Read the following question and decide which of the given statements is/are sufficient. Statements:
What is the total number of illegal immigrants?
1. 30% of the total illegal immigrants are from Bangladesh.
2. Remaining are from India.
Neither 1 nor 2 is sufficient to answer the question.
Analyzing the Sufficiency of Statements for Total Illegal Immigrants
The question asks for the total number of illegal immigrants. We are given two statements and need to determine if either statement alone or both statements together are sufficient to answer the question.
Understanding the Statements
Let $T$ represent the total number of illegal immigrants.
- Statement 1: 30% of the total illegal immigrants are from Bangladesh.
- Statement 2: Remaining are from India.
Evaluating Statement 1 Alone
Statement 1 tells us that illegal immigrants from Bangladesh constitute 30% of the total. Mathematically, this means:
Number of illegal immigrants from Bangladesh $= 0.30 \times T$
This statement provides a percentage relationship between the number of immigrants from Bangladesh and the total number of illegal immigrants. However, it does not give us a specific number for the immigrants from Bangladesh or the total number of illegal immigrants. We cannot find the value of $T$ based on this statement alone.
Therefore, Statement 1 alone is not sufficient to determine the total number of illegal immigrants.
Evaluating Statement 2 Alone
Statement 2 says the "Remaining" immigrants are from India. The term "Remaining" implies it is based on a previous statement. If we consider Statement 2 independently, it doesn't provide any percentage or number of illegal immigrants from India or any relationship to the total number of illegal immigrants. It simply states their origin. Thus, Statement 2 alone provides no information to calculate the total number of illegal immigrants.
Therefore, Statement 2 alone is not sufficient to determine the total number of illegal immigrants.
Evaluating Both Statements Together
Now, let's consider both statements together. Statement 1 says 30% are from Bangladesh. Statement 2 says the remaining are from India. The "remaining" refers to the illegal immigrants who are not from Bangladesh.
If 30% are from Bangladesh, then the percentage of illegal immigrants from India must be $100\% - 30\% = 70\%$.
So, combining both statements, we know:
- Illegal immigrants from Bangladesh = 30% of $T$
- Illegal immigrants from India = 70% of $T$
While we now know the percentage distribution of illegal immigrants by origin (assuming they are only from these two countries), we still do not have any absolute number (the actual count of immigrants from Bangladesh, or from India, or the total count). Knowing that 30% are from Bangladesh and 70% are from India does not help us find the total number $T$ unless we know the value of 30% of $T$ or 70% of $T$ as a numerical quantity.
For example, if there are 100 illegal immigrants total, 30 are from Bangladesh and 70 are from India. If there are 1000 illegal immigrants total, 300 are from Bangladesh and 700 are from India. The percentages remain the same, but the total changes. Without a count, we cannot find the total.
Therefore, both statements together are not sufficient to determine the total number of illegal immigrants.
Conclusion on Data Sufficiency
Neither Statement 1 alone nor Statement 2 alone is sufficient. Combining both statements also does not provide enough information to determine the total number of illegal immigrants.
| Statement(s) Used | Sufficient? | Reason |
|---|---|---|
| Statement 1 Alone | No | Gives percentage from one country, not the total or a count. |
| Statement 2 Alone | No | Gives origin of remaining, no percentage or count independently. |
| Both Statements Together | No | Give percentage breakdown by origin, but no absolute count. |
Based on this analysis, neither statement nor both statements together are sufficient to answer the question about the total number of illegal immigrants.
Revision Table: Key Concepts in Data Sufficiency
| Concept | Explanation | Example |
|---|---|---|
| Sufficiency | A statement (or set of statements) is sufficient if the information provided allows you to definitively answer the question asked, without needing additional information. | Question: What is x? Statement: x = 5. (Sufficient) |
| Necessity vs. Sufficiency | Information might be necessary for a solution but not sufficient on its own. Sufficiency means the information guarantees a unique answer. | To find the area of a rectangle, length is necessary, but length alone is not sufficient; width is also needed. Length and width together are sufficient. |
| Evaluating Statements | Test each statement alone first. If neither is sufficient, then test both statements together. If combined information helps answer the question, then both are sufficient. | Systematically check sufficiency for each case: S1 alone? S2 alone? S1 & S2 together? |
Additional Information on Determining Sufficiency
In Data Sufficiency problems, the goal is not to find the actual answer to the question, but to determine if the given information is enough to find that answer. Here are some points to keep in mind:
- Assume Independence: When evaluating statements individually, assume they are independent of each other. Don't carry information from Statement 1 when evaluating Statement 2 alone.
- Combining Statements: When evaluating both statements together, you can use information from both. The question becomes: "Given both Statement 1 AND Statement 2, can I find a unique answer?"
- Avoid Calculations Unless Necessary: Sometimes you don't need to complete the calculation, just determine if it's possible. If you can set up a solvable equation or find a unique value, the statement(s) are sufficient.
- Look for Unique Values: Sufficiency usually requires being able to arrive at one specific, unique value for the variable or quantity asked in the question. If the information leads to multiple possible values, it is not sufficient.
- Percentages vs. Counts: Percentages alone are rarely sufficient to find a total count unless an actual count corresponding to a percentage is also given. For example, "30% are boys" isn't enough to find the total number of students, but "30% are boys, and there are 15 boys" is sufficient.
In this specific problem about illegal immigrants, the percentages from Bangladesh and India provide a ratio or proportion but no actual number, which is why the total number of illegal immigrants remains unknown.
Similar Questions
A question is followed by two statements. Decide which of the given statements is sufficient to answer the question.
What is the percentage increase in the profit of Company X in 2016 with respect to that in 2014?
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Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
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Which of these natural numbers X, Y, Z, U, and V are even numbers?
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The trains are very punctual in Malaysia. For a maximum of how long should Mr. Z wait for the train?
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Consider the given question and decide which of the following statements is sufficient to answer the question.
What is the weight of ten iron balls if each ball is of the same weight?
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Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
