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If tank contains only gasoline, how many kiloliters of

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el1981
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If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 08:23
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Can someone help to solve this question. i got cofused... thanks.
If tank contains only gasoline, how many kiloliters of gasoline are in tank X?
1. If 1/2 of the gasoline in tank X were pumped out, the tank would be be filled to 1/3 of its capacity.
2. If 0.75 kiloliters of gasoline were pumped into tank X, it would be filled to capacity.



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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 09:06
el1981 wrote:
Can someone help to solve this question. i got cofused... thanks.
If tank contains only gasoline, how many kiloliters of gasoline are in tank X?
1. If 1/2 of the gasoline in tank X were pumped out, the tank would be be filled to 1/3 of its capacity.
2. If 0.75 kiloliters of gasoline were pumped into tank X, it would be filled to capacity.


C,

Let`s say,

Y - present amount of gasoline in the tank.
Z- capacity of the tank in gasoline kiloliters.

The stem is asking what Y is.

1st: Y-(1/2)*Y=(1/3)*Z, two unknows one equation, we can`t find Y.
2nd: 0,75+Y=Z, two unknows one equation, we can`t find Y.

Both:

Y-(1/2)*Y=(1/3)*Z
0,75+Y=Z

It is a system of equations with two unknows and two equations.

Enough to find value of Y.
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 15:55
Agree, C

1. not sufficient. only we know that 2/3 of the tank X is empty

2. we are give that 0.75 kilolitres will make it full, but not suff. alone

combined: assume total capacity is C
then C*2/3=0.75 --> C=9/8 kilolitres
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 19:13
el1981 wrote:
Can someone help to solve this question. i got cofused... thanks.
If tank contains only gasoline, how many kiloliters of gasoline are in tank X?
1. If 1/2 of the gasoline in tank X were pumped out, the tank would be be filled to 1/3 of its capacity.
2. If 0.75 kiloliters of gasoline were pumped into tank X, it would be filled to capacity.


This is C.

I accidently did this backwards:

x= Capacity of tank
z= amount in tank

S1 gives us:
z-x/2=x/3 ---> z= 5x/6 --> x=6/5z (I accidently did x/2-z, but still got C).

S2: gives us

.75+z=x.

1&2: plug in x: .75+z=6/5z ---> 3/4=1/5z ---> z=15/4
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 19:41
el1981 wrote:
Can someone help to solve this question. i got cofused... thanks.
If tank contains only gasoline, how many kiloliters of gasoline are in tank X?
1. If 1/2 of the gasoline in tank X were pumped out, the tank would be be filled to 1/3 of its capacity.
2. If 0.75 kiloliters of gasoline were pumped into tank X, it would be filled to capacity.



from ( i )

assumed all units are in kilolitres.

Let's say the capacity of the tank is V and the amont of gasoline present in the tank is X.

Amount of gasoline pumped out is X/2, then the tank would be filled to V/3. That means the volume V/3 contains the remaining half of the gasoline.

implies: V/3 = X/2 , that is X = (2/3)*V

But as we don't know the V ( capacity of the tank ) we can't give the definite answer.

from ( ii )

Let's say the capacity of the tank is V and the amont of gasoline present in the tank is X.

X+0.75 = V


from ( i ) and ( ii ), you can easily solve for X.

X = (2/3)*( X+0.75 )

X= 1.5kilolitres.
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   24 Sep 2007, 19:50
Assuming tank has capacity x kilo-litres, amount of gasoline is g kilo-litres

St1:
g/2 = x/3 --> Insufficient.

St2:
g + 0.75 = x --> insufficient.

Using both:

g/2 = x/3
(x-0.75)/2 = x/3
3x - 2.25 = 2x
x = 2.25 --> sufficient.

Ans c
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   25 Sep 2007, 13:11
I get the same answer of C but my math seems to be different from others.

Stmt 1: If 1/2 is taken out the tank then there will be 1/3 left.

x - 1/2 = 1/3
x - 3/6 = 2/6
x = 2/6 + 3/6
x = 5/6

So the tank is 5/6 full.

Stmt 2: Tells me that .75 kiloliters will make it full.

Stmt 1 & 2:

1/6x = .75
x = 4.5

So the tank holds 4.5 kiloliters - .75 kiloliters = 3.75 Kiloliters
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Re: If tank contains only gasoline, how many kiloliters of [#permalink] New post   25 Sep 2007, 18:20
gixxer1000 wrote:
I get the same answer of C but my math seems to be different from others.

Stmt 1: If 1/2 is taken out the tank then there will be 1/3 left.

x - 1/2 = 1/3
x - 3/6 = 2/6
x = 2/6 + 3/6
x = 5/6

So the tank is 5/6 full.

Stmt 2: Tells me that .75 kiloliters will make it full.

Stmt 1 & 2:

1/6x = .75
x = 4.5

So the tank holds 4.5 kiloliters - .75 kiloliters = 3.75 Kiloliters


Just to check my numbers:

x - total capacity
y - liters of gasoline in the tank

S1: 2x=3y ==> 2x-3y = 0;
S2: x = y + 0.75

Solving for x & y we get
x = 2.25 [Total capacity]
y = 1.50 [Litres of gasoline in the tank]

Verification:
S1: y/2 = 0.75 == 1/3[2.25] - HOLDS
S2: y + 0.75 = 1.50 + 0.75 = 2.25 - full capacity of the tank - HOLDS



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Re: If tank contains only gasoline, how many kiloliters of [#permalink]
25 Sep 2007, 18:20
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