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17 Apr 2024, 14:32
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A
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Difficulty:
55%
(hard)
Question Stats:
69% (02:39) correct
31%
(02:42)
wrong
based on 520
sessions
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Date
Time
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Not Attempted Yet
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
Attachment:
GMAT-Club-Forum-ymey5o25.png [ 26.2 KiB | Viewed 4354 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 4321 times ]
19 Apr 2025, 19:41
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