1. Company T's business model predicted the company's revenue for the years 2001 through 2006, based on the company's revenue for the year 2000. For each of the years 2001 through 2006, the predicted revenue was 10% more than the predicted revenue for the preceding year. What was the first year for which the predicted revenue was more than $16,000,000? (1) The predicted revenue for 2001 was $11,000,000. (2) The predicted revenue for 2004 was $4,641,000 more than the revenue for 2000.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Explanation
Statement (1) gives 2001 revenue as $11,000,000. With 10% annual growth: 2002 = 12.1M, 2003 = 13.31M, 2004 = 14.641M, 2005 = 16.1051M. Revenue first exceeds $16M in 2005. Statement (2) alone gives only the difference between 2004 and 2000, which is insufficient to determine when $16M is crossed. Thus (1) alone is sufficient.
2. For each of the following products, select Sufficient if the information provided is sufficient to determine whether the unit price of the product is less than €3. Otherwise, select Insufficient.
A. Product A
B. Product B
C. Product C Correct
D. Product D
Explanation
The table provides sufficient information for Products A and D but not for B and C. For Product A, all subtotals are multiples of 6 and the GCD of the values is exactly 6, forcing the unique unit price of 6 € (> 3 €). For Product D, the presence of 7.0 €, 14.0 €, and 17.5 € combined with 59.5 € forces the unit price to be a divisor of 3.5 € (possible prices 1 €, 1.75 €, or 3.5 €), all of which are below 3 €, so D is definitively less than 3 €. In contrast, Product B is perfectly explained by both 2.5 € (< 3 €) and 5 € (? 3 €), and Product C is perfectly explained by both 1.5 € (< 3 €) and 3 € (? 3 €), so in both cases we cannot determine whether the unit price is less than 3 €. Therefore, the information is sufficient for A and D, and insufficient for B and C.
3. Two people will be selected from a group of n (n ? 10) people. If there are at least 2 adults and 2 children, and n is an even number, how many people in the group are adults? (1) The probability of selecting 2 adults is 1/3. (2) Adults are more than 50% of the total number of people.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Explanation
Let a = adults, c = children, n = a + c even. P(2 adults) = C(a,2)/C(n,2) = 1/3, a(a-1)/[n(n-1)] = 1/3. Testing even n from 6 to 10 with a,c ≥ 2 yields only n=10, a=8. Statement (2) alone allows multiple solutions. Thus (1) alone is sufficient.
4. The average[arithmetic mean] age of the nontenured faculty members in the Physics Department at University M is 40 years. What is the average age, in years, of all faculty members in the Physics Department? (1) There are 4 times as many nontenured faculty members as tenured faculty members. (2) There are 7 tenured faculty members.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient. Correct
Explanation
The average age of nontenured faculty members is given as 40 years. Statement (1) tells us there are 4 times as many nontenured as tenured faculty members, which gives a 4:1 ratio, but we still need the average age of the tenured faculty to find the overall average; statement (1) alone is insufficient. Statement (2) gives the number of tenured faculty members as 7, which together with statement (1) tells us there are 28 nontenured and 35 total faculty members, but we still have no information about the tenured members’ average age, so even together the statements provide no way to calculate the overall average age. Therefore, statements (1) and (2) together are not sufficient.
5. Five volunteers signed up to work a bake sale. George signed up for the 9:00 a.m.-10:00 a.m. slot, and Juan signed up for the 10:00 a.m.-11:00 a.m. slot. The start of Cora's time slot begins with an even number. Which time slot does Cora work? (1) Cora's time slot is not immediately before George's time slot. (2) Cora's time slot is later in the day than George's time slot.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient. Correct
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Explanation
George works 9:00–10:00 a.m. and Juan works 10:00–11:00 a.m.; Cora’s slot starts on an even hour (possible times include 8:00, 10:00, 12:00, 2:00, etc.). Statement (1) alone says Cora’s slot is not immediately before George’s, so she is not in 8:00–9:00 a.m., but many even-start slots remain, making it insufficient. Statement (2) alone says Cora’s slot is later than George’s, so after 9:00–10:00 a.m., but again several even-start slots (10:00, 12:00, 2:00, etc.) are still possible, making it insufficient. Together, the statements rule out anything at or before 9:00 a.m. and place Cora after George’s slot; among standard bake-sale hour blocks, the only slot that satisfies both conditions uniquely is the 12:00 p.m.–1:00 p.m. slot (noon start). Thus, both statements together are sufficient, but neither alone is sufficient.