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

**Problem**

**Problem**

50% of a number is equal to 7% of another number. The sum of these numbers is 171. What is the smaller of the two numbers?

- 17
- 14
- 21
- 28
- 36

**The Usual Method**

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Let the smaller of the two numbers be ‘*x*’. Hence the larger number will be (171 – *x*).

Also 7% of (171 – *x*) = 50% of *x*.

(Note: We are not taking 7% of *x* and 50% of (171 – *x*) as *x* is a smaller number than (171 – *x*) and 7% of *x* would be further reduced as compared to 50% of (171 – *x*). Hence 7% of *x* << 50% of (171 – *x*) and not 7% of *x* = 50% of (171 – *x*)).

Hence,

**(Ans: 3)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Between the two numbers, the smaller one would be the one whose 50% is taken and the larger one would be the one whose 7% is taken. This is discussed in the note above of the usual method.

Hence we need to find the number whose 50% is equal to 7% of some other number. Also note that sum of these two numbers is 171. Hence one of the two numbers is even and the other is odd. (‘*y*’ = (171 – *x*)). Thus ‘x’ to be a multiple of 7; the likely values that x can take from the options is 14, 21 and 28. Also note that the other number should be a multiple of 5.

Now if *x* = 14, *y* = 171 – 14 (can’t be a multiple of 5, as the last digit will be 7)

If *x* = 21, *y* = 171 – 21 = 150 (is a multiple of 5)

If *x* = 28, *y* = 171 – 28 (can’t be a multiple of 5, as the last digit will be 3)

(Note: You actually do not even have to subtract 171 – 14 = 167 and 171 – 28 = 143 as just by observing you will know that 171 – 14 and 171 – 28 cannot result in a multiple of 5.)

Hence the answer has to be option ‘3’.

**(Ans: 3)**

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

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