Seven surgeons, W, X, Y, Z, A, B and C, were sitting around a square table, facing the centre. Four of them are sitting at the corners while three are sitting at the exact centre of the sides. One of the centres of the sides was empty. C, at one of the corners, was immediately next to both B and Y. Z was immediately next to both B and X. A was at the immediate right of X.
Which surgeon was third to the right of W?
The problem describes a seating arrangement around a square table with seven people and one empty spot. We need to deduce the positions of all individuals based on the given clues and then find the person third to the right of W.
Understand the setup: There are 8 possible spots around a square table (4 corners, 4 mid-sides). Seven surgeons are sitting, so one mid-side spot is empty. All are facing the centre.
Place C: "C, at one of the corners, was immediately next to both B and Y." This means B and Y must be on either side of C. Since C is at a corner, B and Y must be at the two adjacent mid-side positions. Let's assume C is at the bottom-left corner. Then B is at the left mid-side and Y is at the bottom mid-side (or vice-versa).
Initial arrangement (example, C at bottom-left corner):
_ _ _
| Y |
B C _
Place Z: "Z was immediately next to both B and X." This means B and X are on either side of Z. Since B is already placed next to C (at a mid-side), Z must be at the other side of B. If B is at the left mid-side, then Z must be at the top-left corner. X would then be at the top mid-side. (This confirms our initial placement of B and Y relative to C, as B must be at a mid-side for Z to be at a corner).
Updated arrangement:
X Z _
| Y |
B C _
Place A: "A was at the immediate right of X." X is at the top mid-side. Since everyone is facing the centre, the immediate right of X would be the top-right corner. So, A is at the top-right corner.
Updated arrangement:
X Z A
| Y |
B C _
Identify the empty spot and W: We have placed C, B, Y, Z, X, A. That's 6 people. The remaining person is W. The remaining spots are the right mid-side and the bottom-right corner. One of the mid-sides is empty. Since the left mid-side (B), top mid-side (X), and bottom mid-side (Y) are occupied, the right mid-side must be empty.
Therefore, W must be at the bottom-right corner.
Final arrangement (clockwise from bottom-left corner C):
X (mid) Z (corner) A (corner)
| |
B (mid) (Empty) (mid)
| |
C (corner) Y (mid) W (corner)
Find the surgeon third to the right of W: W is at the bottom-right corner. Facing the centre, the positions to the right of W are:
C) B is incorrect. Let's re-evaluate the final arrangement and the question. My step 5 and 6 had an error in identifying the positions. Let's re-draw and re-verify.
Let's use a standard numbering for a square table, starting from a corner and going clockwise. Let's assume C is at position 1 (corner).
Positions: 1 (corner), 2 (mid), 3 (corner), 4 (mid), 5 (corner), 6 (mid), 7 (corner), 8 (mid).
1. C is at a corner, next to B and Y. Let C be at position 1. Then B and Y are at positions 2 and 8 (mid-sides). Let's assume B at 2, Y at 8.
C (1) - B (2) - ? (3) - ? (4) - ? (5) - ? (6) - ? (7) - Y (8)
2. Z is next to B and X. B is at position 2. So Z must be at position 3 (corner) and X at position 4 (mid-side).
C (1) - B (2) - Z (3) - X (4) - ? (5) - ? (6) - ? (7) - Y (8)
3. A is at the immediate right of X. X is at position 4 (mid-side). Facing the center, the immediate right of X is position 5 (corner).
C (1) - B (2) - Z (3) - X (4) - A (5) - ? (6) - ? (7) - Y (8)
4. Identify W and the empty spot. We have placed C, B, Z, X, A, Y. The remaining person is W. The remaining spots are 6 (mid-side) and 7 (corner). One mid-side is empty. Since 2, 4, 8 are occupied, position 6 must be the empty spot. Therefore, W must be at position 7 (corner).
C (1) - B (2) - Z (3) - X (4) - A (5) - Empty (6) - W (7) - Y (8)
5. Find the surgeon third to the right of W. W is at position 7 (corner). Facing the center, moving right (clockwise):
The surgeon third to the right of W is B.
Correct Option: C) B
The problem involves finding a number based on a given ratio and the difference between the two numbers. We can represent the numbers using a common multiple and then use the given difference to find the value of that multiple.
Let the two numbers be \(N_1\) and \(N_2\). The given ratio is \(N_1 : N_2 = 5 : 3\).
This means we can express the numbers as multiples of a common variable, say \(x\). So, let the first number be \(N_1 = 5x\) and the second number be \(N_2 = 3x\).
The difference between the numbers is given as 54. Since \(5x\) is greater than \(3x\), the difference is \(N_1 - N_2\).
So, we have the equation:
\[ 5x - 3x = 54 \]Simplify the equation:
\[ 2x = 54 \]Solve for \(x\):
\[ x = \frac{54}{2} \]\[ x = 27 \]Now that we have the value of \(x\), we can find the two numbers:
First number \(N_1 = 5x = 5 \times 27 = 135\)
Second number \(N_2 = 3x = 3 \times 27 = 81\)
The question asks for the smaller number. Comparing \(N_1 = 135\) and \(N_2 = 81\), the smaller number is 81.
Correct Option: C) 81
Simplify 3(3x − 2) + x(\( \frac{4x}{2} \)) + 15 − 12.
To simplify the given algebraic expression, we will use the distributive property to expand the terms, perform multiplication, and then combine like terms.
Expand the first term: Apply the distributive property to \(3(3x - 2)\).
\[ 3(3x - 2) = (3 \times 3x) - (3 \times 2) = 9x - 6 \]
Simplify the second term: Simplify \(x\left(\frac{4x}{2}\right)\).
\[ x\left(\frac{4x}{2}\right) = x(2x) = 2x^2 \]
Combine all terms: Substitute the expanded and simplified terms back into the original expression.
The original expression is: \(3(3x - 2) + x\left(\frac{4x}{2}\right) + 15 - 12\)
Substitute the simplified parts: \[ (9x - 6) + (2x^2) + 15 - 12 \]
Rearrange and combine like terms: Group terms with the same variable and exponent, and constant terms.
\[ 2x^2 + 9x - 6 + 15 - 12 \]
Combine the constant terms: \[ -6 + 15 - 12 = 9 - 12 = -3 \]
So the expression becomes: \[ 2x^2 + 9x - 3 \]
D) The simplified expression is \(2x^2 + 9x - 3\), which matches option D.
To calculate the discount percentage, we need to determine the total number of items a customer receives and the number of items they actually pay for. The discount is then calculated based on the free items received as a percentage of the total items.
A) 40 % is the correct discount percentage, as calculated by dividing the number of free sarees (2) by the total number of sarees received (5) and multiplying by 100.
51 men can complete a work in 12 days. Four days after they started working, 6 more men joined them. How many days will they now take to complete the remaining work?
8 \( \frac{1}{19} \) days
5 \( \frac{9}{19} \) days
7 \( \frac{3}{19} \) days
6 \( \frac{7}{19} \) days
This is a work and time problem. We will calculate the total work in terms of "man-days". Then, we'll determine the work completed in the initial days and the remaining work. Finally, we'll calculate the time taken to complete the remaining work with the increased number of men.
Calculate Total Work:
Given that 51 men can complete a work in 12 days.
Calculate Work Done in the First 4 Days:
51 men worked for 4 days.
Calculate Remaining Work:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done} \]Calculate New Number of Men:
After 4 days, 6 more men joined.
Calculate Days to Complete Remaining Work:
Now, 57 men will complete the remaining 408 man-days of work.
C) 7 \( \frac{3}{19} \) days
The pH scale is a measure of the acidity or alkalinity of a solution. It is inversely related to the hydrogen ion concentration (\([\text{H}^+]\)). A lower pH indicates a higher \([\text{H}^+]\) and thus a more acidic solution, while a higher pH indicates a lower \([\text{H}^+]\) and a more alkaline (basic) solution. The relationship is given by the formula:
\[ \text{pH} = -\log_{10}[\text{H}^+] \]From this, we can deduce that:
\[ [\text{H}^+] = 10^{-\text{pH}} \]Therefore, to arrange the solutions in increasing order of \([\text{H}^+]\) concentration, we need to arrange them in decreasing order of their pH values.
As pH increases, \([\text{H}^+]\) decreases. Conversely, as pH decreases, \([\text{H}^+]\) increases. So, to arrange in increasing order of \([\text{H}^+]\), we need to arrange in decreasing order of pH.
The pH values in decreasing order are: 11 (C), 9 (E), 7 (D), 4 (A), 1 (B).
Since decreasing pH means increasing \([\text{H}^+]\), the order of increasing \([\text{H}^+]\) concentration will be:
C (pH 11) < E (pH 9) < D (pH 7) < A (pH 4) < B (pH 1)
C) C < E < D < A < B is the correct order, as it represents the solutions arranged from the lowest \([\text{H}^+]\) concentration (highest pH) to the highest \([\text{H}^+]\) concentration (lowest pH).
The given series is a numerical sequence. We need to identify the pattern or rule that generates the numbers in the series and then apply that rule to find the missing number.
D) 1285 is the correct answer because it follows the established pattern of \(\text{Previous Term} \times n + n\).
The question asks to identify which aspect of large dams has NOT been criticized. We need to evaluate each option based on common criticisms leveled against large dam projects.
Based on this analysis, social, environmental, and economic aspects are widely recognized areas of criticism for large dams, whereas "psychological" is not typically cited as a distinct category of criticism.
Correct Option: A) Psychological — While the displacement caused by dams can lead to significant psychological distress for affected individuals, "psychological" is not commonly categorized as a direct, independent aspect of criticism against large dams in the same way as social, environmental, or economic impacts. The psychological effects are generally considered part of the broader social impact of displacement and loss of traditional ways of life.
To solve this problem, we need to identify the largest two-digit prime number and the largest three-digit prime number. Then, we will perform the specified arithmetic operations (doubling the first and tripling the second) and sum the results.
Two-digit numbers range from 10 to 99. We need to check prime numbers downwards from 99.
Thus, the largest two-digit prime number is 97.
Three-digit numbers range from 100 to 999. We need to check prime numbers downwards from 999.
Thus, the largest three-digit prime number is 997.
Correct Option: A) 3185
The question asks us to identify the statement that is NOT true about a rectangle. We need to evaluate each option based on the properties of a rectangle.
Correct Option: B) Diagonals of a rectangle do not bisect each other.
This statement is false because diagonals of a rectangle (being a type of parallelogram) always bisect each other.