DAT Quantitative Reasoning Quiz: Tables Graphs And Charts

What this quiz covers

This quiz focuses on Tables Graphs And Charts, giving you a quick way to practice the rules, question types, and explanations that matter most for DAT Quantitative Reasoning.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 3
2. 4 (correct answer)
3. 5
4. 6

Explanation: f(x) = x² − 4 and g(x) = 2x. Evaluate at each integer in [−4,4]: x=−4: f(16−4)=12, g(−8), so 12>−8 ✓. x=−3: f(9−4)=5, g(−6), so 5>−6 ✓. x=−2: f(4−4)=0, g(−4), so 0>−4 ✓. x=−1: f(1−4)=−3, g(−2), so −3<−2 ✗. x=0: f(0−4)=−4, g(0), so −4<0 ✗. x=1: f(1−4)=−3, g(2), so −3<2 ✗. x=2: f(4−4)=0, g(4), so 0<4 ✗. x=3: f(9−4)=5, g(6), so 5<6 ✗. x=4: f(16−4)=12, g(8), so 12>8 ✓. Therefore f(x) > g(x) for x = −4, −3, −2, 4, which is 4 values.

Question 2

1. $\dfrac{1}{4}$ (correct answer)
2. $\dfrac{1}{3}$
3. $\dfrac{3}{8}$
4. $\dfrac{1}{2}$

Explanation: Orthodontics bar totals $400 k: North 100 k, South 120 k, East 90 k, West 90 k. North share = 100/400 = 1/4. Other fractions use wrong component or wrong total.

Question 3

1. Hour 1 to Hour 2
2. Hour 2 to Hour 3
3. Hour 3 to Hour 4
4. Hour 5 to Hour 6 (correct answer)

Explanation: Rates of change: Hour 1→2: 8−3 = +5. Hour 2→3: 18−8 = +10. Hour 3→4: 15−18 = −3. Hour 4→5: 9−15 = −6. Hour 5→6: 2−9 = −7. Greatest magnitude is |−7| = 7, during Hour 5 to Hour 6. Distractor A: +5, smaller magnitude. Distractor B: +10 is the greatest positive change; students ignoring 'magnitude' will pick this. Distractor C: −3, smaller magnitude than Hour 5→6.

Question 4

1. 33.30%
2. 40.00%
3. 46.70%
4. 53.30% (correct answer)

Explanation: Emergency visits per day: Mon 3, Tue 2, Wed 5, Thu 3, Fri 2. Total = 15. Wed + Thu = 5 + 3 = 8. Percentage = 8/15 ≈ 53.3%. Distractor A: 5/15 = 33.3%, using only Wednesday. Distractor B: 6/15 = 40%, miscounting Thursday's emergency segment as 1. Distractor C: 7/15 ≈ 46.7%, using Wed=5, Thu=2 (misread).

Question 5

1. 12.5 minutes
2. 17.5 minutes (correct answer)
3. 22.5 minutes
4. 27.5 minutes

Explanation: Frequencies: 0–10: 8, 10–20: 22, 20–30: 18, 30–40: 10, 40–50: 2. Total = 60. Median is the average of the 30th and 31st values. Cumulative: after 0–10 → 8; after 10–20 → 30; after 20–30 → 48. The 30th value is the last in the 10–20 bin; the 31st is the first in the 20–30 bin. Using linear interpolation in the median class (10–20): median ≈ 10 + ((30−8)/22)×10 = 10 + 10 = 20. The 30th and 31st values straddle this; 17.5 (midpoint of the median bin) is the best choice of the options. Distractor A: Midpoint of first large bin, but only 8 values lie in 0–10. Distractor C: Midpoint of 20–30 bin; student who miscounts cumulative frequency. Distractor D: Midpoint of 30–40 bin; would require median in upper tail.

Question 6

1. The mean age is 42.
2. Exactly 25% of patients are between 30 and 42 years old.
3. The interquartile range is 25. (correct answer)
4. More than 75% of patients are younger than 50.

Explanation: From the box plot: Q1 = 30 and Q3 = 55. The interquartile range (IQR) = Q3 − Q1 = 55 − 30 = 25. Choice A is incorrect because box plots show the median (42), not the mean. Choice B is incorrect because while approximately 25% fall between Q1 and the median, the exact percentage depends on ties at boundaries. Choice D is incorrect because we cannot determine what percentage falls below 50 from the given information.

Question 7

1. Town W
2. Town X
3. Town Y (correct answer)
4. Town Z

Explanation: Target ratio 3:5 = 0.60. Town W: 45/80 = 0.5625. Town X: 30/40 = 0.75. Town Y: 60/100 = 0.60. Town Z: 50/90 ≈ 0.556. Town Y matches exactly. Distractor A: 0.5625, close to 0.6 but not the closest. Distractor B: 0.75, matches 3:4, a common confusion. Distractor D: 0.556, close but farther from 0.60 than Town Y.

Question 8

1. 60 students
2. 80 students
3. 100 students (correct answer)
4. 120 students

Explanation: From the cumulative graph: at score = 60, cumulative frequency ≈ 40; at score = 80, cumulative frequency ≈ 140. Students scoring between 60 and 80 = 140 − 40 = 100. Distractor A: Confusing cumulative with a single bin value (e.g., just reading 60 mark). Distractor B: Slight misreading of the cumulative values (e.g., 130−50). Distractor D: Including students who scored above 80 up to 90, or misreading 160−40.

Question 9

1. 2
2. 3 (correct answer)
3. 4
4. 5

Explanation: Line of best fit: y = 5x + 50. For each data point, compare actual y to predicted y = 5x+50 and check if residual > 5. Points: (1,60): pred 55, residual +5 (NOT strictly >5). (2,58): pred 60, res −2. (3,72): pred 65, res +7 ✓. (4,68): pred 70, res −2. (5,82): pred 75, res +7 ✓. (6,78): pred 80, res −2. (7,90): pred 85, res +5 (not strictly). (8,88): pred 90, res −2. (9,102): pred 95, res +7 ✓. (10,98): pred 100, res −2. Three points satisfy: (3,72), (5,82), (9,102). Distractor A: Missing one of the three qualifying points. Distractor C: Including a point with residual exactly +5 (not strictly greater). Distractor D: Counting all points above the line regardless of distance.

Question 10

1. Waiting Time (correct answer)
2. Patient Satisfaction
3. Treatment Variety
4. Equipment Quality

Explanation: In the radar chart, Waiting Time spokes differ by 4 units (P = 3, Q = 7) while other spokes differ by at most 2. Therefore Waiting Time shows the greatest gap.

Question 11

1. Strong positive correlation (correct answer)
2. Weak positive correlation
3. No correlation
4. Strong negative correlation

Explanation: The plotted points consistently rise with only a handful of outliers--and even those furoutliers that do not fit the overall trend increase relative to one another. This shows a strong positive correlation. No or negative correlation do not fit the upward slope.

Question 12

1. Option I
2. Option II
3. Option III
4. Option IV (correct answer)

Explanation: Cost per 100 calories = (Price / Calories) × 100. Option I: (6.00/600)×100 = $1.00. Option II: (7.50/750)×100 =$1.00. Option III: (4.80/400)×100 = $1.20. Option IV: (8.40/900)×100 ≈$0.93. Option IV is lowest. Distractor A: $1.00 — tied for second-lowest. Distractor B:$1.00 — tied for second-lowest. Distractor C: Lowest absolute price but highest cost/calorie.

Question 13

1. 0.19
2. 0.22
3. 0.23 (correct answer)
4. 0.29

Explanation: Using inclusion-exclusion principle: P(Rh− OR AB) = P(Rh−) + P(AB) − P(Rh− AND AB). From the table: Rh-negative donors = 28 + 16 + 8 + 8 = 60, so P(Rh−) = 60/400 = 0.15. AB donors = 32 + 8 = 40, so P(AB) = 40/400 = 0.10. AB-negative donors = 8, so P(Rh− AND AB) = 8/400 = 0.02. Therefore: P(Rh− OR AB) = 0.15 + 0.10 − 0.02 = 0.23.

Question 14

1. 32 units
2. 48 units
3. 72 units
4. 96 units (correct answer)

Explanation: Current totals per machine over 8 hours: Machine 1: 8×50 = 400. Machine 2: 8×55 = 440. Machine 3: 8×48 = 384. Grand total = 1224 units. For an overall average of 55 units/hour across all three machines for 8 hours: Total machine-hours = 3 machines × 8 hours = 24 machine-hours. Required total output = 55 × 24 = 1320 units. Needed increase = 1320 − 1224 = 96 units. Distractor A: Using only 8 hours instead of 24 machine-hours in calculation. Distractor B: Miscalculating the current total or required total. Distractor C: Error in the target average or shift duration calculation.

Question 15

1. Q1
2. Q2
3. Q3 (correct answer)
4. Q4

Explanation: Calculate percentage increase for each quarter: Q1: (132-120)/120 = 10.0%. Q2: (165-150)/150 = 10.0%. Q3: (198-160)/160 = 23.75%. Q4: (210-180)/180 = 16.67%. Q3 has the largest increase at 23.75%. Distractor A (Q1): Only 10% increase, though the absolute dollar increase ($12K) may seem noteworthy. Distractor B (Q2): Also 10$15K. Distractor D (Q4): 16.67%, the second-largest; students who misread the table or calculate Q4 first may stop there.