You are given a question and two statements about the ages of two sisters. Question: What will be the total age of the two sisters 10 years from now? Statements: (1) Lina is 20 years old now. (2) Lina's sister's present age is twice Lina's present age. Which statement(s) are sufficient to answer the question?

Introduction / Context:
This is a data sufficiency question involving the ages of two sisters. Instead of directly asking for a numerical answer, it asks which combination of the given statements is sufficient to determine the total age of the sisters 10 years from now. Understanding how to interpret and combine such statements is essential for data sufficiency problems in aptitude exams.

Given Data / Assumptions:

- We need the total of the two sisters' ages 10 years from now.
- Statement 1: Lina is 20 years old now.
- Statement 2: Lina's sister's present age is twice Lina's present age.
- We must decide which statement(s) provide enough information to uniquely determine the total age after 10 years.

Concept / Approach:
For data sufficiency, we are not primarily focused on computing the exact answer, though we may do so to check. Instead, we determine whether each statement alone, or both together, provide enough information to get a unique numerical result. If the value is uniquely determined, the statements used are sufficient; if multiple values are possible, they are not sufficient.

Step-by-Step Solution:
Step 1: Using Statement 1 alone: Lina is 20 years old now. We know nothing about her sister's age. Therefore, we cannot find their total age in 10 years because the sister's age is unknown. So, Statement 1 alone is not sufficient. Step 2: Using Statement 2 alone: Lina's sister's age is twice Lina's age. Without knowing Lina's actual age, this only tells us that sister = 2 × Lina, but not any concrete values. Hence, we still cannot determine the total age of both sisters in 10 years. So, Statement 2 alone is also not sufficient. Step 3: Using Statements 1 and 2 together: From Statement 1, Lina's present age is 20 years. From Statement 2, sister's present age = 2 × 20 = 40 years. Step 4: Ten years from now, Lina will be 20 + 10 = 30 years old, and her sister will be 40 + 10 = 50 years old. Step 5: Their total age after 10 years will be 30 + 50 = 80 years, which is uniquely determined.

Verification / Alternative check:
As soon as both statements are used, there is no ambiguity: Lina is fixed at 20 years, the sister at 40 years, and their future ages after 10 years are fixed at 30 and 50 years respectively. No other values can satisfy both statements if Lina is 20. Therefore, the total age after 10 years is uniquely determined, proving that the combination of Statement 1 and Statement 2 is sufficient.

Why Other Options Are Wrong:
Option a (Statement 1 alone) is wrong because we still do not know the sister's age. Option b (Statement 2 alone) is wrong because Lina's age itself is unknown. Option c claims that both together are not sufficient, which is false as shown. Option e claims that the statements are insufficient even combined, which is also incorrect since we clearly found a unique total age with both statements.

Common Pitfalls:
In data sufficiency questions, students sometimes try to compute the final numerical answer when the question only asks which statements are sufficient. Others may overlook the fact that statement 2 alone still leaves Lina's age undefined. The safest approach is to test each statement individually and then in combination, checking whether you can derive a unique numerical result for the quantity asked.

Final Answer:
Only Statements 1 and 2 together are sufficient to determine the total age of the sisters 10 years from now.