GMAT Club Official Solution:During a two-session fundraising campaign, Maya and Noah each contacted some number of potential donors. By the end of the campaign, each had persuaded exactly 24 of those people to make a donation. Did Maya contact more people than Noah?We need to determine whether Maya contacted more people than Noah. Since both Maya and Noah persuaded exactly 24 people to donate, Maya contacted more people than Noah if and only if Maya’s overall success rate was lower than Noah’s overall success rate.
(1) In the first session, Noah persuaded a greater percentage of the people he contacted than Maya did.
This tells us only that Noah’s success rate was higher in the first session. That alone is not enough to determine whose overall success rate was lower. Not sufficient.
(2) In the second session, Maya persuaded a lower percentage of the people she contacted than Noah did.
This tells us only that Noah’s success rate was higher in the second session. That alone is not enough to determine whose overall success rate was lower. Not sufficient.
(1) + (2) Now we know that Noah’s success rate was higher in both sessions. But that still does not determine whose overall success rate was lower, because the two people may have contacted very different numbers of potential donors in the two sessions.
Yes case:
Maya: session 1 = 12 out of 100 (12%), session 2 = 12 out of 100 (12%), total = 24 out of 200
Noah: session 1 = 12 out of 24 (50%), session 2 = 12 out of 24 (50%), total = 24 out of 48
Both statements are satisfied, and Maya contacted more people than Noah.
To get a no answer: make Maya do most of her contacting in the session where her own success rate is higher, and make Noah do most of his contacting in the session where his own success rate is lower. That makes Maya’s overall success rate higher than Noah’s, so Maya must have contacted fewer people.
No case:
Maya: session 1 = 23 out of 24 (< 100%), session 2 = 1 out of 11 (< 10%), total = 24 out of 35
Noah: session 1 = 1 out of 1 (100%), session 2 = 23 out of 230 (10%), total = 24 out of 231
Both statements are satisfied, but Maya did not contact more people than Noah.
So even together, the statements are not sufficient.
Answer: E.