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17 Apr 2024, 14:32
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69% (02:41) correct
31%
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The figure above shows an array of 30 square tiles, each of which is solid white, solid gray, or diagonally hatched. Each solid white tile is priced at $x, each solid gray tile is priced at $y, and each diagonally hatched tile is priced at $z. If the total price of the 12 tiles in Columns B and D is $39, what is the total price of all 30 tiles in the array?
(1) x = 3
(2) y = 2
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GMAT-Club-Forum-ymey5o25.png [ 26.2 KiB | Viewed 5891 times ]
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17 Apr 2024, 14:39
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The figure above shows an array of 30 square tiles, each of which is solid white, solid gray, or diagonally hatched. Each solid white tile is priced at $x, each solid gray tile is priced at $y, and each diagonally hatched tile is priced at $z. If the total price of the 12 tiles in Columns B and D is $39, what is the total price of all 30 tiles in the array?
There are a total of 16 white, 7 gray, and 7 diagonally hatched tiles in the square. Hence, the question asks to find the value of 16x + 7y + 7z, while we are given that 6x + 3y + 3z = $39 (the total price of the 12 tiles in Columns B and D is $39).
(1) x = 3
Substituting x = 3 into 6x + 3y + 3z = $39, we deduce that 3y + 3z = $21. Thus, y + z = $7. Therefore, 16x + 7y + 7z = 16x + 7(y + z) = 48 + 7*7 = $95. Sufficient.
(2) y = 2
Substituting y = 2 into 6x + 3y + 3z = $39, we deduce that 6x + 3z = $33. However, knowing 6x + 3z = $33 we cannot get the value of 16x + 7y + 7z = 16x + 7z + 14. For instance, consider x = 1 and z = 9, and x = 5 and z = 1 for two different values of 16x + 7z + 14. Not sufficient.
Answer: A.
Attachment:
GMAT-Club-Forum-cy75wf6b.png [ 26.2 KiB | Viewed 5836 times ]
General Discussion
06 Jul 2026, 00:17
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My experience with these kinds of questions is that I can do them, but I feel like it is a lot of number crunching. Between reading the question, constructing the equations and reading the statements, I feel like I am already over the 135s quota. Is there a way to be more efficient with questions that require a lot of computation? I have found myself strapped for time on data insights questions.
