content in tempeh is $3.3\%$ greater than the protein content in beef.

Explanation

Let's analyze each option based on the data in the table. Remember that we are looking for the conclusion that best describes the data.

Option Analysis

1. Statement: If consuming tempeh, then one will get little fat.

   Tempeh contains $8.8$ gr of fat. The term "little" is relative. Although it is lower than beef ($22$ gr), this statement is not specific enough because there is no clear comparison in the sentence.

2. Statement: If consuming meat, then the nutrients obtained are only few.

   This statement is incorrect. Beef contains high energy ($273$ kcal), high protein ($17.5$ gr), and high fat ($22$ gr). Saying the nutrients are "only few" contradicts the fact that it is rich in certain macronutrients.

3. Statement: If consuming tempeh, then the nutrients obtained are more than the nutrients in beef.

   This statement is ambiguous. If it refers to the "types" of nutrients, the table does list carbohydrates and fiber for tempeh (which are absent in beef). However, if it refers to the "total amount" or calorie/fat value, beef is higher. This ambiguity makes this statement not the best conclusion.

4. Statement: If consuming tempeh, then one will get little energy.

   Similar to the first point, the term "little" for $201$ kcal is relative and subjective without a comparison context.

5. Statement: If consuming meat, then one will get a lot of energy and fat.

   Based on the table, beef has the highest energy content ($273$ kcal vs $201$ kcal) and the highest fat content ($22$ gr vs $8.8$ gr) between the two food items. Therefore, concluding that meat provides "a lot" of energy and fat is the statement most supported by this comparative data.

Therefore, the most appropriate conclusion is that if one consumes meat, one will get a lot of energy and fat.

Explanation

Let's translate the statements into mathematical logic.

Let:

• $p$: Nakafa students work on conditional empathy questions.
• $q$: Nakafa students can work on TOBK questions on the Nakafa app.
• $r$: Nakafa students get Learning Achievement Evaluation (EPB) results.

The given statements are:

1. If Nakafa students work on conditional empathy questions, then they can work on TOBK questions on the Nakafa app ($p \rightarrow q$).
2. If Nakafa students work on TOBK questions on the Nakafa app, then they get Learning Achievement Evaluation (EPB) results ($q \rightarrow r$).
3. Fact: Dito works on TOBK questions on the Nakafa app ($q$).

We have the premise $q \rightarrow r$ and the fact $q$. Based on the Modus Ponens rule of inference:

Therefore, the conclusion is $r$, which is Dito gets Learning Achievement Evaluation (EPB) results.

Note that the first premise ($p \rightarrow q$) is not directly used to draw this conclusion because the fact we have is $q$, not $p$. Even though $q$ occurs, we cannot conclude $p$ (affirming the consequent is a fallacy). The main focus is the implication from $q$ to $r$.

Explanation

Let's translate the statements into mathematical logic.

Let:

• $p$: Nakafa students work on conditional empathy questions.
• $q$: Nakafa students can work on TOBK questions in the Nakafa application.
• $r$: Nakafa students get Learning Achievement Evaluation (EPB) results.

The given statements are:

1. If Nakafa students work on conditional empathy questions, then they can work on TOBK questions in the Nakafa application ($p \rightarrow q$).
2. If Nakafa students work on TOBK questions in the Nakafa application, then they get Learning Achievement Evaluation (EPB) results ($q \rightarrow r$).
3. Dito does not get Learning Achievement Evaluation (EPB) results ($\sim r$).

From premises 1 and 2, we can use syllogism:

Next, we use that conclusion ($p \rightarrow r$) with premise 3 ($\sim r$) using the Modus Tollens rule:

The conclusion is $\sim p$, which means Dito does not work on conditional empathy questions.

Explanation

To determine the correct statement, let's analyze each option based on the text:

1. Free radicals grow cancer cells: The text mentions that free radicals "cause the growth of cancer cells", not that they actively "grow" cancer cells. The focus of the text is on the benefits of Matoa fruit in warding off these free radicals.

2. Scientific definition of Matoa fruit: The text provides a general description of the Matoa fruit (origin, physical characteristics, fruiting season, taste, and benefits), not just a scientific definition.

3. Matoa trees do not bear fruit every year: The text states that the Matoa tree bears fruit "from July to October each year". So, this statement is false.

4. Matoa fruit has many benefits: The text mentions various benefits of Matoa fruit, including:

   • Contains high nutrients and antioxidants.
   • Able to ward off free radicals.
   • Acts as an energy booster.
   • Increases body resistance.

   Therefore, this statement is true as it summarizes the benefits mentioned.

5. Matoa fruit does not resemble any fruit: The text explicitly states that its texture and color are "like rambutan, longan, or lychee" and its taste is also "almost similar". So, this statement is false.

In conclusion, the most appropriate statement supported by the text is that the Matoa fruit has many benefits.

Explanation

Let's analyze the sentence structure and vocabulary of the hypothetical language.

Vocabulary Analysis:

• bluwpz: fish
• ckeeck?: young bird

Sentence Structure Analysis

Example sentence: bo ckeeck? mwbluwpz

Meaning: "a fish watches a young bird"

If we break down the structure:

• bo: Sentence starter (marker).
• ckeeck?: Object (young bird). Notice that the object is placed after the word "bo".
• mwbluwpz: Subject (fish) with the prefix mw-. The root word "bluwpz" (fish) gets the "mw-" prefix.

So, the sentence pattern for "Subject watches Object" is:

Application to the Question

We are asked to translate: "a young bird watches a fish".

• Subject: young bird (ckeeck?) $\rightarrow$ must add the mw- prefix to become mwckeeck?.
• Object: fish (bluwpz) $\rightarrow$ placed after "bo".

So the arrangement becomes:

1. Starter word: bo
2. Object: bluwpz
3. Subject (with mw-): mwckeeck?

Combination: bo bluwpz mwckeeck?

Explanation

Let's calculate the percentage decrease in price for each given option. The formula for percentage decrease is:

Analysis of Answer Choices

1. Noodle A in 2019—2020

   • Price 2019: $3350$
   • Price 2020: $3000$
   • Decrease: $3350 - 3000 = 350$
   $$\frac{350}{3350} \times 100\% \approx 10.4\%$$

2. Noodle B in 2017—2018

   • Price 2017: $4500$
   • Price 2018: $4250$
   • Decrease: $4500 - 4250 = 250$
   $$\frac{250}{4500} \times 100\% \approx 5.6\%$$

3. Noodle B in 2018—2019

   • Price 2018: $4250$
   • Price 2019: $4000$
   • Decrease: $4250 - 4000 = 250$
   $$\frac{250}{4250} \times 100\% \approx 5.9\%$$

4. Noodle C in 2019—2020

   • Price 2019: $2800$
   • Price 2020: $2650$
   • Decrease: $2800 - 2650 = 150$
   $$\frac{150}{2800} \times 100\% \approx 5.4\%$$

5. Noodle A in 2017—2018

   • Price 2017: $3500$
   • Price 2018: $2500$
   • Decrease: $3500 - 2500 = 1000$
   $$\frac{1000}{3500} \times 100\% \approx 28.6\%$$

Conclusion

Based on the calculations above, the highest percentage decrease was experienced by Noodle A in 2017—2018, which is 28.6%.

Explanation

Let's analyze each option based on the data in the chart.

Answer Choice Analysis

1. Product Noodle A never experienced a price decrease

   • 2017 to 2018: $3500 \to 2500$ (Decrease)
   • 2019 to 2020: $3350 \to 3000$ (Decrease)
   • This statement is false because Noodle A experienced price decreases twice.

2. The price increase of Noodle B in 2019—2020 was higher than the price increase of Noodle B from 2017—2019

   • Increase 2019—2020: $4500 - 4000 = 500$
   • Change 2017—2019: $4000 - 4500 = -500$ (Decrease)
   • Comparing an increase with a decrease implies both increased, which is not true. Since 2017—2019 saw a decrease, this statement is incorrect.

3. There is a Noodle product that experienced only one price decrease

   • Noodle C experienced price increases in 2017—2018 ($2250 \to 2500$) and 2018—2019 ($2500 \to 2800$).
   • However, in 2019—2020, the price decreased ($2800 \to 2650$).
   • Thus, Noodle C experienced only one price decrease, making this statement true.

4. Almost all Instant Noodle products frequently experience price increases

   • There are 9 price transitions in total (3 products $\times$ 3 periods).
   • Increases occurred 4 times: Noodle A (1x), Noodle B (1x), Noodle C (2x).
   • Decreases occurred 5 times: Noodle A (2x), Noodle B (2x), Noodle C (1x).
   • The frequency of decreases is higher than increases, so this statement is false.

5. The price of Noodle A did not experience a drastic decrease

   • From 2017—2018, the price of Noodle A dropped from $3500$ to $2500$ (a drop of $1000$ or approximately $28.6\%$).
   • This decrease is quite significant, so this statement is likely false.

Conclusion

The correct conclusion based on the data is that there is a Noodle product that experienced only one price decrease, which is Noodle C.

Explanation

We can solve this problem using the filling slots method for the 4-digit passcode.

The available numbers are natural numbers less than 7, which are:

Here is the analysis of possibilities for each digit position:

Additional Explanation for Digit 2

Since the passcode must consist of distinct numbers, we must subtract the numbers already used in other positions from the total available numbers.

• Total available numbers: 6
• Used in Digit 1: 1 number
• Used in Digit 3: 1 number
• Remaining choices: $6 - 1 - 1 = 4$ numbers.

Total Calculation

The maximum number of passcodes is the product of the possibilities for each position:

Thus, Dito has to try a maximum of 16 passcodes.

Explanation

We will first find the speed of engine A, then calculate the speed of engine B, and finally determine the distance traveled by engine B.

Given:

• Speed of engine A: $v_A$
• Speed of engine B: $v_B = \frac{1}{3} v_A$
• Distance traveled by engine A ($s_A$) = $20\text{ km}$
• Time taken by engine A ($t_A$) = $2\text{ hours}$
• Time taken by engine B ($t_B$) = $3\text{ hours}$

Calculating Speed of Engine A

Speed is defined as distance divided by time ($v = \frac{s}{t}$).

Calculating Speed of Engine B

Since $v_B = \frac{1}{3} v_A$, then:

Calculating Distance Traveled by Engine B

Distance traveled is speed multiplied by time ($s = v \times t$).

Thus, the distance traveled using engine B is $10\text{ km}$.

Explanation

We need to calculate the probability for each scenario given in the options.

Total books in each shelf:

• Shelf A = $5 + 3 + 4 = 12$.
• Shelf B = $3 + 3 + 6 = 12$.

The total possible pairs of books taken is $12 \times 12 = 144$.

Analysis of Each Option

We will calculate the probability ($P$) for each event.

1. 2 fiction books

   Taking 1 fiction from Shelf A and 1 fiction from Shelf B.

   $$P(\text{2 Fiction}) = \frac{5}{12} \times \frac{3}{12} = \frac{15}{144}$$

2. 1 fiction book and 1 science book

   There are two possibilities:

   • Fiction from Shelf A and Science from Shelf B: $\frac{5}{12} \times \frac{3}{12} = \frac{15}{144}$
   • Science from Shelf A and Fiction from Shelf B: $\frac{3}{12} \times \frac{3}{12} = \frac{9}{144}$
   $$P(\text{1 Fiction, 1 Science}) = \frac{15}{144} + \frac{9}{144} = \frac{24}{144}$$

3. 1 science book and 1 history book

   There are two possibilities:

   • Science from Shelf A and History from Shelf B: $\frac{3}{12} \times \frac{6}{12} = \frac{18}{144}$
   • History from Shelf A and Science from Shelf B: $\frac{4}{12} \times \frac{3}{12} = \frac{12}{144}$
   $$P(\text{1 Science, 1 History}) = \frac{18}{144} + \frac{12}{144} = \frac{30}{144}$$

4. 2 history books

   Taking 1 history from Shelf A and 1 history from Shelf B.

   $$P(\text{2 History}) = \frac{4}{12} \times \frac{6}{12} = \frac{24}{144}$$

5. 2 science books

   Taking 1 science from Shelf A and 1 science from Shelf B.

   $$P(\text{2 Science}) = \frac{3}{12} \times \frac{3}{12} = \frac{9}{144}$$

Conclusion

Let's compare the probability results (all denominators are 144):

• 2 fiction books: 15
• 1 fiction book and 1 science book: 24
• 1 science book and 1 history book: 30
• 2 history books: 24
• 2 science books: 9

The smallest value is 9.

Thus, the smallest probability is for the child to get 2 science books.

Explanation

This question asks us to find the incorrect conclusion or the negation of the statement found in the text.

Consider the following sentence:

"Brown rice has a higher fiber content... Thus making one feel full faster and not overeat."

This statement is in the form of an implication ($p \rightarrow q$):

• $p$: Brown rice has high fiber content.
• $q$: Makes one feel full faster and not overeat.

An incorrect conclusion means we are looking for the negation of that implication. The negation of $p \rightarrow q$ is $p \land \sim q$ (p and not q).

Let's analyze the components:

• $p$: Brown rice has high fiber.
• $q$: Makes one feel full faster and not overeat.
• $\sim q$: Does not make one feel full faster or leads to overeating (De Morgan's Law: negation of "and" is "or").

Thus, the negation is:

"Brown rice has high fiber and (does not make one feel full faster or leads to overeating)."

Let's check the options:

• Matching option: "Brown rice has high fiber and does not make one feel full faster or lead to overeating."

This option matches the logical form $p \land \sim q$.

Thus, the incorrect conclusion is Brown rice has high fiber and does not make one feel full faster or lead to overeating.

Explanation

The main focus of the text is on the importance of nutrition for child development, where the IDAI Chairman emphasizes one key point:

"These nutrients can be fulfilled through main meals and snacks including street food."

Here is a concise analysis of why the other options are less accurate compared to the fact above:

Thus, the most valid conclusion directly supported by the text is that snacks including children's snacks can be used as a source of nutrition.