Here’s and example of a **SMART MATH** problem for **ALGEBRA.**

**Problem**

**Problem**

Three years ago A’s age was double that of B’s. Seven years later, the sum of their united ages will be 83 years. How old is A?

- 24 years
- 35 years
- 45 years
- 48 years
- 54 years

**The Usual Method**

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Let the present age of A be ‘1’ years.

And the present age of B be ‘2’ years.

and

Hence

…… Eq. 1

and …… Eq. 2

Solving both the equations simultaneously, we get:

+ (Multiplying Eq. 2 by 2 on both sides)

3*a* = 135

**(Ans: 3)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

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Note that the age of A three years earlier should have been as even number . From the options, the various values of (*a* – 3) that we get are:

Option # Value of (*a* – 3)

a 24 – 3 = 21 (Odd)

b 35 – 3 = 32 (Even)

c 45 – 3 = 42 (Even)

d 48 – 3 = 45 (Odd)

e 54 – 3 = 51 (Odd)

Options ‘1’, ‘4’ and ‘5’ are eliminated as there yield odd values.

Note that half of 83 = 41.5. From the given conditions, we can also deduce that *a* > *b*. Hence, *a* > 41.5. This leaves us only with option ‘3’.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 15 seconds.*

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