Pertanyaan
Ethan sold exactly eight TVs this quarter. Frank sold exactly twice as many TVs as'Gina. Gabriel sold more TVs than Ethan. Gina sold exactly three more TVs than Gabriel and Ethan combined Which statement must betrue? Gabriol and Gina combined sold more TVs than Frank. Frank sold more than 40 TVs. Gina sold more than twice as many TVs as Ethan. Gina sold exactly twice as many TVs as Gabrlel. Ethan, Gabriel, Gina, and Frank combined sold more than 80 TVs.
Jawaban
* Ethan: Sold 8 TVs.
* Frank: Sold twice as many TVs as Gina (Frank = 2 * Gina).
* Gabriel: Sold more TVs than Ethan (Gabriel > 8).
* Gina: Sold three more TVs than Gabriel and Ethan combined (Gina = Gabriel + Ethan + 3 = Gabriel + 8 + 3 = Gabriel + 11).
Now let's substitute and solve:
Since Frank = 2 * Gina, and Gina = Gabriel + 11, then Frank = 2 * (Gabriel + 11) = 2Gabriel + 22.
Let's examine each statement:
1. Gabriel and Gina combined sold more TVs than Frank: Gabriel + Gina > Frank. Substituting, we get Gabriel + (Gabriel + 11) > 2Gabriel + 22. This simplifies to 2Gabriel + 11 > 2Gabriel + 22, which is false. This statement is not true.
2. Frank sold more than 40 TVs: Frank = 2Gabriel + 22. We know Gabriel > 8. If Gabriel were 9, Frank would be 40. If Gabriel were 10, Frank would be 42. Since Gabriel must be greater than 8, Frank *could* be more than 40, but it's not guaranteed. This statement is not necessarily true.
3. Gina sold more than twice as many TVs as Ethan: Gina > 2 * Ethan. Gina = Gabriel + 11, and Ethan = 8. So Gabriel + 11 > 16, meaning Gabriel > 5. Since Gabriel > 8, this statement is true.
4. Gina sold exactly twice as many TVs as Gabriel: Gina = 2 * Gabriel. This contradicts our earlier equation: Gina = Gabriel + 11. This statement is not true.
5. Ethan, Gabriel, Gina, and Frank combined sold more than 80 TVs: Ethan + Gabriel + Gina + Frank > 80. Substituting, we get 8 + Gabriel + (Gabriel + 11) + (2Gabriel + 22) > 80. This simplifies to 4Gabriel + 41 > 80, or 4Gabriel > 39, meaning Gabriel > 9.75. Since Gabriel must be a whole number representing TVs sold, Gabriel ≥ 10. If Gabriel were 10, the total would be 8 + 10 + 21 + 42 = 81, which is greater than 80. This statement is true.
Therefore, the statements that must be true are:
* Gina sold more than twice as many TVs as Ethan.
* Ethan, Gabriel, Gina, and Frank combined sold more than 80 TVs.
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