What we see: a yes or no Data Sufficiency question about growth. Did the bacteria grow by at least 15% in total from 1922 to 1937?
Step 1. Count the years and set the target.
What we see: 1922 to 1937.
What it means: that is 15 yearly increases. "At least 15%" means the final amount is at least \(1.15\) times the starting amount.
What we do and why: we check whether each statement forces the total growth above or below \(1.15\).
Step 2. Test Statement 1 alone.
What we see: the bacteria grew by the same percent every year.
What it means: we do not know that percent.
What we do and why: 10% a year gives far more than 15%, so yes. 0.1% a year gives about 1.5% in total, so no. Not sufficient.
Step 3. Test Statement 2 alone.
What we see: growth was at most 1% each year.
What it means: the yearly growth could be 1% every year, or much less.
What we do and why: try the biggest case, 1% every year: \(1.01^{15} \approx 1.161\), a 16.1% increase, so yes. Try 0.1% every year: about 1.5%, so no. Not sufficient.
Step 4. Use both statements together.
What we see: the same yearly percent \(r\), with \(r\) at most 1%.
What it means: \(r\) can still be anything from just above 0 up to 1%.
What we do and why: \(r = 1\%\) gives \(1.01^{15} \approx 1.161\), so yes. \(r = 0.5\%\) gives \(1.005^{15} \approx 1.078\), only 7.8%, so no. Two answers, so even together they are not sufficient.
The trap: choice C (or B). Many people think "1% a year for 15 years is at most 15%, so the answer is always no." Two mistakes: growth compounds, so 1% a year for 15 years is 16.1%, which passes 15%; and the rate could also be smaller.
Faster way: you do not need to work out \(1.01^{15}\). Compound growth always beats simple growth, so \(1.01^{15} > 1 + 15(0.01) = 1.15\). The top case is yes, a tiny rate is no, done.
Takeaway: growing by \(r\%\) a year for \(n\) years always gives more than \(n \times r\%\) in total, because each year's growth is taken on a bigger amount.
Answer: E
