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

**Problem**

**Problem**

The sum of cubes of three numbers is 8072 and the ratio of the first to the second as also the second to the third is 3 : 2. What is the second number?

- 2
- 4
- 6
- 9
- 12

**The Usual Method**

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Let the three numbers be ‘1’, ‘2’ and ‘3’.

Hence *a* : *b* = 3 : 2 and *b* : *c* = 3 : 2

*a* : *b* : *c*

= 3 : 2

3 : 2

9 : 6 : 4

Hence, *a* = 9*x*,

*b* = 6*x*

*c* = 4*x*

Now, 8072

Hence the second number is 6*x* = 6 x 2 = 12

**(Ans: 5)**

*Estimated Time to arrive at the answer = 75 seconds.*

**Using Technique**

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Simply by knowing that the ratios are in the form 3 : 2 between the first & second and 3 : 2 between the second & third number, we can know that the second number is a multiple of 6. (Since *a* : *b* : *c* = 9 : 6 : 4)

This means that the answer from amongst the options is either 6 or 12. All other options are eliminated.

Now assuming that *b* = 6, we will have *a* = 9 and *c* = 4 (Since *a* : *b* : *c* = 9 : 6 : 4)

Now simply add the last digits of the cubes 9, 6 and 4 i.e. 9 + 6 + 4 = 19 (Last digit of cubes of 9, 6 and 4 are 9, 6 and 4 respectively). Here the last digit is 9 (from 19). But the last digit of the sum of cubes of these number is actually 2 (from 8 072). Hence the middle number is not 6 but 12.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 30 seconds.*

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