CAT 2026 Slot 2 DILR: Set 5: Set 5 – Smartphone Radar Chart with Solutions

4 questions: Q19, Q20, Q21, Q22. Solve each one here: tap the answer, press Check, then open the solution.

DI/DS

The set

SET 5: SMARTPHONE PERFORMANCE
Five smartphones—Alpha, Beta, Gamma, Delta and Epsilon—are evaluated on six aspects. Every score is on a 0–100 scale, and a higher score is better on every aspect, including Price (value for money). Use the accompanying radar chart and exact score table. There are no tied scores within an aspect.

Phone	Durability	Coverage	Performance	Design	Support	Price
Alpha	70	80	85	35	25	50
Beta	50	60	55	45	60	58
Gamma	90	70	60	25	30	80
Delta	40	55	65	90	70	57
Epsilon	30	40	45	65	40	48

Question 19Data Interpretation

MCQ · +3 / −1 · medium

On which aspect is the median score of the five smartphones the lowest?

Answer and solution

Correct answer: A

Solution

Answer: A — Support

1. For five numbers, the median is the third number after sorting.

2. Durability:30,40,50,70,90 →50. Coverage:40,55,60,70,80 →60. Performance:45,55,60,65,85 →60.

3. Design:25,35,45,65,90 →45. Support:25,30,40,60,70 →40. Price:48,50,57,58,80 →57.

4. The lowest of 50,60,60,45,40,57 is 40 for Support. Answer A.

Detailed setup and verification:
The median of five scores is the middle score after sorting, not the mean of the highest and lowest or the third phone in the legend. Sorting is necessary independently for each aspect because the phone ranking changes around the radar.

The six aspect medians are 50,60,60,45,40,57 in the order Durability, Coverage, Performance, Design, Support, Price. Support 40 is below Design 45 and every other median. The exact accompanying table removes any need to estimate a close crossing of radar lines.

G Strategy shortcut

Method: Sort each column; take the third score. Support’s median 40 is lowest.
Verification: 4. The lowest of 50,60,60,45,40,57 is 40 for Support. Answer A.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

G Strategy: Method: Sort each column; take the third score. Support’s median 40 is lowest. Verification: 4. The lowest of 50,60,60,45,40,57 is 40 for Support. Answer A. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

Question 20Data Interpretation

MCQ · +3 / −1 · medium

A smartphone’s final score is the average of its scores on all six aspects. Which smartphone has the highest final score?

Answer and solution

Correct answer: D

Solution

Answer: D — Delta

1. All phones have six equally weighted scores. Compare their sums; dividing each by 6 cannot change the ranking.

2. Totals: Alpha 345, Beta 328, Gamma 355, Delta 377, Epsilon 268.

3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.

Detailed setup and verification:
Write each sum from the table: Alpha 70+80+85+35+25+50=345; Beta 50+60+55+45+60+58=328; Gamma 90+70+60+25+30+80=355; Delta 40+55+65+90+70+57=377; Epsilon 30+40+45+65+40+48=268.

Each mean divides its sum by the same positive 6. Therefore ranking the sums is exact and saves five divisions. Delta’s mean 62.833… exceeds Gamma 59.166… and Alpha 57.5. A phone leading on one axis need not have the highest overall average.

G Strategy shortcut

Method: Equal denominators: compare sums, not six separate decimal averages. Delta 377 wins.
Verification: 3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

G Strategy: Method: Equal denominators: compare sums, not six separate decimal averages. Delta 377 wins. Verification: 3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

Question 21Data Interpretation

MCQ · +3 / −1 · medium

Which option lists all the smartphones that are among the top two scorers on the greatest number of aspects?

Answer and solution

Correct answer: C

Solution

Answer: C — Alpha, Gamma and Delta

1. Rank phones separately within each aspect. Durability top two: Gamma, Alpha. Coverage: Alpha, Gamma. Performance: Alpha, Delta.

2. Design top two: Delta, Epsilon. Support: Delta, Beta. Price: Gamma, Beta.

3. Counts: Alpha 3, Beta 2, Gamma 3, Delta 3, Epsilon 1.

4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.

Detailed setup and verification:
Create one tally mark per top-two appearance, not one per win. Alpha qualifies on Durability, Coverage, Performance; Gamma on Durability, Coverage, Price; Delta on Performance, Design, Support. Each has three appearances. Beta qualifies on Support, Price and Epsilon only on Design.

There are six aspects and two places per aspect, so the total number of tally marks must be 12. The counts 3+2+3+3+1=12 verify that none was omitted or double-counted. The answer must name every phone tied for the highest tally.

G Strategy shortcut

Method: Mark only the top two per column and tally. A/G/D each have 3 appearances.
Verification: 4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

G Strategy: Method: Mark only the top two per column and tally. A/G/D each have 3 appearances. Verification: 4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

Question 22Data Interpretation

MCQ · +3 / −1 · medium

Which of the following smartphones is among the top three scorers on all six aspects?

Answer and solution

Correct answer: D

Solution

Answer: D — None of the smartphones

1. To eliminate a phone, find one aspect on which its rank is below third.

2. Alpha is fourth on Design (35). Beta is fourth on Performance (55). Gamma is fifth on Design (25).

3. Delta is fourth on Durability (40), and Epsilon is fifth on Durability (30).

4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.

Detailed setup and verification:
A universal condition such as top three on all six aspects can be rejected by a single counterexample. There is no need to calculate every full ranking for a phone once one failing aspect is found. For example, Design scores 90,65,45,35,25 place Alpha fourth and Gamma fifth.

Performance scores 85,65,60,55,45 put Beta fourth. Durability scores 90,70,50,40,30 eliminate Delta and Epsilon. All five phones have a failing aspect, proving None rather than merely showing that one listed candidate fails.

G Strategy shortcut

Method: One counterexample eliminates each phone; no need to calculate all 30 ranks.
Verification: 4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

G Strategy: Method: One counterexample eliminates each phone; no need to calculate all 30 ranks. Verification: 4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.

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