Practice Examples 1 , Practice Examples 2
Q.5
(5m+3)2 =4, which of the following could be the least value of m?
A. m>0
B. m=-1/2
C. cannot find
D. m=1
E. m < – 0.5
Solution;
(5m+3)2= 4
25m2 + 30m + 9 = 4
25m2 + 30 m + 9 – 4 = 0
25m2 + 25 m + 5 m + 5=0
25m (m+1) + 5(m+1) = 0
(m+1) (25m+ 1) = 0
(m+1) = 0 or (25m +1) = 0
m = -1 or m = -1/25 = -0.04
So, least value of m = -1 which is lesser than -0.5
Hence, the correct answer is ‘E’.
Q.6
m2 – 2m – 15 = 0 and n2 – 6n + 8 = 0
Quantity A Quantity B
m 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;
Let us solve both the equation one by one.
First Equation;
m2 – 2m – 15 = 0
m2 – 5m + 3m -15 = 0
m (m – 5 ) + 3(m – 5 ) = 0
(m -5) (m + 3) = 0
(m- 5) = 0 or (m+3) = 0
m = 5 or m = -3
Second Equation;
n2 – 6n + 8 = 0
n2 – 4n – 2n + 8 = 0
n (n-4) – 2(n – 4) = 0
(n-4) ( n- 2) = 0
(n – 4) = 0 or (n – 2) = 0
n = 4 or n = 2
Now compare the two quantities.
If m = 5 than for both the values of n = 4 or n = 2 Quantity A is greater.
If m = -3 than for both the values of n = 4 or n = 2 Quantity B is greater.
Hence, we cannot arrive any conclusion with the information given; the correct answer is ‘D’.
Q.7
x2 + 2x – 35 = 0, which of the following could be x , mark all such answers.
A. x is 2 less than 7
B. x = 0
C. x < -1
D. x > -8
E. -1<x<2
Solution;
x2 + 7x – 5x -35 = 0
x(x+7) – 5(x + 7) = 0
( x + 7) ( x – 5) = 0
(x +7 ) = 0 or ( x – 5) = 0
x = -7 or x = 5
We have two solutions for the x , now we will check each answer choice
If we look at the answer choices for one of the solution of x = 5 , ‘A’ is correct.
Choice B; x = 0 , Invalid
Choice C; x < -1 , this is right for x = -7
Choice D; x > -8, this is right for x = -7
Choice E; -1< x < 2, invalid as solutions for is lesser than-1 or greater than 2.
The correct answer is A, C and D.
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