#Algebra
Practice Examples
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Q.1
Solve the following equation and find the value of y?
y – ( 4 – y ) = 2
A. 9
B. 3
C. 2
D. 7
E. 8
Solution
Correct answer choice is B.
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Q.2
Quantity A Quantity B
12(2x – 1 ) = 0 6(4)x-6-6 = 0
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution
Let us solve the equation for Quantity A
12(2x-1) = 0
24x-12 = 0
24x = 12
x = 1/2
Now we will solve the equation for Quantity B
6(4) x – 6 – 6 = 0
24x -12 = 0
24x =12
x =12/24
x = 1/2
If we compare Quantity A with Quantity B, both are equal thus, correct answer choice is C.
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Q.3
Solve the following equation form and n.
2m+ 2m – n = 6
m + n = 4
A. m =2 , n = 2
B. m = -2, n = 2
C. m= 4 , n = 0
D. m = 8 , n = -2
E. m= 3 , n = 3
Solution
Let us solve this problem using substitution method
Let us solve this problem using substitution method
4m – n = 6 ———— Equation 1
m + n =4 ———— Equation 2
Taking the value of m from equation 2
m = 4 –n
Substitute this value of m in equation 1 we will get;
4 ( 4 -n)-n= 6
16 – 4n-n = 6
-5n = 6-16
-5n = -10
n = 10/5
n = 2
Now we can easily find the value of m by substituting the value of n in equation 1
4m – n = 6
4m = 6 + n
4m = 6 + 2
m = 8/4
m = 2
Correct answer choice is A.
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Q.4
Find the value of x which satisfies following equation.
3(11x – 5 ) = 3x – 4
33x – 15 = 3x – 4
33x – 3x = 15 – 4
30x = 11
x = 11/30
Correct answer choice is D.
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Q.5
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution
Let us solve the equation for Quantity A
(10x- 2)/3 + 3x = 5/2
Multiply both side by 2
20x – 4 + 18x = 15
38 x = 19
x =19/38
x =1/2
Now we will solve equation for Quantity B
( 4x + 48- 42)/12 = 1
4x + 48 – 42 = 12
4x = 12 – 6
4x = 6
x=6/4
x =3/2
If we compare Quantity A with Quantity B, The value of for quantity B is greater, hence correct answer choice is B.
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Q.6
= -3/4
Hence, correct answer choice is ‘D’.
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Q.7
Quantity A Quantity B
5x- 1 = 5(x + 8) 2
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution
First we will solve the equation for Quantity A
5x- 1 = 5(x + 8)
5x – 1 = 5x + 40
5x will be cut both sides so;
-1 = 40. Here we are not able to arrive at any solution. Thus, Quantity A cannot be compared to Quantity B. Correct answer choice is D.
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Q.8
Solve the following equation for the value of m?
Cross multiply both sides;
121( m-5) = 144(6-m-2)
121m – 605 = 576 –144 m
121m + 144m = 576 + 605
265m = 1181
m =1181/265
m = @ 4.45
This value is lesser than 5, thus correct answer is ‘B’.
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Q.9
Find the values of m and n?
5m + 6n + 2 = 9
6n – 2m = 6
m = ____ , n = ____?
Solution
5m + 6n + 2 = 9
6n – 2m = 6
We will solve this equation using elimination method
5m + 6n = 7
6n – 2m = 6
5m + 6n = 9 ———- Equation 1
-2m + 6n = 6 ——— Equation 2
To make variable m equivalent, multiply both the equations with coefficients of m by interchanging each other;
5m + 6n = 9 x 2
-2m + 6n = 6 x 5
10m + 12n = 18
-10m+ 30n = 30
Add both the equations
10m + 12n = 18
-10m+ 30n = 30
42n = 48
n =48/42
= 8/7
Subsitute the value of n in equation 1 to get the value of m
5m + 6n = 7
5m + 6 x 8/7= 7
5m = 7-48/7
5m = 49 -48/7
5m =1/7
m =1/35
The answer is m =1/35 and n = 8/7
Let us cross check these values
5m + 6n = 7
5 x 1/( 35) + 6 x 8/( 7) =7
1/7+48/7 =7
49/7 =7
7 = 7
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Q.10
From the following options which are not a solution of the equation
5m + 5n = 2n – 4m + 15?
A. m = 1 , n = 2
B. m = -1 , n = 8
C. m = 2 , n = -1
D. m = 3 , n = -4
E. m = -2 , n = 9
Solution
5m + 5n = 2n – 4m + 15
5m + 4m + 5n – 2n = 15
9m + 3n = 15
Solve this sum by putting answers in the equations
Let us start substituting the values given in the option choices
- If m = 1, n = 2 ; 9 x 1 + 3 x 2 = 15
- If m = -1, n = 8 ; 9 x (-1 ) + 3 x 8 = 15
- If m = 2, n = -1 ; 9 x 2 + 3 x (-1) = 15
- If m = 3, n = -4 ; 9 x 3 + 3 x (- 4) = 15
- If m = -2, n = 9 ; 9 x (-2 )+ 3 x 9 = 9
So, correct answer choice is E.
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Q.11
m + 8 = n
(m-3) (n- 1) = 0
Quantity A Quantity B
2n 3m
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution;
m + 8 = n ……………….Equation 1
(m-3) (n- 1) = 0………………..Equation 2
In this equation 2 product of two variables is ‘0’ that means either of the variables or both variables can be zero.
So, m-3 = 0 or n -1 = 0
m = 3 or n = 1
Condition 1.If m =3, then 3+ 8 = n
n = 11
2n = 2x 11 = 22, 3 x m = 3 x3 = 9, Quantity A is greater.
Condition 2.If n = 1, then m + 8 = 1, m = 1 – 8 = – 7
m = -7
3m = 3 x -7 = -21, 2n = 2 x 1 = 2, Quantity A is greater.
In both the condition, Quantity A is greater. Correct answer choice is ‘A’.
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Q.12
m ( n-5 ) = 0
m + n = 15
Quantity A Quantity B
4m n
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution:
( m + 1) ( n-5 ) = 0………………Equation 1
m + n = 15 …………………Equation 2
In equation 1, multiplication of two variables is zero which is possible only, if m is zero or n is zero or mn is zero.
(m + 1) (n – 5) = 0
m = 0 or n-5 = 0
m = 0 or n = 5
Condition 1; If m = 0 then m + n = 15 will be
0 + n = 15
n = 15
Quantity A: m= 0, 4m = 4 x 0 = 0
Quantity B: n = 15
n > 4m, Quantity B is greater
Condition 2; If n = 5 then m + n = 15 will be
m + 5 = 15
m = 10
Quantity A: 4m = 4 x m = 4 x 10 = 40
Quantity B: n = 5
4m > n, Quantity A is greater
One time n is greater and 2nd time 4m is greater, hence the relationship cannot be determined from given information.
The correct answer is ‘D’.
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