Mixture Problem: 35% acid to obtain 10% solution

[Deepak_J_Shah]

http://gmatclub.com/forum/mixture-probl ... ml#p544540

Need solution, MGMAT way, if you could please plug in values in an xls grid, the way MGMAT strategy guide does...

How much water (in grams) should be added to the 35%-solution of acid to obtain the 10%-solution?

1. There are 50 grams of the 35%-solution
2. In the 35%-solution the ratio of acid to water is 7:13


Volume Original Change New
Acid 35% 0 17.5
Water x gms?
Total Solution 10% of what (?)

Statement 1: There are 50 grams of the 35%-solution
Volume Original Change New
Acid 35% of 50 = 17.5 0 17.5
Water 50-17.5 = 32.5 +x gms (32.5 + x)
Total Solution 50 gms +x (50+x)


Statement 2: In the 35%-solution the ratio of acid to water is 7:13
Volume Original Change New
Acid 35%
Water ?
Total Solution 10% (?)

[Deepak_J_Shah]

IS THIS SOLUTION CORRECT?

(I wish the forum's format was compatible to allow pasting xls grid! - tried using space while editing but that didnt help either - so the xls grid is all messed up)

How much water (in grams) should be added to the 35%-solution of acid to obtain the 10%-solution?

( I am assuming that "obtain the 10%-solution" means "˜10%-solution of acid’ - since the purpose to add water is to dilute it! -DAMN- IT TOOK ME FOREVER TO CONCLUDE THIS!)

1. There are 50 grams of the 35%-solution
2. In the 35%-solution the ratio of acid to water is 7:13


ANSWER:

35% solution = 35% acid / 65% water
Volume Original Change New
Acid 35% 0 ?
Water 65% x gms? x?
Total Solution can be anything. +x 10% of acid - what is the total or
what is the acid %

STATEMENT 1:
There are 50 grams of the 35%-solution- we can know the current value for acid which will be the same in the final solution since we are not changing acid concentration, we are only adding water!- 35% of 50 = 17.5 current and final- to obtain 10% solution of acid would mean that total solution would have to be 175 for it to have 17.5 acid (10%)

Volume Original Change New
Acid 35% of 50 = 17.5 0 17.5
Water (50-17.5) = 32.5 +x gms (32.5 + x)
(or 65% of 50-same thing)
Total Sol 50 gms +x (50+x) = 175
OR
17.5+(32.5+x)=175
- same thing!

50 + x = 175
x = 175 - 50 = 125gms
x= 125
OR
17.5 + (32.5+x) = 175 (same thing)
THIS IS SUFFICIENT


STATEMENT 2:
In the 35%-solution the ratio of acid to water is 7:13Note: We already know the ratio of acid to water - 35%/65%. And 35/65 = 7/13 - same thing - no additional information - NOT SUFFICIENT - 35% solution = 35% acid / 65% water
Volume Original Change New
Acid 35%
Water 65% ?
Total Sol 10% (?)


FYI:
Weighted average - so careful with the % AND PARTS logic/lingo...

so say if the total solution was 100gms you cannot say:
7th part of 100 = 100(1/7) = 14.29
and
13th part of 100 = 100(1/13) = 7.69

Here is the reason why:
14.29+7.69 = 21.98 (DOES NOT MAKE A WHOLE)

The way this needs to be done =
(The UNKNOWN MULTIPLIER method - gives the "weight")
7x + 13x = 100
20x = 100 è x = 5
ACID: 7x = 7*5 = 35
WATER: 13x = 13*5 = 65
SUM = 35+65=100!

[RonPurewal]

( I am assuming that "obtain the 10%-solution" means "˜10%-solution of acid’ - since the purpose to add water is to dilute it! -DAMN- IT TOOK ME FOREVER TO CONCLUDE THIS!)

good news and bad news for ya.

the good news:
the gmat is REALLY meticulous about labeling these sorts of things properly. they will almost certainly go out of their way to say "of acid" EVERY SINGLE TIME, so that you don't have to worry.

the bad news:
you should have IMMEDIATELY figured out, BY DEFAULT, that this is what they meant. IF TWO PERCENTAGES ARE GIVEN, THEN, BY PARALLELISM, YOU SHOULD ASSUME THAT THEY REFER TO PERCENTAGES OF THE SAME THING, unless you can find EXPLICIT evidence that they don't.

--

you can solve MIXTURE problems using an RTD STYLE GRID.

instead of labeling the columns as "rate", "time", and "distance", label them as "% husk", "total lbs", and "lbs of husk". then, just as in rtd problems, the product of the first two columns equals the third column.

here's how the table looks (note that it won't line up when it's typed on here)

----------- % ACID ---- TOTAL GMS ---- GMS OF ACID ---
original ----- 0.35 ----- __ ------------- ____
water add ---- 0 --------- __ -------------- 0
new --------- 0.10 ------ ___ ------------- ____

the point is to fill in the blank that's in the middle of all this hot mess.

statement (1)
fill in this information, and then use % x TOTAL AMOUNT = AMOUNT OF ACID to fill in the other spots:

----------- % ACID ---- TOTAL GMS ---- GMS OF ACID ---
original ----- 0.35 ----- 50 ------------- 17.5
water add ---- 0 --------- x -------------- 0
new --------- 0.10 ------ 50 + x ------------- 17.5

therefore, 0.10(50 + x) = 17.5.
sufficient.

--

statement (2)
you should immediately know that a RATIO is exactly the same information as the FRACTIONS of the components. therefore, without having to do any actual computation, you know that this statement contributes NOTHING.
since prompt questions never solve themselves - and you don't have any information that's not in the original prompt - this must be insufficient.

if you want more information on the equivalence between ratios and fractional components, post back.