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avigutman
Expert
Tutor
Joined: 17 Jul 2019
Last visit: 27 Jun 2026
Posts: 1,285
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
KarishmaB
Can you please explain how did you get this - " for every 10 cups/liters/ml/gallons/units etc of 5% solution, you need 7 cups/liters/ml/gallons/units etc of 2% solution and 3 cups/liters/ml/gallons/units etc of 12% solution."
0,02∗x+0,12∗(60−x)=0,05∗600,02∗x+0,12∗(60−x)=0,05∗60
0,02∗x+7,2−0,12∗x=30,02∗x+7,2−0,12∗x=3
4,2=0,1∗x4,2=0,1∗x
x=0,42
0,02∗x+7,2−0,12∗x=30,02∗x+7,2−0,12∗x=3
4,2=0,1∗x4,2=0,1∗x
x=0,42
cant we do this problem in allegation way if so how?
Thanks
Thanks
Hoozan
Not sure why. They are working for me. You can access the weighted average post here: https://anaprep.com/arithmetic-weighted-averages/
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avigutman
avigutman
This is so helpful! To confirm, you are using the "seesaw" method starting at around the one-minute mark, correct?
avigutman
Expert
Tutor
Joined: 17 Jul 2019
Last visit: 27 Jun 2026
Posts: 1,285
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
2% of Sulfuric acid + 12% of Sulfuric acid = 60ltrs of 5% sulfuric acid
0.05 * 60 = 3ltrs of Sulfuric acid
Let the 2% Sulfuric acid solution be represented by x
Let the 12% Sulfuric acid solution be represented by y
x + y = 60 => x = 60 - y [these solutions are mixed in appropriate quantities to produce 60 liters]
(2/100 * x) + (12/100 * y) = 3
=> [2/100 * (60 - y)] + (12/100 * y) = 3
=> 120 + 10y = 300
=> y= 18
Therefore x(or 2% sulfuric acid solution) = 60 - 18 = 42ltrs
0.05 * 60 = 3ltrs of Sulfuric acid
Let the 2% Sulfuric acid solution be represented by x
Let the 12% Sulfuric acid solution be represented by y
x + y = 60 => x = 60 - y [these solutions are mixed in appropriate quantities to produce 60 liters]
(2/100 * x) + (12/100 * y) = 3
=> [2/100 * (60 - y)] + (12/100 * y) = 3
=> 120 + 10y = 300
=> y= 18
Therefore x(or 2% sulfuric acid solution) = 60 - 18 = 42ltrs
Let's assume that the volume of the 2 percent sulfuric acid solution needed is x liters. Therefore, the volume of the 12 percent sulfuric acid solution needed would be 60−x liters to make a total of 60 liters.
To calculate the amount of sulfuric acid in the final mixture, we can set up the following equation:
(0.02x+0.12(60−x))/60=0.05
Let's solve this equation:
0.02x+0.12(60−x)=0.05∗60
0.02x+7.2−0.12x=3
−0.1x=3−7.2
−0.1x=−4.2
Dividing both sides by -0.1:
x=−0.1/−4.2=42
Therefore, approximately 42 liters of the 2 percent sulfuric acid solution will be required.
The correct answer is (E) 42 liters.
To calculate the amount of sulfuric acid in the final mixture, we can set up the following equation:
(0.02x+0.12(60−x))/60=0.05
Let's solve this equation:
0.02x+0.12(60−x)=0.05∗60
0.02x+7.2−0.12x=3
−0.1x=3−7.2
−0.1x=−4.2
Dividing both sides by -0.1:
x=−0.1/−4.2=42
Therefore, approximately 42 liters of the 2 percent sulfuric acid solution will be required.
The correct answer is (E) 42 liters.
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
With formula, the resulting mixture % can be calculated as avg= (n1x1+n2x2)/n+n2
A) 18
B) 20
C) 24
D) 36
E) 42
With formula, the resulting mixture % can be calculated as avg= (n1x1+n2x2)/n+n2
Nrj0601
Joined: 15 May 2019
Last visit: 23 May 2024
Posts: 38
Status:Engineering Manager
Concentration: Leadership, Strategy
Schools: IIMA PGPX"20
WE:Engineering (Consulting)
Schools: IIMA PGPX"20
Posts: 38
I'll tell you an easy trick to solve these problems quickly.
2%........12%. --Current Mix
.....\...../
........5%. --Final Mix (60L)
...../.....\
7%........3%. -- what ratio of current mix req to form Final mix. (|12-5| =7 : |2-5| = 3)
So from above, we need the solution in 7:3 ratio. TF, 7/10*60 = 42. Ans
2%........12%. --Current Mix
.....\...../
........5%. --Final Mix (60L)
...../.....\
7%........3%. -- what ratio of current mix req to form Final mix. (|12-5| =7 : |2-5| = 3)
So from above, we need the solution in 7:3 ratio. TF, 7/10*60 = 42. Ans
GMATCoachBen
Expert
Tutor
Joined: 21 Mar 2017
Last visit: 09 Sep 2026
Posts: 462
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Location: United States (WA)
GMAT Focus 1: 775 Q87 V90 DI88 (Online)
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Expert reply
Short video solution here, using the Teeter Totter Timesaver Method (1:42):
Teeter Totter Method Steps:
1) Draw the Endpoints and Weighted Average numbers on the Teeter Totter Diagram (the weighted average represents the final mixture, and goes above the triangle-shaped fulcrum)
2) Draw the weights on each side. The LARGER weight goes on the side with the SHORTER distance from the fulcrum
3) Draw the distances from the Endpoints to the Weighted Average
4) Solve the equation: (W2)/(W1) =(D1)/(D2)
(the weights and distances are in an INVERSE RATIO)
Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP
_________________
Teeter Totter Method Steps:
1) Draw the Endpoints and Weighted Average numbers on the Teeter Totter Diagram (the weighted average represents the final mixture, and goes above the triangle-shaped fulcrum)
2) Draw the weights on each side. The LARGER weight goes on the side with the SHORTER distance from the fulcrum
3) Draw the distances from the Endpoints to the Weighted Average
4) Solve the equation: (W2)/(W1) =(D1)/(D2)
(the weights and distances are in an INVERSE RATIO)
Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP
Attachments
2023-12-29 21_28_13-No name - 29 December 2023 (4).mp4 - VLC media player.png [ 2.98 MiB | Viewed 1576 times ]
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- GMATCoachBen Thank you for the explanation. I just have a quick question: what does "by volume" mean here?
Allegation formula:
(Final - B)/(A - B) * 1/100%
(5%-12%)/(2%-12%) * 1/100% = 70%
70% of 60 L = 42 L
E.
(Final - B)/(A - B) * 1/100%
(5%-12%)/(2%-12%) * 1/100% = 70%
70% of 60 L = 42 L
E.
Let 2% solution have x litres; 12% solution will have 60-x litres
now i represnt this diagramatically:
Using this criss cross method i know that x:60-x will be in ratio of 7:3
We have been asked to find x and in the given options; only options (E) is a multiple of 7
GMAT-Club-Forum-3xetadp4.png [ 150.52 KiB | Viewed 52 times ]
now i represnt this diagramatically:
Using this criss cross method i know that x:60-x will be in ratio of 7:3
We have been asked to find x and in the given options; only options (E) is a multiple of 7
Attachment:
GMAT-Club-Forum-3xetadp4.png [ 150.52 KiB | Viewed 52 times ]
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