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

** **

**Problem**

**Problem**

The LCM and HCF of two numbers is 300 and 15 respectively. The difference between the two numbers is equal to the HCF. Find the numbers.

- 15, 30
- 60, 75
- 80, 95
- 40, 55
- 90, 05

**The Usual Method**

[contentblock id=google-adsense-post]

Since the product of two numbers = product of LCM and HCF of two numbers,

*x* = –75 or *x* = 60

Negative (as the LCM and the HCF both will be negative)

*x* = 60 and *x* + 15 = 60 + 15 = 75

**(Ans: 2)**

*Estimated Time to arrive at the answer = 90 seconds.*

**Using Technique**

[contentblock id=google-adsense-post]

Since the product of two numbers = product of LCM and HCF of two numbers, just multiply the options to see which is = = 4500 as follows:

15 x 30 = 450 4500

60 x 75 = 4500 = 4500 hence this should be the answer. There is no need to check further as there cannot be more than one correct answer.

** **

**(Ans: 2)**

*Estimated Time to arrive at the answer = 10 seconds.*

[starrater tpl=10]

[contentblock id=smartmath-blockquote]