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18 Feb 2026, 05:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (03:03) correct
58%
(02:11)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
At a local cinema, adult tickets cost $9 each and children’s tickets cost $4 each. Did Brenda buy more than 10 tickets at the local cinema yesterday?
(1) She spent $73 on the tickets.
(2) If she had bought an extra ticket for Tom, she would have spent $77.
(1) She spent $73 on the tickets.
(2) If she had bought an extra ticket for Tom, she would have spent $77.
18 Feb 2026, 14:32
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This is a classic Data Sufficiency question testing whether a system of equations yields enough information to answer a Yes/No question definitively.
Key concept: Data Sufficiency — Yes/No questions and integer constraints
Let a = number of adult tickets, c = number of children's tickets. The question asks: is a + c > 10?
Step 1: Evaluate Statement (1) alone — "She spent $73"
This gives: 9a + 4c = 73. We need non-negative integer solutions.
- a = 1: 9 + 4c = 73 → c = 16. Total = 17 > 10 ✓
- a = 5: 45 + 4c = 73 → c = 7. Total = 12 > 10 ✓
- a = 3: 27 + 4c = 73 → c = 11.5. Not an integer. ✗
- a = 7: 63 + 4c = 73 → c = 2.5. Not an integer. ✗
- a = 9: 81 > 73. Stop.
Only valid solutions are (a=1, c=16) with total 17, and (a=5, c=7) with total 12. In both cases, total > 10. The answer to "more than 10?" is always YES. Statement (1) is sufficient.
Step 2: Evaluate Statement (2) alone — "An extra ticket would cost $77"
This tells us her current spend + one more ticket = $77, so she currently spent $77 − (cost of one ticket). Either $77 − $4 = $73 (child's ticket) or $77 − $9 = $68 (adult's ticket).
Case A: She spent $73 → same as Statement (1) → sufficient by same logic above.
Case B: 9a + 4c = 68. Try solutions:
- a = 4: 36 + 4c = 68 → c = 8. Total = 12 > 10 ✓
- a = 0: 4c = 68 → c = 17. Total = 17 > 10 ✓
- a = 8: 72 + 4c = 68. Negative c. ✗
In both cases the total is > 10. Statement (2) is also sufficient.
Answer: D — Each statement alone is sufficient.
Common trap: Many students see Statement (2) and freeze because it doesn't explicitly state how much Brenda spent. The key is recognising that "an extra ticket for Tom" implies Tom's ticket costs either $4 or $9, giving you two possible current spend amounts — and you need to check BOTH cases to confirm sufficiency. The trap is dismissing Statement (2) as ambiguous without fully testing both cases.
Quick DS check habit: Before doing algebra, remind yourself this is a Yes/No question. You don't need a unique value of a + c — you just need all valid scenarios to give the same yes-or-no answer. Here they all give "yes," so both statements are sufficient.
Takeaway: In Yes/No DS questions, sufficiency requires a consistent answer across all valid scenarios — not a unique numerical value.
Key concept: Data Sufficiency — Yes/No questions and integer constraints
Let a = number of adult tickets, c = number of children's tickets. The question asks: is a + c > 10?
Step 1: Evaluate Statement (1) alone — "She spent $73"
This gives: 9a + 4c = 73. We need non-negative integer solutions.
- a = 1: 9 + 4c = 73 → c = 16. Total = 17 > 10 ✓
- a = 5: 45 + 4c = 73 → c = 7. Total = 12 > 10 ✓
- a = 3: 27 + 4c = 73 → c = 11.5. Not an integer. ✗
- a = 7: 63 + 4c = 73 → c = 2.5. Not an integer. ✗
- a = 9: 81 > 73. Stop.
Only valid solutions are (a=1, c=16) with total 17, and (a=5, c=7) with total 12. In both cases, total > 10. The answer to "more than 10?" is always YES. Statement (1) is sufficient.
Step 2: Evaluate Statement (2) alone — "An extra ticket would cost $77"
This tells us her current spend + one more ticket = $77, so she currently spent $77 − (cost of one ticket). Either $77 − $4 = $73 (child's ticket) or $77 − $9 = $68 (adult's ticket).
Case A: She spent $73 → same as Statement (1) → sufficient by same logic above.
Case B: 9a + 4c = 68. Try solutions:
- a = 4: 36 + 4c = 68 → c = 8. Total = 12 > 10 ✓
- a = 0: 4c = 68 → c = 17. Total = 17 > 10 ✓
- a = 8: 72 + 4c = 68. Negative c. ✗
In both cases the total is > 10. Statement (2) is also sufficient.
Answer: D — Each statement alone is sufficient.
Common trap: Many students see Statement (2) and freeze because it doesn't explicitly state how much Brenda spent. The key is recognising that "an extra ticket for Tom" implies Tom's ticket costs either $4 or $9, giving you two possible current spend amounts — and you need to check BOTH cases to confirm sufficiency. The trap is dismissing Statement (2) as ambiguous without fully testing both cases.
Quick DS check habit: Before doing algebra, remind yourself this is a Yes/No question. You don't need a unique value of a + c — you just need all valid scenarios to give the same yes-or-no answer. Here they all give "yes," so both statements are sufficient.
Takeaway: In Yes/No DS questions, sufficiency requires a consistent answer across all valid scenarios — not a unique numerical value.
