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Difficulty:
85%
(hard)
Question Stats:
38% (02:45) correct
62%
(02:59)
wrong
based on 50
sessions
History
Date
Time
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Not Attempted Yet
A technology reviewer ranks three tablets on a scale from 1 (best) to 3 (worst) with respect to battery life, processor performance, and screen quality. No two tablets receive the same ranking for any parameter,
A tablet with battery, processor, and screen rankings b, p, and s is assigned a composite score equal to
4 - (kb + mp + (1 - k - m)s),
where k and m are positive constants and k + m is less than 1. A higher composite score indicates a better tablet. Is k greater than 0.5?
(1) Tablet 1 has a higher composite score than Tablet 2 but is ranked worse than Tablet 2 in both processor performance and screen quality.
(2) Tablet 2 has a higher composite score than Tablet 3 but is ranked worse than Tablet 3 in both processor performance and screen quality and is ranked worse than Tablet 1 in battery life.
A tablet with battery, processor, and screen rankings b, p, and s is assigned a composite score equal to
4 - (kb + mp + (1 - k - m)s),
where k and m are positive constants and k + m is less than 1. A higher composite score indicates a better tablet. Is k greater than 0.5?
(1) Tablet 1 has a higher composite score than Tablet 2 but is ranked worse than Tablet 2 in both processor performance and screen quality.
(2) Tablet 2 has a higher composite score than Tablet 3 but is ranked worse than Tablet 3 in both processor performance and screen quality and is ranked worse than Tablet 1 in battery life.
26 Feb 2026, 13:36
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The key concept here is algebraic inequality in Data Sufficiency — specifically, isolating the weight of one variable by manipulating a composite score expression. Most students panic at the custom formula and start plugging in numbers randomly. The better move is to set up the score inequality and see what it forces.
Setting up the expression:
Score = 4 − (kb + mp + (1−k−m)s). A higher score is better. Rankings run 1 (best) to 3 (worst), and no two tablets share a rank for any attribute.
Statement 1 alone — Insufficient
T1 beats T2 in composite score, but T1 is ranked worse than T2 in both processor (p1 > p2) and screen (s1 > s2). This means T1 must rank better in battery (b1 < b2) to compensate.
Setting up Score1 > Score2 and simplifying:
k(b2 − b1) > m(p1 − p2) + (1−k−m)(s1 − s2)
This tells us k needs to be "large enough" to overcome the processor/screen disadvantage — but without knowing the exact ranking gaps (is b2 − b1 equal to 1 or 2?), we can't pin down whether k > 0.5. Two different valid ranking assignments give k > 2/3 in one case and only k > 1/3 in another. Not sufficient.
Statement 2 alone — Insufficient
Same structure: T2 beats T3 despite worse processor and screen, and T2's battery is worse than T1's. Again, we know k has to carry the weight — but we still can't determine how large it needs to be without fixing the exact ranking gaps. Not sufficient.
Combined — Sufficient
Here's where it clicks. Statement 1 says p1 > p2 and s1 > s2. Statement 2 says p2 > p3 and s2 > s3, and b1 < b2.
Chain them: p1 > p2 > p3 → p3=1, p2=2, p1=3. Same for screen: s3=1, s2=2, s1=3. Battery: b2 > b1 and T2 needs better battery than T3 to overcome its processor/screen disadvantage → b1=1, b2=2, b3=3.
All rankings are now fully determined. Plug into Score1 > Score2:
k(2−1) + m(2−3) + (1−k−m)(2−3) > 0
→ k − m − (1−k−m) > 0
→ 2k − 1 > 0 → k > 0.5 ✓
Common trap: Trying to test specific values for k and m rather than setting up the inequality algebraically. Also missing that the two statements together uniquely determine all six rankings — that's the unlock.
Answer: C
Takeaway: When a DS question involves a custom formula with unknown constants, translate the given comparisons into algebraic inequalities — the constraint you need often emerges cleanly once you've chained the inequalities together.
(Kavya | 725 on GMAT Focus Edition)
Setting up the expression:
Score = 4 − (kb + mp + (1−k−m)s). A higher score is better. Rankings run 1 (best) to 3 (worst), and no two tablets share a rank for any attribute.
Statement 1 alone — Insufficient
T1 beats T2 in composite score, but T1 is ranked worse than T2 in both processor (p1 > p2) and screen (s1 > s2). This means T1 must rank better in battery (b1 < b2) to compensate.
Setting up Score1 > Score2 and simplifying:
k(b2 − b1) > m(p1 − p2) + (1−k−m)(s1 − s2)
This tells us k needs to be "large enough" to overcome the processor/screen disadvantage — but without knowing the exact ranking gaps (is b2 − b1 equal to 1 or 2?), we can't pin down whether k > 0.5. Two different valid ranking assignments give k > 2/3 in one case and only k > 1/3 in another. Not sufficient.
Statement 2 alone — Insufficient
Same structure: T2 beats T3 despite worse processor and screen, and T2's battery is worse than T1's. Again, we know k has to carry the weight — but we still can't determine how large it needs to be without fixing the exact ranking gaps. Not sufficient.
Combined — Sufficient
Here's where it clicks. Statement 1 says p1 > p2 and s1 > s2. Statement 2 says p2 > p3 and s2 > s3, and b1 < b2.
Chain them: p1 > p2 > p3 → p3=1, p2=2, p1=3. Same for screen: s3=1, s2=2, s1=3. Battery: b2 > b1 and T2 needs better battery than T3 to overcome its processor/screen disadvantage → b1=1, b2=2, b3=3.
All rankings are now fully determined. Plug into Score1 > Score2:
k(2−1) + m(2−3) + (1−k−m)(2−3) > 0
→ k − m − (1−k−m) > 0
→ 2k − 1 > 0 → k > 0.5 ✓
Common trap: Trying to test specific values for k and m rather than setting up the inequality algebraically. Also missing that the two statements together uniquely determine all six rankings — that's the unlock.
Answer: C
Takeaway: When a DS question involves a custom formula with unknown constants, translate the given comparisons into algebraic inequalities — the constraint you need often emerges cleanly once you've chained the inequalities together.
(Kavya | 725 on GMAT Focus Edition)
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