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20 Dec 2023, 07:00
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C
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71% (01:50) correct
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
During a Christmas dinner, Timmy enjoyed several candies for dessert. If each candy was either a $0.50 piece or a $0.40 piece, how many $0.50 candies did Timmy have?
(1) The total cost of the candies Timmy ate was $4.90.
(2) Timmy ate more $0.50 candies than $0.40 candies.
During a Christmas dinner, Timmy enjoyed several candies for dessert. If each candy was either a $0.50 piece or a $0.40 piece, how many $0.50 candies did Timmy have?
(1) The total cost of the candies Timmy ate was $4.90.
(2) Timmy ate more $0.50 candies than $0.40 candies.
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21 Dec 2023, 04:49
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GMAT Club Official Explanation:
During a Christmas dinner, Timmy enjoyed several candies for dessert. If each candy was either a $0.50 piece or a $0.40 piece, how many $0.50 candies did Timmy have?
Let the number of $0.50 candies be x and the number of $0.40 candies be y. The question asks to find the value of x.
(1) The total cost of the candies Timmy ate was $4.90.
This implies 0.5x + 0.4y = 4.9. Multiplying by 10 gives: 5x + 4y = 49. Don't rush to conclude that this is automatically insufficient, since we have one equation and two variables. We should still check because x and y must be integers here, so it's possible for the equation to have only one set of (x, y) satisfying it. However, this is not the case for this specific equation. By trial and error, we can find that three sets of (x, y) satisfy 5x + 4y = 49: (1, 11), (5, 6), and (9, 1). Not sufficient.
(2) Timmy ate more $0.50 candies than $0.40 candies.
This implies that x > y. Clearly insufficient.
(1)+(2) Given that from (2) x > y, the only pair of (x, y) which satisfies this is (9, 1). Therefore, x = 9. Sufficient.
Answer: C.
General Discussion
20 Dec 2023, 14:27
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Bunuel
(1) Timmy incurred a total cost of $4.90 for the candies he consumed.
We can express the equation as 0.5x + 0.4y = 4.90, where x and y represent the quantities of $0.50 and $0.40 candies, respectively.
Some of the potential solutions are (9,1) and (5,6). Hence, this information alone is insufficient.
(2) It is stated that Timmy consumed more $0.50 candies than $0.40 candies, but this statement lacks specific numerical details. Hence, it insufficient in providing information about the actual quantities of candies.
Combining both statements (1) and (2), we can deduce that Timmy indeed ate more $0.50 candies than $0.40 candies, The only option that fits this criteria is (9,1). This combined information proved to be sufficient to answer the problem.
IMO C
