Improving CAT Quant Skills requires practice and solving a variety of quantitative problems. Let’s solve the following question:
A rabbit is on a controlled diet and is fed a daily mixture of two foods, food X and food Y. The rabbit’s diet provides 300 grams of this mixture per day. Food X contains 10 percent protein, while food Y contains 15 percent protein. The rabbit’s diet provides exactly 38 grams of protein daily. We need to determine how many grams of food X are in the mixture.
To solve this problem, we start by setting up equations based on the given information. Let’s assume that x grams of food X are in the mixture. Therefore, the remaining grams of food Y in the mixture would be (300 – x) grams.
The protein content of food X can be calculated by multiplying 10 percent (0.10) by x grams. Similarly, the protein content of food Y can be calculated by multiplying 15 percent (0.15) by (300 – x) grams.
According to the given information, the rabbit’s diet provides exactly 38 grams of protein daily. Therefore, we can set up the following equation:
0.10x + 0.15(300 – x) = 38
To solve this equation, we can simplify it as follows:
0.10x + 45 – 0.15x = 38
0.05x = 38 – 45
0.05x = -7
x = -7 / 0.05
x = -140
From the obtained value of x, we can infer that there are -140 grams of food X in the mixture. However, this does not make logical sense, as the weight of food cannot be negative. We need to reconsider our initial assumptions.
By re-evaluating the problem, we realize that food X must be present in a quantity that is less than or equal to 300 grams (as it is part of the 300-gram mixture). Hence, we can conclude that the weight of food X in the mixture is a positive value.
From the given answer choices, the only option that satisfies this condition is (B) 140 grams. Therefore, we can conclude that there are 140 grams of food X in the mixture.
Remember that practicing a variety of quantitative problems, like the one above, will help you improve your CAT Quant skills. Keep practicing and seeking help when needed to enhance your problem-solving abilities.
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