To solve this direction-based problem, we need to visualize the man's movement step-by-step relative to his starting point. We'll establish a coordinate system based on the house's facing direction and track his path.
Correct Option: D) North-West
Two Statements are given followed by two Conclusions:
Statements:
All numbers are divisible by 2.
All numbers are divisible by 3.
Conclusion-I: All numbers are divisible by 6.
Conclusion-II: All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?
Only Conclusion-I
Only Conclusion-II
Neither Conclusion-I nor conclusion-II
Both Conclusion-I nor Conclusion-II
The problem asks us to determine which conclusions logically follow from two given statements about numbers being divisible by certain integers. We need to analyze the properties of divisibility and prime factorization to evaluate each conclusion.
Correct Option: A) Only Conclusion-I
Two Statements are given followed by two Conclusions:
Statements:
All cats are dogs.
All cats are black.
Conclusion-I: All dogs are black.
Conclusion-II: Some dogs are not black.
Which of the above Conclusions two given Statements, disregarding commonly known facts?
Only Conclusion-I
Only Conclusion-II
Neither Conclusion-I nor conclusion-II
Both Conclusion-I nor Conclusion-II
This is a syllogism question. We need to evaluate the given conclusions based on the provided statements, disregarding real-world knowledge. Venn diagrams or logical deductions are useful methods to solve such problems.
C) Neither Conclusion-I nor Conclusion-II
Based on the analysis, neither conclusion can be logically derived from the given statements. There is insufficient information to confirm or deny either conclusion.
Consider the following sequence of numbers:
5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
How many odd numbers are followed by the odd number in the above sequence?
To solve this problem, we need to identify all the odd numbers in the given sequence. Then, for each odd number, we check if the number immediately following it is also an odd number. We count how many such pairs exist.
5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
Correct Option: B) 6
This problem involves determining the total number of boys in a row based on their relative positions. We are given the positions of two individuals, A and V, from opposite ends, and the position of a third individual, G, relative to both A and V. By finding the position of G from both ends, we can calculate the total number of boys.
Three Statements S1, S2 and S3 are given below followed by a Question:
S1: C is younger than D, but older than A and B.
S2: D is the oldest.
S3: A is older than B
Question: Who among A, B, C and D is the youngest?
Which one of the following is correct in respect of the above Statements and the Question?
S1 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question
S2 and S3 together are sufficient to answer the question.
S1 and S3 together are sufficient to answer the Question.
The problem asks us to determine which combination of statements is sufficient to identify the youngest person among A, B, C, and D. We need to analyze each statement individually and in combination to establish the age order of the individuals.
Let's represent "older than" with the symbol \(>\) and "younger than" with \(<\).
From S1, we can write the following relationships:
Combining these, we get: \(D > C > A\) and \(D > C > B\). However, the relationship between A and B is not established by S1. So, A or B could be the youngest.
From S2, we know that D is older than A, B, and C. This can be written as:
This statement alone does not help in finding the youngest, as it only confirms D's position as the oldest.
From S3, we have: \(A > B\).
From S1: \(D > C > A\) and \(D > C > B\).
From S3: \(A > B\).
Combining these, we can establish a complete order:
Since \(C > A\) and \(A > B\), it implies \(C > A > B\).
Also, we know \(D > C\).
Therefore, the complete order from oldest to youngest is \(D > C > A > B\).
From this order, it is clear that B is the youngest.
Thus, S1 and S3 together are sufficient to answer the question.
D) S1 and S3 together are sufficient to answer the Question.
As shown in the step-by-step analysis, combining S1 (\(D > C > A\) and \(D > C > B\)) and S3 (\(A > B\)) allows us to deduce the complete order \(D > C > A > B\), which clearly identifies B as the youngest.
We need to find integers between 1 and 100 that contain the digit 4 but are not divisible by 4. We will first list all numbers containing the digit 4, then identify which of these are divisible by 4, and finally subtract the latter from the former.
List all numbers between 1 and 100 that contain the digit 4:
Total numbers containing the digit 4: \(10 + 9 = 19\).
From this list, identify numbers that are divisible by 4:
Numbers from 40s divisible by 4: 40, 44, 48 (3 numbers).
Numbers ending in 4 (excluding 40s) divisible by 4: 4, 24, 64, 84 (4 numbers).
Total numbers containing the digit 4 and divisible by 4: \(3 + 4 = 7\).
Calculate the numbers that contain the digit 4 but are NOT divisible by 4:
Total numbers with digit 4 - Total numbers with digit 4 and divisible by 4
\(19 - 7 = 12\)
C) 12
This problem involves comparing the densities of two metallic cubes, P and Q, based on their dimensions and masses. We need to establish relationships between their volumes and masses given the scaling factors, and then compare the defined quantities \(u\) and \(v\), which represent their densities.
A) u=4v
As derived in step 6, the relationship between \(u\) and \(v\) is \(u = 4v\).
This problem involves calculating ages based on average and difference. We will set up equations using variables for the ages of the teacher and students, then solve for the teacher's age.
Let \(T\) be the age of the teacher.
Let \(S\) be the age of each student. Since all three students are of the same age, their individual ages are all \(S\).
The problem states that the difference between the age of the teacher and each student is 20 years. This means:
\[ T - S = 20 \]From this, we can express the student's age in terms of the teacher's age:
\[ S = T - 20 \]The average age of the teacher and three students is 20 years. There are a total of \(1\) teacher and \(3\) students, making \(4\) individuals. The sum of their ages divided by the number of individuals equals the average age:
\[ \frac{\text{Sum of ages}}{\text{Number of individuals}} = \text{Average age} \]\[ \frac{T + S + S + S}{4} = 20 \]\[ \frac{T + 3S}{4} = 20 \]Now, substitute the expression for \(S\) from step 3 into the equation from step 4:
\[ \frac{T + 3(T - 20)}{4} = 20 \]Solve the equation for \(T\):
\[ T + 3(T - 20) = 20 \times 4 \]\[ T + 3T - 60 = 80 \]\[ 4T - 60 = 80 \]\[ 4T = 80 + 60 \]\[ 4T = 140 \]\[ T = \frac{140}{4} \]\[ T = 35 \]So, the age of the teacher is 35 years.
Correct Option: C) 35 years
This problem involves calculating the original cost price of an item given its selling price and the percentage loss incurred. We will use the formula relating cost price, selling price, and loss percentage.
Loss percentage is calculated as:
\[ \text{Loss}\% = \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100 \]We know that if there is a loss of \(\text{L}\%\), then the Selling Price is \((100 - \text{L})\%\) of the Cost Price. So, we can write:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss}\%}{100}\right) \]Let \(\text{CP}\) be the cost price of the car.
\[ 3,00,000 = \text{CP} \times \left(1 - \frac{20}{100}\right) \]So, the person spent ₹ 3,75,000 to buy the car.
D) ₹ 375,000 is the correct cost price of the car, calculated by accounting for the 20% loss on the selling price.