Please read the below equation and select an appropriate option from the following. x + y = 10 ; y = x - 2 Quantity A is x. Quantity B is y.
Quantity A is greater.
Solving System of Equations and Comparing Quantities
The question provides a system of two linear equations with two variables, x and y. We are asked to compare the value of x (Quantity A) with the value of y (Quantity B).
The given equations are:
- \( x + y = 10 \)
- \( y = x - 2 \)
Quantity A is \( x \).
Quantity B is \( y \).
Solving the System of Linear Equations
We can solve this system using the substitution method because the second equation already gives us an expression for \( y \) in terms of \( x \).
Substitute the expression for \( y \) from equation (2) into equation (1):
\( x + (x - 2) = 10 \)
Now, we solve this equation for \( x \):
\( x + x - 2 = 10 \)
\( 2x - 2 = 10 \)
Add 2 to both sides of the equation:
\( 2x = 10 + 2 \)
\( 2x = 12 \)
Divide both sides by 2:
\( x = \frac{12}{2} \)
\( x = 6 \)
Now that we have the value of \( x \), we can substitute it back into either equation to find the value of \( y \). Using equation (2) is simpler:
\( y = x - 2 \)
Substitute \( x = 6 \):
\( y = 6 - 2 \)
\( y = 4 \)
Comparing Quantity A and Quantity B
We found the values for \( x \) and \( y \):
- Quantity A = \( x = 6 \)
- Quantity B = \( y = 4 \)
Now, we compare these two values:
\( 6 \) versus \( 4 \)
Since \( 6 \> 4 \), Quantity A is greater than Quantity B.
Let's summarize the values in a table:
| Quantity | Value |
|---|---|
| Quantity A (x) | \( 6 \) |
| Quantity B (y) | \( 4 \) |
Based on the comparison, Quantity A is greater.
Revision Table: System of Linear Equations
| Concept | Description |
|---|---|
| System of Equations | A set of two or more equations with the same variables. |
| Substitution Method | A technique to solve a system of equations by solving one equation for one variable and substituting that expression into the other equation. |
| Solution to System | The values of the variables that satisfy all equations in the system simultaneously. In this case, \( x=6 \) and \( y=4 \). |
Additional Information: Solving and Comparing Variables
When faced with questions asking to compare quantities defined by algebraic equations, the key is often to solve for the specific values of the variables involved. Here are some points to remember:
- Always try to isolate the variables to find their numerical values.
- Systems of linear equations can be solved using various methods like substitution, elimination, or graphing. The choice of method depends on the structure of the equations.
- Once the values are found, perform the direct comparison as required by the question. Pay attention to whether the question asks if one quantity is greater, smaller, equal, or if it's impossible to determine.
- An "impossible to determine" outcome usually arises when the comparison depends on other unknown factors, or when the system of equations has infinite solutions or no solutions, making specific values for the variables impossible to find. In this problem, we found unique values for x and y, allowing for a direct comparison.
Important Questions from Data Sufficiency
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
One question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: What is the length of the rectangle?
Statement:
I. The perimeter of the rectangle is 80 meters.
II. The sum of the adjacent sides is 40 meters.
III. The width of the rectangle is 10 meters.
Choose the correct option.
A. Only I is sufficient.
B. Only I and II are sufficient.
C. III and one from I or II are sufficient.
D. II and one from I or III are sufficient.
