Jim needs to mix a solution in the following ratio: 1 part bleach for

Question

Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much bleach did Jim put into the solution?

A. 1mL
B. 2mL 
C. 3mL 
D. 4mL 
E. 5mL

To solve this problem:
The ratio is  1:4 , meaning there should be  x  parts bleach and  4x  parts water. However, Jim put in half as much bleach as he should have, so he put in  \frac{x}{2}  parts bleach. So the equation would be:
 \frac{x}{2} + 4x = 18   => x=4 
This part is clear, however, according to the MGMAT Guide the correct answer is not  4 , but it's  \frac{4}{2} , but we already used  \frac{x}{2}  in the equation.

Now,  4(2) + 2 = 18  which makes sense. However, my main concern is with the reasoning, that to solve the equation, we have already halved Jim's amount, and then we are halving it again. Please explain.

EMPOWERgmatRichC · Accepted Answer

Hi All,

While this is an old series of posts, there is a rather straight-forward way to approach this question that is more about real-world math than anything else.

The original prompt tells us that Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water.

So, if we have 1 part bleach + 4 parts water we get 5 parts total mixture....

Next, we're told that when mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have.

So, he ACTUALLY mixed 1/2 part bleach + 4 parts water and gets 4.5 parts total mixture....

The total solution consists of 18 mL. How much did Jim put into the solution?

18 = (4.5)(4) so the 18mL is made up of 4 "sets" of the 4.5 parts mixture. This means there are 4(4) = 16 mL of water and 4(1/2) = 2mL of bleach.

GMAT assassins aren't born, they're made,
Rich

Vips0000 · Answer

if you look at the equation that you've set up. you would notice that you actually added x/2 part of bleach in 4x water not x part. Thus if x=4, the amount of bleach is x/2=4/2.
It is not x that you are looking for, but the value that you used in mixture ie x/2

vy3rgc · Answer

1 part bleach for every 4 parts water = 1:4
1/2 part bleach for every 4 parts water = 1/2 : 4 = 1:8

9x = 18
x = 2 <-- Answer

PKPKay · Answer

as vy3rgc mentioned, 1/2:4 ratio is a 1:8 ratio.

I figured it out this way.
in a 10 part solution, there is 2 bleach and 8 water.
Jim only added 1/2 the amount of bleach needed so instead of 2 bleach he added 1 bleach and 8 water.
This also changes it from a 10 part mixed solution to a 9 part mixed solution.

In a 18 part solution with this mistake, he'll have 2 parts bleach and 16 parts water.

dcummins · Answer

Think about this logically.
The intended ratio is 1 part bleach per 4 parts water
Bleach:water: total
1:4: 5

He mixes in 1/2 as much bleach or, in other words, twice as much water, so the ratio is actually
Bleach:water: total
1:8:9

Thus the amount of bleach present
= 1/9 * 18 
= 2 units

mm229966 · Answer

Bleach/ Water was = 1/4 BUT it got 1/2 * 1/4 = 1/8;
So now we have 9 parts and: 9X = 18 and X = 2.

Aashav27 · Answer

Experts, where am I going wrong with my approach?

Originally, for every x part of bleach, there are 4x parts of water. Total parts=x+4x=5x, Total volume of the solution: 18mL
5x=18
x=3.6
Original amount of bleach = 3.6mL
Since, he used only half the amount=1.8mL (Not an option)

Thanks,

EMPOWERgmatRichC · Answer

Hi Aashavpatel27,

There's a small logical mistake in your work: Jim made the mistake when he STARTED mixing the ingredients together, so you have to consider how the original 'recipe' changed based on that initial step.

You are correct that when we have 1 part bleach for every 4 parts water, we can write that as 1X + 4X = 5X.

However, since Jim makes a mistake and mixes in HALF as much bleach as he ought to have, then the equation becomes....

(1/2)X + 4X = 4.5X..... (not 5X)

The total solution consists of 18 mL, so we can write this as...

4.5X = 18
9X = 36
X = 4

So when Jim made his mixture, he mixed 2 mL of bleach and 16 mL of water.

GMAT assassins aren't born, they're made,
Rich

errorlogger · Answer

Can someone please edit the question?
How much  bleach  did Jim put into the solution?

GinoRako · Answer

The final question of  How much did Jim put into the solution?  is very unclear. How much what?

It should have been How much  BLEACH  did Jim put into the solution?

bumpbot · Answer

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Jim needs to mix a solution in the following ratio: 1 part bleach for

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