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X grams of a solution containing 20 percent P (by weight) is mixed

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X grams of a solution containing 20 percent P (by weight) is mixed  [#permalink]

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New post 27 Oct 2018, 06:00
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X grams of a solution containing 20 percent P (by weight) is mixed with Y grams of a solution containing 15 percent P (by weight). The resulting mixture is 18 percent P (by weight) and has a total weight of Z grams. What is the value of X?
1) Y = 2 grams
2) Z = 5 grams

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Re: X grams of a solution containing 20 percent P (by weight) is mixed  [#permalink]

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New post 27 Oct 2018, 19:45
X grams of a solution containing 20 percent P (by weight) is mixed with Y grams of a solution containing 15 percent P (by weight). The resulting mixture is 18 percent P (by weight) and has a total weight of Z grams. What is the value of X?

Use weighted average method..
15.....18...20
\(\frac{X}{Y}=\frac{18-15}{20-18}=\frac{3}{2}\)=1.5
Now X=1.5Y and X+Y=1.5Y+Y=2.5Y=Z
So any one value out of X, Y or Z will give all three values

1) Y = 2 grams
X=1.5Y=1.5*2=3 gms
Sufficient

2) Z = 5 grams
Z=2.5Y=5....Y=2
Thus X=1.5Y=1.5*2=3 gms
Sufficient

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: X grams of a solution containing 20 percent P (by weight) is mixed  [#permalink]

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New post 28 Oct 2018, 01:44
On solving the data given in question by weighted avg method.

X/Y=(15-18)/(18-20)=3/2
Now X=3/5
Y= 2/5
Z= 5
now we can see that the option 1 and 2 both has the data which we have already calculated,
hence (D)
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Re: X grams of a solution containing 20 percent P (by weight) is mixed &nbs [#permalink] 28 Oct 2018, 01:44
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