IQ Test - FSC

Explanation
In the given table, each number in the first row is obtained by adding the corresponding numbers in the second row. Similarly, each number in the second row is obtained by adding the corresponding numbers in the third row. Therefore, to find the missing number, we need to add the numbers in the second column: 3 + 2 = 5. Hence, the missing number in the third row is 5.

Explanation
The given statement is correct because it follows the logical reasoning that if all students are examiners and all examiners are educators, then all students must definitely be educators.

Explanation
The given sequence follows a pattern where each number is obtained by adding the next odd number to the previous number. Starting with 1, the next odd number is 3, so 1 + 3 = 4. The next odd number is 5, so 4 + 5 = 9. The next odd number is 7, so 9 + 7 = 16. Continuing this pattern, the next odd number is 9, so 25 + 9 = 34. Finally, the next odd number is 11, so 34 + 11 = 45. Therefore, the next number in the sequence is 45.

Explanation
The answer is 6. The question states that the person picks at least 1/7 of the total number of mushrooms and at most 1/5 of the total number of mushrooms. The only number that satisfies both conditions is 6, as 1/7 of 6 is less than 1 and 1/5 of 6 is also less than 1. Therefore, the group must have 6 people.

Explanation
The average of 10 positive integers that differ by 2 is 10. This means that the sum of these 10 integers is 100. To maximize the largest number, we want to distribute the sum as evenly as possible. Since the integers differ by 2, we can start with the smallest number (let's call it x) and add 2 to it repeatedly until we reach the largest number. So, x + (x+2) + (x+4) + ... + (x+18) = 100. Solving this equation, we find that x = 45. Therefore, the largest number is 45 + 18 = 55.

Explanation
The given scenario describes a situation where Long made a mistake while performing calculations. Instead of adding a positive number to 3, he accidentally divided it by 3. Then, instead of taking the square root of the result, he squared it. The incorrect result obtained was 16. To find the correct answer, we need to reverse the incorrect operations. Since 16 is the square of 4, the correct result should be the square root of 4, which is 2. Therefore, the correct answer is 6, as it is the only option provided that matches the correct result.

Explanation
The number of trailing zeros in a factorial can be determined by counting the number of times the number can be divided evenly by 10. Since 10 can be factored into 2 * 5, we need to count the number of pairs of 2 and 5 in the prime factorization of the factorial number. Since there are always more multiples of 2 than 5, we only need to count the number of multiples of 5. In the case of 70!, there are 14 multiples of 5 (5, 10, 15, ..., 70), but some of these multiples have additional factors of 5. For example, 25 has two factors of 5. So, we need to count these additional factors as well. In total, there are 16 factors of 5 in the prime factorization of 70!, which means it has 16 trailing zeros.

Explanation
The remaining rectangle will have an area equal to 100% - 10% = 90% of the original width, and 100% - 30% = 70% of the original length. Therefore, the remaining rectangle will have an area equal to 90% * 70% = 63% of the original rectangle.

Explanation
The difference between the 3-digit number and the 2-digit number is 989. To find the sum of these two numbers, we need to add 989 to the 2-digit number. Since the difference is 989, the 2-digit number must be 10 less than 989, which is 979. Adding 989 to 979 gives us a sum of 1968. Therefore, the correct answer is 1009.

Explanation
The given sequence consists of prime numbers. The numbers are increasing by 4, 4, 6, and 4 respectively. Therefore, the next number in the sequence should be 3.

Explanation
The correct answer is C. The question asks for the percentage increase in the price of oranges. Statement 1 provides the original price of 5000 dong per kilogram, but does not provide any information about the increase. Statement 2 provides the additional increase of 2000 dong per kilogram. By combining both statements, we can calculate the percentage increase by dividing the increase of 2000 dong by the original price of 5000 dong and multiplying by 100. Therefore, statement 2 alone is sufficient to answer the question.

Explanation
If l/g is an odd number, it means that l and g have opposite parities. Since gl is even (as stated in statement 1), it implies that g and l must both be even. Therefore, the sum of g and l will also be even.

Explanation
The correct answer is B. According to statement (2), if S divided by 6 leaves a remainder of 1, it means that S is not divisible by 2 evenly, therefore S is not an even number.

Explanation
The question asks for the weight of the heaviest bag out of three bags that weigh a total of 60kg. Option B states that there is a bag weighing 31kg, which is heavier than the bag weighing 22kg mentioned in option A. Therefore, option B is the correct answer as it provides the weight of the heaviest bag.

Explanation
The given correct answer is D. However, without the options provided, it is difficult to determine the exact explanation for why D is the correct answer. The question appears to be incomplete or not readable, so a proper explanation cannot be generated.