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The volume of water in a certain tank is x percent greater [#permalink]
 20 Jan 2013, 01:49
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26% (01:07) wrong based on 4 sessions
The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. what is the value of r in terms of x? A) x+10 b) 10x+1 c) 100(x+10) d) 100( x+10/x+100) e) 100 ( 10x+1/10x+10)
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Re: The volume of water in a certain tank is x percent greater [#permalink]
20 Jan 2013, 03:54
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Best approach for solving this specific problem would be "Pick numbers". You can also solve it in Algebraic way, but it could be time consuming and tedious. Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago. Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units. i.e. Pick numbers as x = 20% and r = 25% Substitute x=20 and identify the answer that gives r=25A) x+10 --20+1=30b) 10x+1 --200+1=201c) 100(x+10) --100(20+10)=3000d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)Hence choice(D) is the answer.
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Re: The volume of water in a certain tank is x percent greater [#permalink]
20 Jan 2013, 03:42
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Volume now is x% greater than volume one week ago => Vnow = Vweekago (1+x/100) If r percent of the current volume is removed, the resulting volume will be 90 percent of the volume a week ago => Vnow (1-r/100) = 0.9*Vweekago Using the first equation, Vnow/Vweekago = (1+x/100) Putting this in the second equation, (1-r/100) (1+x/100) = 0.9 => (100 - r) (100 + x) = 9000 => r = 100 - [9000/(100+x)] => r = 100* (10+x)/(100+x) Option D
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Re: The volume of water in a certain tank is x percent greater [#permalink]
20 Jan 2013, 10:24
PraPon wrote: Best approach for solving this specific problem would be "Pick numbers". You can also solve it in Algebraic way, but it could be time consuming and tedious.
Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago.
Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units.
i.e. Pick numbers as x = 20% and r = 25%
Substitute x=20 and identify the answer that gives r=25
A) x+10 --20+1=30
b) 10x+1 --200+1=201
c) 100(x+10) --100(20+10)=3000
d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25
e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)
Hence choice(D) is the answer. I think that in this scenario under pressure someone could not visualize 25% to obtain 90 and to go in the wrong way. better an hybrid approach and in this case algebraic translation maybe is a bit safer 
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Re: The volume of water in a certain tank is x percent greater [#permalink]
20 Jan 2013, 16:09
Yes I agree, not all problems can be solved using pick numbers strategy or not always will be able to come up with ideal pick numbers under pressure. At times for complex problems, you need pen down that lengthy/heavy algebraic computations. However, giving 5 seconds to think about execution method (pick numbers, backsolving or algebraic) after reading the problem, can help saving over 40-50 seconds of 'extra' time taken by algebraic method. In this specific problem, I tried to visualize how can I increase 100 to certain number and decrease to obtain 90?? First comes 110, but reducing it by 20 doesnt give integer percentage on 110. Next we have 120 that includes 20% increase and then 25% decrease gives 90..bingo! It took 5-7 seconds to think & 15-20 seconds to back-solve, but saved 40-50 seconds of algebraic calculations! Picking number requires strategy of identifying optimum numbers using LCM, LCD, prime factors, multiples of 10/100s. How do we get used to this method? Practice!! When solving OG or practice problems, always see if you can solve it using multiple ways. Try same problem with Algebra, back-solving, pick numbers, hybrid approach (whichever methods are applicable) and even try guessing it. You may also automatically build that intuition over the time.
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Re: The volume of water in a certain tank is x percent greater [#permalink]
20 Jan 2013, 16:44
Another consideration. be flexible here we have something go up for a certain % and the go down for a certain % to have some result, here is 90. Ok 90 is our target value or our landmark but what about if we think in a more abstract way ?? even if I increase my % of 20 or 30 and then decrease the same by any % to obtain a value of less than 100........the process is the same. The gmat questions are so consistent and coherent (two word to say the same thing, indeed) that if you use several approachs they conduct you to the same answer, MUST conduct you to the same place. For this reason you can attack a problem with different stategies Infact, even if you have 85 and not 90 as target value the answer is still D. Of course , this kind of resilience is acquired after you repeat over and over again the concepts behind
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Re: The volume of water in a certain tank is x percent greater [#permalink]
21 Jan 2013, 03:32
PraPon wrote: Best approach for solving this specific problem would be "Pick numbers". You can also solve it in Algebraic way, but it could be time consuming and tedious.
Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago.
Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units.
i.e. Pick numbers as x = 20% and r = 25%
Substitute x=20 and identify the answer that gives r=25
A) x+10 --20+1=30
b) 10x+1 --200+1=201
c) 100(x+10) --100(20+10)=3000
d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25
e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)
Hence choice(D) is the answer. kudos at you prapon Posted from my mobile device 
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Re: The volume of water in a certain tank is x percent greater [#permalink]
26 Jan 2013, 07:43
PraPon wrote: Best approach for solving this specific problem would be "Pick numbers". You can also solve it in Algebraic way, but it could be time consuming and tedious.
Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago.
Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units.
i.e. Pick numbers as x = 20% and r = 25%
Substitute x=20 and identify the answer that gives r=25
A) x+10 --20+1=30
b) 10x+1 --200+1=201
c) 100(x+10) --100(20+10)=3000
d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25
e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)
Hence choice(D) is the answer. Thanks so much for this way. My owm method costs me 5 minutes to solve this question. The most difficult point is to estimate x and r as interger (First time I tried picking randomly and reached r=2/11% which made me unable to put into the formula). I try starting with 100 as the amount of water last week --> the amount of water this week after removing r percent is 90% of 100 = 90. I figure out r and x by finding a common multiple of 9 and 10 and larger than 100 (e.g. 180) --> figure out 180 for the first week (x=80%) and r=50%.
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Re: The volume of water in a certain tank is x percent greater [#permalink]
28 Jan 2013, 14:39
Hey! I chose volume = 100 , x=5% , r=10% Help plz?  Thanks Aj
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Re: The volume of water in a certain tank is x percent greater [#permalink]
29 Jan 2013, 06:22
(1+x/100)*V-(1+x/100)v*r/100=9/10*V (V is an initial volume) solve this and u will get the answer D
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Re: The volume of water in a certain tank is x percent greater
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29 Jan 2013, 06:22
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