Part 1: DS vs PS (The Key Difference)
Consider the question: What is the value of x?
Step 1The Problem Solving (PS) Way
In a standard math problem, if you are told:
$$ x = y + z, \text{ where } y=100, z=20 $$You must calculate: $$ x = 100 + 20 = 120 $$ The answer is the number 120.
Step 2The Data Sufficiency (DS) Way
In DS, we don't care that x is 120. We only ask:
"Can we find a single, unique value for x?"
Since we have the formula and the values for y and z, the answer is YES. The data is SUFFICIENT.
Part 2: The 5 Options (AD / BCE)
💡 Key Takeaways
- AD: If Statement (1) works, the answer must be A or D.
- BCE: If Statement (1) fails, the answer must be B, C, or E.
Part 3: Yes/No Questions
For questions asking "Is x > 0?", a definite NO is just as good as a definite YES. Sufficiency means getting a firm answer, not necessarily a positive one.
Step 1Question
Is John under 32 years of age?
Goal: A definite YES (he is <32) or a definite NO (he is ≥32).
Step 2Statement 1
"John's age is a prime number between 8 and 36."
Primes: 11, 13, 17, 19, 23, 29, 31.
All these values are < 32. The answer is always YES.
SUFFICIENT
Step 3Statement 2
"John's age is a multiple of 19 between 12 and 47."
Multiples: 19, 38.
If 19 -> Is he under 32? YES.
If 38 -> Is he under 32? NO.
We get both Yes and No.
INSUFFICIENT
Step 4Conclusion
Statement (1) Alone is Sufficient.
Statement (2) Alone is Not.
Final Answer: (A)
