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There are two bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into a 8-kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?
There are two bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into a 8-kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?
a. 1 kg b. 3 kg c. 5 kg d. 6 kg e. 7 kg
Here is how I solve it: 1)First bar: 2x+3x=a 2)Second bar: 3y+7y=b 3)Combined bar: 5n+11n=8; n=0.5; So, we have 2.5kg gold and 5.5kg silver in total. 4)total gold: 2x+3y=2.5 5)total silver: 3x+7y=5.5 From 4&5 we find that x=0.2 kg => Substituting in equation 1 yields a=1
There are two bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into a 8-kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?
a. 1 kg b. 3 kg c. 5 kg d. 6 kg e. 7 kg
w1= weight of Ist bar w2= weight of IInd bar w1 +w2 = 8 w2 = 8 - w1
I bar: g1/s1 = 2/3 gold weight = w1(2/5) = 2w1/5 silver weight = w1(3/5) = 3w1/5
There are two bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into a 8-kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?
a. 1 kg b. 3 kg c. 5 kg d. 6 kg e. 7 kg
Let weight of bar1 be x kgs. So the weight of bar2 will be ( 8 - x) kgs The first bar is 2/5 gold, the second 3/10 gold
2/5 (x) + 3/10 ( 8 - x)
2x/5 + 24/10 - 3x/10
4x/10 + 24/10 - 3x/10
x/10 + 24/10 ( This is the amount of gold in the mixture)
given: weight of the mixture is 8 kgs and the ratio of gold to total weight is 5/16
I think the fastest way to answer the question is to look at the composition of the two bars. The first bar contains 40% (2/5) of gold, while the second bar contains 30% (3/10) of gold. They are to be melted into a 8kg bar, which contains slightly more than 30% of gold (5/16).
Given that the gold content of the final bar is very close to the gold content of the second bar, it has to consist to an overwhelming majority of the second bar (i.e. close to 8kg). This means that the weight of the first bar has to be very low, hence choice A.
Here is how I solve it: 1)First bar: 2x+3x=a 2)Second bar: 3y+7y=b 3)Combined bar: 5n+11n=8; n=0.5; So, we have 2.5kg gold and 5.5kg silver in total. 4)total gold: 2x+3y=2.5 5)total silver: 3x+7y=5.5 From 4&5 we find that x=0.2 kg => Substituting in equation 1 yields a=1
This is the easiest to understand and usually how I solve this kind of problems. Thank you so much!
There are two bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver, and the other has 3 parts of gold to 7 parts of silver. If both bars are melted into a 8-kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?
(A) 1 kg (B) 3 kg (C) 5 kg (D) 6 kg (E) 7 kg We can solve this by the rule of Alligation
1) Gold content in bar 1 = 2/2+3 = 2/5 2) Gold content in bar 2 = 3/3+7 = 3/10 3) Gold content in mixture of bar 1 and bar 2 = 5/16 4) Now by rule of Alligation we have:
2/5 3/10 5/16 So ratio of mixing is (5/16-3/10)/ (2/5 - 5/16) = 1/7 Since total weight given is 8 kg so 1 Kg is weight of bar 1 and 7 kg is weight of bar 2. This is known as rule of alligation which can be used to solve questions on mixtures. Using this technique we can solve the problem is less than 2 minutes.
All you guys are spinning around in circles setting up equations and stuff. I think I'm pretty good at math; however, I think the mnemonic makes these mixtures very easy.
In my opinion, doing well on the GMAT is about eliminating steps in your processes so that you have less chances to make mistakes. Setting up equations is basically give yourself more opportunities to make simple mistakes that tend to happen when you're doing the GMAT at the 70th minute.
5g + 11s = 8 Therefore, 2.5 kgs of gold 5.5 kgs of silver Solving for gold, there is 1 kg of gold in the first bar Solving for silver, there is 1.65 kg of silver in the first bar The total weight of the first bar is 2.65 kg. _________________