What we see: a Data Sufficiency probability question. We need the chance of picking a boy, which is the number of boys divided by the number of students.
Step 1. See what the probability really needs.
What we see: probability of a boy \(= \frac{\text{boys}}{\text{boys} + \text{girls}}\).
What it means: this is a fraction. A fraction only needs the share of boys, not the real head count. 3 boys out of 7 and 30 out of 70 give the same chance.
What we do and why: we look for any fact that fixes the share of boys.
Step 2. Statement 1 alone.
What we see: 35 students.
What it means: the class could have 5 boys (chance \(\frac{5}{35} = \frac{1}{7}\)) or 30 boys (chance \(\frac{30}{35} = \frac{6}{7}\)).
What we do and why: the total alone says nothing about the split. Not sufficient.
Step 3. Statement 2 alone.
What we see: boys to girls is \(3:4\).
What it means: out of every 7 students, 3 are boys. The chance is \(\frac{3}{3 + 4} = \frac{3}{7}\), whatever the class size.
What we do and why: one value. Sufficient.
The trap: (C). Many people think a probability needs real counts, so they join both statements to get 15 boys out of 35. That works, but Statement 2 already gave \(\frac{3}{7}\) by itself.
Faster way: when the question asks for a fraction, percent or probability, a ratio is always enough. Check that statement first.
Takeaway: a probability is a share, and a ratio gives the share; the total number only matters when the question asks "how many."
Answer: B
