GMAT Challenge Series (700+): Q9

Trail Mix.jpeg

Question:

A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts? 

A. 40%

B. 48%

C. 49%

D. 50%

E. 58%

MBA Wisdom's Answer:

$$\text{peanuts : cashews : almonds}$$ $$\text{10 :4 :1}$$ $$\text{50 : 20 : 5}$$ $$\text{Peanuts have to be greater than the cashews and almonds}$$ $$\text{peanuts} > \text{cashews} + \text{almonds}$$ $$\text{peanuts} > {20} + {5}$$ $$\text{peanuts} > {25}$$ $$\text{As peanuts have to be an integer the lowest number is 26}$$ $$\text{decrease} = {\text{reduction} \over \text{original number}}$$ $$\text{decrease} = \frac{50 - 26}{50} = \frac{24}{50}$$ $$\text{decrease} = \text{48%}$$