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Updated on: 24 Jul 2019, 04:17
Originally posted by bytatia on 16 Aug 2014, 17:56.
Last edited by Sajjad1994 on 24 Jul 2019, 04:17, edited 1 time in total.
Last edited by Sajjad1994 on 24 Jul 2019, 04:17, edited 1 time in total.
Added Source.
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Difficulty:
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Question Stats:
81% (01:16) correct
19%
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wrong
based on 639
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In what proportion must rice at $0.8 per pound be mixed with rice at $0.9 per pound so that the mixture costs $0.825 per pound?
(A) 1 : 3
(B) 1 : 2
(C) 1 : 1
(D) 2 : 1
(E) 3 : 1
(A) 1 : 3
(B) 1 : 2
(C) 1 : 1
(D) 2 : 1
(E) 3 : 1
Source: Nova GMAT
Difficulty Level: 600
Difficulty Level: 600
JeffTargetTestPrep
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bytatia
We can let x = the number of pounds of the $0.8 per pound flour and y = the number of pounds of the $0.9 per pound flour and create the equation:
0.8x + 0.9y = 0.825(x + y)
800x + 900y = 825x + 825y
75y = 25x
3y = x
3/1 = x/y
Answer: E
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Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.825
0.9 – 0.1x = 0.825
0.1x = 0.075
x = 0.75
Thus ¾ of the mixture contains $0.8 per pound flour. Thus ratio of both flours is 3:1
If one has knowledge of weighted averages… the method by acegmat1 solves the questions in approx. 45 seconds…
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.825
0.9 – 0.1x = 0.825
0.1x = 0.075
x = 0.75
Thus ¾ of the mixture contains $0.8 per pound flour. Thus ratio of both flours is 3:1
If one has knowledge of weighted averages… the method by acegmat1 solves the questions in approx. 45 seconds…
General Discussion
acegmat1
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bytatia
IMO E
Ratio :- 0.075/0.025 = 3:1
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Schools: Cambridge'16
Posts: 405
Differential approach is my favourite in this type:
0.8----0.825-----------0.9
No need any counting, 0.825 is three times closer 0.8 than 0.9. So, the ratio is 3:1
E
0.8----0.825-----------0.9
No need any counting, 0.825 is three times closer 0.8 than 0.9. So, the ratio is 3:1
E
Posts: 6,727
bytatia
We can solve this using weighted averages
Weighted average of groups COMBINED = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Let C = pounds of Cheap flour ($0.8 per pound) needed
Let E = pounds of Expensive flour ($0.9 per pound) needed
So, the TOTAL weight = C + E
The proportion of Cheap Flour in the final mix = C/(C+E)
The proportion of Expensive Flour in the final mix = E/(C+E)
Plug all values into formula to get: 0.825 = [C/(C+E)][0.8] + [E/(C+E)][0.9]
Simplify: 0.825 = 0.8C/(C+E) + 0.9E/(C+E)
Simplify: 0.825 = (0.8C + 0.9E)/(C+E)
Multiply both sides by (C+E) to get: 0.825(C+E) = 0.8C + 0.9E
Expand: 0.825C + 0.825E = 0.8C + 0.9E
Subtract 0.8C from both sides: 0.025C + 0.825E = 0.9E
Subtract 0.825E from both sides: 0.025C = 0.075E
This is the same as: 25C = 75E
And this is the same as C = 3E
This tells is that C is 3 TIMES the value of E
So, the ratio C : E = 3 : 1
Answer: E
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bytatia
8 ---- 8.25 ---- 9 = 0.75 -----------0.25
So, the required ratio is 3:1 , answer will be (E)
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Bunuel
use allegation method
we get
ratio 3:1
IMO E
Using Allegation:
0.8 0.9
0.825
To make the calculation easier, we multiply all of them with the LCM of the fractions which is 1000.
Now, we get
800 900
825
75 : 25
3 : 1
Therefore, the answer is E.
Posted from my mobile device
0.8 0.9
0.825
To make the calculation easier, we multiply all of them with the LCM of the fractions which is 1000.
Now, we get
800 900
825
75 : 25
3 : 1
Therefore, the answer is E.
Posted from my mobile device
ThatIndianGuy
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Location: India
Concentration: Strategy, Technology
WE:General Management (Technology)
Posts: 74
bytatia
---
Solution:
Let Qty of Type A rice be X and Qty of Type B rice be Y
0.8X + 0.9Y = 0.825 (X+Y)
0.8X + 0.9Y = 0.825X + 0.825Y
X/Y = 3:1
Answer is E
---
Weighted average can be used to solve this problem. In my case, I did a series of trial and error. Final solution is as follows:
Step 1: 0.8(3) + 0.9(1) = 0.33
Step 2: 0.33 / 4 = 0.825
E is our answer.
Step 1: 0.8(3) + 0.9(1) = 0.33
Step 2: 0.33 / 4 = 0.825
E is our answer.
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