From the above question If 10 boys did not use any of the white red an...
**Answer:**
The given question provides some information about the number of boys who did not use any colors and the number of boys who used all the colors. We need to analyze whether this information is consistent or not. Let's break down the information provided and analyze it step by step.
**Step 1: Understand the Information Given**
- 10 boys did not use any of the white, red, and blue colors.
- 20 boys used all the colors.
**Step 2: Analyze the Information**
**a) Inconsistent since 50 40 30 -20 - 15 20 100**
Based on the given information, we cannot directly determine whether this statement is consistent or inconsistent. The numbers mentioned in the statement (-20, -15) are not related to the information provided about the boys and colors. Therefore, we cannot consider this statement in our analysis.
**b) Consistent**
We can determine the consistency of the given information by calculating the total number of boys and comparing it to the number of boys who did not use any colors and the number of boys who used all the colors.
- Let's assume the total number of boys is "x".
- According to the given information, 10 boys did not use any colors and 20 boys used all the colors.
- Therefore, the remaining number of boys who used some colors but not all can be calculated as (x - 10 - 20).
- The total number of boys can be represented as the sum of these three groups: (10) + (20) + (x - 10 - 20) = x.
- Simplifying this equation, we get: 10 + 20 + (x - 10 - 20) = x.
- By solving this equation, we find that x cancels out and we are left with 0 = 0, which is a consistent result.
**c) Cannot determine due to data insufficiency**
Based on the information provided, we have enough data to determine the consistency of the given information. Therefore, we can determine that this option is not correct.
**d) None of these**
Based on our analysis, the correct option is **b) Consistent**.
In conclusion, the given information about the number of boys who did not use any colors and the number of boys who used all the colors is consistent. However, the statement in option a) is unrelated to the given information and cannot be considered in our analysis.
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