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A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large? – OG 2020 Question #323 with Solution

OG 2020: Question No. 323

A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large?

  1. In the production lot, 400 of the small toys are green.
  2. In the production lot, 2/3 rd of the toys produced are small.[/two_third] 
    Source OG 2020
    Type Data Sufficiency
    Topic Word Problems
    Sub-Topic Ratio
    Difficulty Medium

    Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

  • A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green.
  • For each size, there are equal numbers of red and green toys in a certain production lot.

We need to determine

  • The fraction of the total number of green toys, which are large.

To determine this, we need to know the total number of green toys, and how many of them are large ones.

Let us assume that

  • Number of small red toys produced = S
  • Number of large red toys produced = L

As there are equal number of red and green toys produced in each production lot, we can say

  • Number of small green toys produced = S
  • Number of large green toys produced = L

Therefore, fraction of the total number of green toys, which are large = L / (S+L)

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, in the production lot, 400 of the small toys are green.

  • Therefore, we can say S = 400.
  • However, from this statement, we cannot determine the value of L.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, in the production lot, 2/3 rd of the toys produced are small.

  • Total number of small toys = S + S = 2S
  • Total number of large toys = L + L = 2L
  • Therefore, we can say = 2S / (2S + 2L) = 2/3
    • Or, S/ S+ L = 2/3
  • Hence, L/ S + L = 1 – 2/3  = 1/3

As we can determine the value of L/ S+ L, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required.

Hence, the correct answer choice is option B.

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