Here’s and example of a SMART MATH problem for RATIO PROPORTION.
Problem
Two numbers are less than 10 and in the ratio 3 : 1. What is their product?
- 10
- 12
- 14
- 16
- 18
The Usual Method
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Let the numbers be 3x and 1x respectively.
any value greater than 3 since for x = 4, 3x will become = 12 which is > 10 and is not allowed as per the question.
Hence x will take values 1, 2 and 3 only.
The product is
When x =1; 3
When x =2; 12
When x =3; 27
From amongst the above values, only 12 appears in the options, so it is the answer.
(Ans: 2)
Estimated Time to arrive at the answer = 30 seconds.
Using Technique
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Let the numbers be 3x and 1x respectively.
So product of these numbers is .
Thus the answer should be a multiple of 3 and a perfect square.
Option ‘2’ and ‘5’ are both multiples of 3, but option ‘5’ is not a multiple of a perfect square when it is a multiple of 3. (i.e. 18 3 x some perfect square). Hence answer is 12.
(Ans: 2)
Estimated Time to arrive at the answer = 5 seconds.
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