How to transform a verbal statement into a simple Equation
In CAT/GMAT/MBA/Other aptitude tests, there are verbal statements in which a problem is given. To solve the problem, we need to express it as algebraic equation.
The unknown quantity is first considered as a variable ‘x’ and a equation is formed based on the information about unknown quantity. The equation is then solved to find the solution for variable ‘x’ which in turn gives the value of unknown quantity.
Some important translations of verbal statements into the equations is given below :
1. Consecutive Natural numbers problem: There are many problems in which unknown quantity is 3 consecutive natural numbers. So, we can consider 3 consecutive natural numbers as x, x+1 & x+2 with ‘x’ as the lowest of the three consecutive natural numbers. We can also consider them as x-1, x & x+1 for easy calculation with ‘x-1’ as the lowest of the three consecutive natural numbers.
2. Consecutive odd numbers problem : There are many problems in which unknown quantity is 4 consecutive odd numbers. So, we can consider 4 consecutive odd numbers as x, x+2, x+4 & x+6 with ‘x’ as the lowest odd number. We can also consider them as 2x-3, 2x-1, 2x+1 & 2x+3 for easy calculation with ‘2x-3’ as the lowest of the 4 consecutive odd numbers.
3. Consecutive even numbers problem : There are many problems in which unknown quantity is 3 consecutive even numbers. So, we can consider 3 consecutive even numbers as x, x+2 & x+4 with ‘x’ as the lowest even number. We can also consider them as 2x-2, 2x & 2x+2 for easy calculation with ‘2x-2’ as the lowest of the three consecutive even numbers.
4. Age problem : There are many problem in which a parent’s present age is given in terms of child’s present age & parent’s age p years ago/hence is given in terms of child’s age p years ago/hence. And present age of either parent or child is to be calculated.
e.g. Let Ram’s present age is x years and his fathers present age ,which is 3 times ram’s age, is 3x years.
Ram’s age 5 years ago was ‘x-5’ years.
Ram’s age 5 years hence will be ‘x+5’ years.
Father’s age 5 years hence, which will be 2 times of ram’s age 5 years hence, will be 2(x+5) = 3x+5.
5. Three digit number problem: There are many problems in which some data about a three digit number is given. And some data after reversing the number is given.
In this cas the three digit number may be considered as ‘xyz’ where x is the hundred’s digit, y is the ten’s digit and z is the unit’s digit. The final number can be expressed as 100x+10y+z.
The number formed by reversing the digit will be expressed as 100z+10y+x.
The interesting thing in such questions is when we subtract the two numbers, the middle expression ’10y’ is eliminated which reduces it to equation of 2 variables.
6. Money Problem: Ram has certain amount of money in 25 paise, 50 paise and 1 Rs. coins. The number of 50 paise coins is 2 more than the number of 25 paise coins. The number of 1 Rs. coins is 2 less than the number of 25 paise coins.
In this case let ‘x’ be the number of 25 paise coins.
So, number of 50 paise coins = x+2
number of 1 Rs. coins = x-2
Total amount of money with the person = 25x + 50 (x+2) + 100 (x-2) paise
Note : 1 Rs. = 100 paise.
In this we can easily transform the verbal problems into equations to solve the problems. There can be many other problem statements. We will add some other important ones, if we find one which is repeated in various exams.
