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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 9

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

Arithmetic

Problem

If g(x)=\frac{3a-5}{2a+1}, then what is the value of \frac{5g(1)-3g(2)+10g(-1)}{8}?

  1. 1141
  2. \frac{\text{1141}}{\text{15}}
  3. \frac{\text{1141}}{\text{120}}
  4. \frac{\text{1141}}{\text{60}}
  5. \frac{\text{1141}}{\text{20}}

The Usual Method

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First get the values of:

g(1)=\frac{3(1)-5}{2(1)+1}=\frac{-2}{3}

g(2)=\frac{3(2)-5}{2(2)+1}=\frac{1}{5}

g(-1)=\frac{3(-1)-5}{2(-1)+1}=\frac{-8}{-1}=8

Now, substitute these values in the given equation, we get:

\frac{5\left( \frac{-2}{3} \right)-3\left( \frac{1}{5} \right)+10\left( 8 \right)}{8}

=\frac{\frac{-10}{3}-\frac{3}{5}+80}{8}

=\frac{\frac{-50-9+1200}{15}}{8}

=\frac{1141}{15}\times \frac{1}{8}=\frac{1141}{120}

(Ans: 3)

Estimated Time to arrive at the answer = 75 seconds.

Using Technique

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Observe from the equation \frac{5g(1)-3g(2)+10g(-1)}{8} has ‘8’ in its denominator. This 8 cannot be reduced in further operations as 5, 3 and 10 are relatively prime to 8 and hence have an HCF of 1. Should the HCF of these numbers be 2 or any multiple of 2, then the denominator ‘8’ will get to 4, 2 or 1 accordingly. But in this particular case, it is not so. Hence, the answer should have 8 or a multiple of 8 in its denominator. The only option satisfying this criterion is options ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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