Questions & explanations
1. A line graph shows the number of books sold by a store over 12 months. The points for months 1 through 11 appear to lie on a straight line, but the point for month 12 is slightly above that line. Is the overall trend in book sales increasing over the 12-month period?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone: A positive slope between first and last points suggests an overall increase, but the graph may not be linear; the trend could be non-monotonic. However, the question asks if the trend is increasing over the entire period; a positive slope from start to end indicates an overall increase, so (1) alone is sufficient (yes). Statement (2) alone: Month 12 > month 11 does not guarantee the overall trend is increasing; earlier months could have decreases. Thus (2) alone is not sufficient. Since (1) alone is sufficient and (2) alone is not, answer would be (a).: The trap is assuming linearity. The graph appears linear for months 1-11 but month 12 deviates. Statement (1) uses only first and last points, which gives a positive slope, so overall trend is increasing. So (1) alone is sufficient. However, re-evaluating: The question asks 'Is the overall trend increasing?' A positive slope from first to last point means the last point is higher than the first, so yes, overall increase. Thus (1) alone is sufficient. (2) alone is insufficient. So answer is (a). But the correct ans
2. A line graph shows the monthly sales of two products, A and B, over the same 6-month period. The graph has two lines, one for each product. In which month did product A's sales first exceed product B's sales?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) alone: In month 3, A > B, but we don't know if this is the first time; earlier months could have A > B as well. Not sufficient. Statement (2) alone: In month 4, A > B, and lines crossed between month 3 and 4, meaning before month 4, A was not > B. But we don't know if month 4 is the first month with A > B; could be that A > B also in month 5 etc., but the question asks for the first month. Since the lines crossed between 3 and 4, and in month 4 A > B, that implies that before month 4, A <= B. However, we don't know if in month 4 it's the first time; it could be that A > B also in month 3? No, because lines crossed between 3 and 4, so at month 3, A <= B. So month 4 is the first month with A > B. But statement (2) alone does not give exact sales, but it gives that the crossing occurred between 3 and 4, and in month 4 A > B. That is sufficient to determine that month 4 is the first month., careful: The crossing could be exactly at month 3.5, but at month 3, A <= B; at month 4, A > B. So the first month with A > B is month 4. So (2) alone is sufficient. But we need to check
3. A bar graph displays the monthly sales (in thousands of dollars) for a retail store from January to December. The bars for January, February, and March show sales of 50, 60, and 55 respectively. What were the total sales for the first quarter (January–March)?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: EACH statement ALONE is sufficient.
Statement (1) alone: gives March sales = 55 (thousand). Combined with given Jan=50, Feb=60, total = 165 thousand. Sufficient. Statement (2) alone: each tick = 10, so 5th tick = 50 (thousand). But we need all three months; however, the question already provides Jan=50, Feb=60, Mar=55 from the graph description. Statement (2) confirms the scale, but the values are already given., the question stem gives the bar heights as 50, 60, 55. Statement (2) alone confirms the scale, but we already have the numbers. So (2) alone is sufficient because we can read the values from the graph. However, careful: the stem says 'the bars for January, February, and March show sales of 50, 60, and 55 respectively.' This is given data. So both statements independently allow calculation of total. (1) gives March explicitly; (2) confirms scale but we already have values., (2) alone: if we only know the scale and that Jan reaches 5th tick, we get Jan=50, but we need Feb and March. The stem already provides those values. So (2) alone is sufficient because the stem provides all three values. But the question is:
4. A scatter plot shows the relationship between hours studied and exam score for 10 students. Is there a positive correlation between hours studied and exam score?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: EACH statement ALONE is sufficient.
Statement (1) alone: The highest study hours correspond to highest score, and lowest to lowest, suggesting a positive trend. However, this does not guarantee all points follow a positive pattern; but in a scatter plot, if the extremes show positive association, it is strong evidence of positive correlation. Typically, this is sufficient to conclude positive correlation. Statement (2) alone: A correlation coefficient of 0.85 indicates a strong positive correlation. Sufficient. Both statements independently give a definite yes. Answer: (d).
5. A scatter plot shows the relationship between advertising spend (x-axis) and sales (y-axis) for 10 products. The points appear to follow a curve that increases steeply then flattens. Is the sales for a product with advertising spend of $50,000 greater than $200,000?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone gives two points, but the relationship is non-linear (curve flattens), so we cannot linearly interpolate; $50,000 could be below or above $200,000. Not sufficient. Statement (2) alone confirms non-linearity but gives no specific values; not sufficient. Together, we know the curve flattens, so sales at $50,000 might be less than the average of $180k and $220k (i.e., $200k) but not certain; could be $190k or $210k. Therefore, even together, not sufficient: answer (e).
6. Three charts show monthly sales for a company: Chart A (total sales in dollars), Chart B (number of units sold), and Chart C (average price per unit). Was the average price per unit in March higher than in February?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: EACH statement ALONE is sufficient.
Statement (1): From Chart A and B, average price per unit = total sales / units sold. March: $10,000/500 = $20; February: $8,000/400 = $20. So March average is not higher than February; it's equal. This gives a definite NO, sufficient. Statement (2): Chart C directly gives average prices: March $20, February $20. Again, March is not higher; definite NO, sufficient. Each statement alone answers the question with a clear NO, so each alone is sufficient. Hence, answer is D.
7. A line graph shows the monthly revenue (in millions) of two companies, A and B, over the same 12-month period. The lines for A and B are plotted on the same axes. In which month did Company A's revenue first exceed Company B's revenue?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone: Knowing A > B in months 6 and 12 does not tell us the first month it happened; it could be month 2, 3, etc. Not sufficient. Statement (2) alone: Only tells us A < B in month 1, but no info on later months. Not sufficient. Together: We know A < B in month 1 and A > B in month 6, so the first exceedance occurred between month 2 and month 6, but we cannot pinpoint the exact month without more data. Not sufficient. Answer: (e).
8. A line graph shows the monthly sales of a product over 12 months. Is the overall trend in sales increasing over the entire period?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone: Only compares endpoints; sales could have dipped in between, so trend may not be consistently increasing. Not sufficient. Statement (2) alone: More increases than decreases, but does not guarantee overall trend is increasing (e.g., large decreases could offset). Not sufficient. Together: Even with more increases, the overall trend could still be flat or decreasing if decreases are large. Not sufficient. Answer (e).
9. A two-way table shows the number of students who passed or failed a test, broken down by whether they attended a review session. The table has the following entries: Attended Review: Pass = 40, Fail = 10; Did Not Attend Review: Pass = 20, Fail = 30. If a student is selected at random from those who passed, what is the probability that the student attended the review session?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The question asks for P(Attended | Pass) = (Attended and Pass) / (Total Pass). From the table, Attended and Pass = 40. Statement (1) alone gives Total Pass = 60, so probability = 40/60 = 2/3. Sufficient. Statement (2) alone gives Total Attended = 50, but we need Total Pass, which is not given; we only know Attended and Pass = 40, but we don't know Pass from Did Not Attend. Not sufficient. Answer: (a).
10. A scatter plot shows the relationship between hours studied and exam score for 20 students. The plot indicates a positive trend. Is the correlation coefficient between hours studied and exam score greater than 0.5?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone: 'strong linear relationship' is subjective; correlation coefficient could be 0.6 or 0.9, but also could be 0.4 if points are moderately scattered. Not sufficient. Statement (2) alone: only two points; cannot determine overall correlation. Not sufficient. Together: still no numerical correlation value; the graph alone does not provide exact coefficient. Not sufficient. Answer (e).
11. A scatter plot shows the relationship between advertising spend (in thousands of dollars) and monthly sales (in thousands of dollars) for 12 companies. Is the trend in sales increasing as advertising spend increases?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statements (1) and (2) TOGETHER are NOT sufficient.
Statement (1) alone does not indicate the direction of the overall trend; it only compares a subset. Statement (2) alone shows a single point, not the trend. Together, they still do not confirm that sales increase with advertising spend across all data points; the trend could be flat or decreasing elsewhere. Thus, even together, the statements are insufficient to determine if the trend is increasing.
12. A bar graph displays the number of units sold by a company each quarter for the past 5 years. The bars for each quarter are labeled with exact values. What was the total number of units sold in the first quarter of Year 3?
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) alone: Year 2 Q1 = 1,000 units. Year 3 Q1 is 20% higher, so exactly 1,200 units. This gives a unique exact value. Sufficient. Statement (2) alone: The bar appears to be about 1,200 units, but this is an estimate; the exact value is not given, and we cannot determine the exact total from an estimate. Not sufficient. Since (1) alone is sufficient and (2) alone is not, answer is (a).