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26 Oct 2021, 06:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
68% (02:52) correct
32%
(03:05)
wrong
based on 378
sessions
History
Date
Time
Result
Not Attempted Yet
Pastries made out of filo dough and brushed with either olive oil or butter (but not both). Pastries made out of shortcrust dough are not brushed with anything. Rashid and Mikhail submitted a total of x pastries to a baking competition. Mikhail used filo dough for all of his pastries, Rashid used shortcrust dough for all of his pastries, and each pastry was made using only one kind of dough. If Rashid made \(\frac{2}{3}\) as many pastries as Mikhail, and \(\frac{5}{8}\) of the filo dough pastries were brushed with olive oil, then how many of the pastries submitted by Rashid and Mikhail, in terms of x, were brushed with butter?
A. \(\frac{3X}{20}\)
B. \(\frac{9X}{40}\)
C. \(\frac{1X}{4}\)
D. \(\frac{3X}{8}\)
E. \(\frac{5X}{12}\)
A. \(\frac{3X}{20}\)
B. \(\frac{9X}{40}\)
C. \(\frac{1X}{4}\)
D. \(\frac{3X}{8}\)
E. \(\frac{5X}{12}\)
27 Oct 2021, 22:32
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Bunuel
Let the number of pastries Michael makes be LCM(3,8) or 24. => M=24, so R=\(\frac{2*24}{3}=16\)
So x=\(M+R=24+16=40\)
Now, all pastries made of filo dough were made by M and 3/8 of these are oiled with butter => \(\frac{3M}{8}=\frac{3*24}{8}=9\)
Substitute x as 40 and look for answer 9.
B gives the answer we are looking for. => \(\frac{9x}{40}=\frac{9*40}{40}=9\)
B
21 Aug 2022, 10:06
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OFFICIAL ANSWER
Step 1: Glance Read Jot
This question is very dense, so take stock of the information before doing any math. In addition to the Fractions, it’s important to note who uses which kind of dough.
Rashid: short, no brush
Mikhail: filo, brush
Rashid = 23 of Mikhail
58 of Mikhail = olive oil
38 of Mikhail = butter
Step 2: Reflect Organize
Because there is a single unknown—the total number of pastries baked by Rashid and Mikhail, x—and fractions are present, use Smart Numbers.
Step 3: Work
Smart Numbers
Because both of the fractions in the problem revolve around Mikhail, start with him. To avoid decimals, pick a number divisible by both 3 and 8, the two denominators in the problem:
Mikhail baked 3 × 8 = 24 pastries
Rashid baked 23 as many, or 24 × 23 = 16 pastries
Total pastries baked = x = 24 + 16 = 40
Next, consider the brushing:
58 of Mikhail’s pastries brushed with olive oil à 24 × 58 = 15
38 of Mikhail’s pastries brushed with butter à 24 × 38 = 9
The question asks for the number of pastries, in terms of the total x, that were brushed with butter. In this case there were 40 total pastries, 9 of which were brushed with butter, so the answer should be 940 of x.
The correct answer is (B).
Step 1: Glance Read Jot
This question is very dense, so take stock of the information before doing any math. In addition to the Fractions, it’s important to note who uses which kind of dough.
Rashid: short, no brush
Mikhail: filo, brush
Rashid = 23 of Mikhail
58 of Mikhail = olive oil
38 of Mikhail = butter
Step 2: Reflect Organize
Because there is a single unknown—the total number of pastries baked by Rashid and Mikhail, x—and fractions are present, use Smart Numbers.
Step 3: Work
Smart Numbers
Because both of the fractions in the problem revolve around Mikhail, start with him. To avoid decimals, pick a number divisible by both 3 and 8, the two denominators in the problem:
Mikhail baked 3 × 8 = 24 pastries
Rashid baked 23 as many, or 24 × 23 = 16 pastries
Total pastries baked = x = 24 + 16 = 40
Next, consider the brushing:
58 of Mikhail’s pastries brushed with olive oil à 24 × 58 = 15
38 of Mikhail’s pastries brushed with butter à 24 × 38 = 9
The question asks for the number of pastries, in terms of the total x, that were brushed with butter. In this case there were 40 total pastries, 9 of which were brushed with butter, so the answer should be 940 of x.
The correct answer is (B).
