Exercise Problem and Solution Part: 4 (Equation, Solving Equations, Systems of liner equations, Quadratic equations, Inequalities)

Question: 23 If X + Y > 3, then which of the following gives all and only possible value of X?

Option: (a) < 3 (b) X > 30 (c) X > 4 (d) X < 5 (e) X > 5
Explore:
By adding up the two given inequalities we get
      2X > 8
Or, X > 4
 Answer: (c)

Question: 24 If 1/2 of a number s 3 less than 3/4 of the number, then what is the number?
Explore:
Let, the number is X. According to the question,
     X/2 = 3X/4 - 3
=> 3X/4 - 3 = X/2
=> 3X/ 4 - X/2 = 3
=> (3X -2X)/4 = 3
=> X = 12
Answer: The number is 12



Question: 25 If the result obtained by multiplying a number, X , by a number  1 less itself is 4 less than multiplying X by itself, then X =?
Option: (a) 2 (b) 3 (c) 4 (d) 5 (e) 6
Explore:
According to the problem,
  X(X - 1) = X ²- 4
:. X ² - X = X ² - 4
:. X = 4
Answer: (c)

Question: 26 Five times a number less 3 is 32. What is twice the number?
Option: (a) 3 (b) 5 (c) 16 (d) 7 (e) None
Explore:
Here the equation is not given as a mathematical equation. But it is given as an English statement. We will find the mathematical expression from it. Let, X be the number.
   :. 5X - 3 = 32
Or, X = 32 + 3
Or, X = 7
Answer: (d)

Question: 27 The difference between the cube and square of a number is 18. Then what is the number?
Option: (a) 6 (b) 5 (c) 4 (d) 3 (e) None
Explore:
The problem statement gives us the following equation.
X ³ - X ²= 18
Solving this equation for its roots (values of X) will e very difficult & time consuming. So, we will try to find the answer by plugging in the values given in the answer options into the equation.
Since the options are arranged in decreasing order, we will start with the middle value 4.
:. 4 ³ - 4 ²= 64 - 16 = 48
So, it is useless to check option A & B as the difference will only increase. We need it to decrease. Let us try 3.
:. 3 ³- 3 ²= 27 - 9 = 18
Answer : (d)

Question: 28 A ferry can carry 20 buses or 32 cars. If there are 15 buses on the ferry how many cars can be loaded into it?
Option: (a) 6 (b) 8 (c) 12 (d) 15 (e) None
Explore:
The ferry has 15 buses. So, it can take 5 more buses. We have 20 buses = 32 cars.
:. 5 buses (32/20) x 5 = 8 cars
Answer : (b)

Question: 29 If X/(b - c) = Y/(c - a) = X/(a - b), then X+Y+Z = ?
Option: (a) 0 (b) a+b+c (c) (a+b+c)/abc (d) 1 (e) None of these
Explore:
Let, x/(b-c) = y/(c-a) =z/(a-b) = m
:. x = m(b-c); y = m(c-a); z = m(a-b)
:. x+y+z = m(b-c+c-a+a-b) = m.0 =0
Answer : (d)

Question: 30 The sum of 2 numbers is 23 and difference is 21. What is the smaller of the two numbers?
Option: (a) 4 (b) 3 (c) 2 (d) 1
Explore:
Let, the smaller one be x.
:. the bigger one is (23-x).
According to the question,
     (23-x) - x = 21
=> 23 - 2x = 21
=> 2x = 23 - 21 = 2
=> x=1
Answer : (d)

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