Multiple choice

Madan picks up three different digit from the set {1, 2, 3, 4, 5} and forms a mixed number by placing the digit in the space $\displaystyle\square \frac{\square }{\square }$ The fractional part of the mixed number should be less than 1 ( for example $\displaystyle4 \frac{2}{3 } $) what is the difference between the largest and smallest possible mixed number that be formed ?

  1. $\displaystyle4 \frac{7}{20 }$
  2. $\displaystyle4 \frac{3}{10 }$
  3. $\displaystyle4 \frac{9}{20 }$
  4. $\displaystyle4 \frac{3}{5 }$
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A Correct answer
AI explanation

The largest mixed number is 5 and 3/4 and the smallest mixed number is 1 and 2/5. Convert these to improper fractions to get 23/4 and 7/5. Subtracting the smallest from the largest gives 23/4 - 7/5 = 115/20 - 28/20 = 87/20, which simplifies to the mixed number 4 and 7/20.

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