Using Statement (1), we can set up the following equation:

The amount of acid in the original solution (40% multiplied by 15 liters) should equal the amount of acid in the final diluted solution (remember there is no acid in water!!!)

Therefore knowing the value of x, we are able to calculate y. We can now find the amount of water used to dilute the solution by subtracting x from y.

Using Statement (2), we set up the following equation:

We can also calculate the amount of water used since we can calculate x from knowing y.

Each Statement ALONE is sufficient to answer the question.

(1) A pound of almonds is twice as expensive as a pound of walnuts.

Let x be the price per pound of walnuts and y the price per pound of almonds.

We don't know the respective amounts of almonds and walnuts and the prices of any of the nuts aren't clearly stated.

Statement(1) Alone is not sufficient.

(2) The mixture contains 0.7 pounds of walnuts and 0.3 pounds of almonds.

Statement (2) alone is not sufficient, it indicates the quantities of almonds and walnuts in a pound of mixture. However the price per pound of each type of nuts is unknown.

Combining both statements, we can write the price of one pound of the mixture as:

We do not know x, the price per pound of walnuts, therefore both statements together are not sufficient.

(1) A mixture of half almonds and half walnuts sells for $14 per pound.

Let x be the price per pound of walnuts and y the price per pound of almonds.

Since we do not know the price per pound of walnuts or the price per pound of almonds, statement(1) is not sufficient.

(2) A pound of almonds is twice as expensive as the pound of walnuts.

Let x be the price per pound of walnuts and y the price per pound of almonds.

Statement (2) alone is not sufficient.

Combining both statements:

The price per pound of almonds is:

(1) The chemist would like the final solution to be 15% chlorine.

The final solution is 150 ml and contains 15% of chlorine. Let x be the amount of water, then 150-x is the amount of the original chlorine solution. The amount of chlorine in the original solution is the same in the final solution, only the concentration changes.

(2) There is no chlorine in water.

Statement (2) is not helpful as it does not help in finding the amount of chlorine in the final solution.

(1) The final solution contains 20% of acid.

Using Statement (1), we know the concentration of acid in the final solution. However, we cannot find the quantity of the final solution as we do not know what quantity of acid was diluted.

So Statement (1) Alone is not sufficient.

(2) x=20 ml

Using statement (2) we know the quantity of the original acid solution, but we do not know what quantity of water was added or the concentration of the final solution.

So Statement (2) Alone is not sufficient.

Combining both Statements,

We have 20 ml of a 100% acid solution. Note that there is 0% acid in water. After diluting the solution, we obtain y ml of a solution containing 20% of acid. The amount (in ml) of acid in the final solution equals the amount of acid of the initial solution:

Therefore 100 ml of solution is obtained by diluting the original acid solution with water.

Both Statements Together are sufficient.

Statement 1 gives us the number of tickets sold but not the price. Insufficient.

Statement 2 gives us the price of the tickets but not the number sold. Insufficient.

Together, the two statements give us both the number of tickets sold AND the price of each ticket. From this we can calculate the total revenue.

Note: We are only trying to determine if we have enough information to answer the question. We don't have to actually do the computations!

We need both statements to find out how much money Mary made.

Statement 1 gives the type and number of hours, and statement 2 gives the amount she made per hour. Both together are sufficient, but neither is sufficient alone.

Ignore the comment about 15% more than the previous year. We want to find net profit and in statement one we are given the gross profit. Statement II gives us the profit margin or percent profit. 

We can use percent profit and gross profit to find net profit, but we cannot do it with only I or only II. Thus, they are both needed.

To find the profit, we either need to know the cost or the percent profit. 

I) Gives us the cost.

II) Gives us the percent profit.

Either of these can be used to find profit.

Using statement 1, it is easy to see how much the total retail amount should have been. The total retail amount discounted by 25% is the amount that Susan spent. So, we name a variable. Let x be the total retail amount. Then x - .25x = $122. We can rewrite this as x(1-.25) or x(.75)=150 thus, x = 200. So we subtract the known retail prices of the skirt and the purse to get the retail price of the jacket. So 200 - 100 - 40 = $60 is the retail price of the jacket.

Now, we should check statement 2. Using statement 2, we can calculate the savings we had on the jacket. We can first calculate how much we saved on the skirt. So 30% of the $40 retail price is $12. After we find this, we use the information from statement 2 to find the savings we had on the jacket. So $12 + $6 = $18 saved on the jacket. 

Now, we need to figure out how much we spent on the jacket. We do this by taking the total amount we spent and subtracting the discounted price of the purse and the discounted price of the skirt. So, a $100 purse, at 20% off, is $80. We calculated our savings on the skirt earlier, so we know we spent $28 on the skirt. So $150 - $80 - $28 = $42.

Now combining these two pieces of information, we see we spent $42 and saved $18 so 42+18 = $60 retail price for the jacket. 

We can see that either statement alone is sufficient to solve the problem.