# GMAT Math : Data-Sufficiency Questions

## Example Questions

### Example Question #8 : Dsq: Understanding Mixture Problems

How much water does a chemist need to dilute a pure solution of chlorine in order to obtain 150 ml of solution?

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

(2) There is no chlorine in water.

Each Statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Explanation:

(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.

### Example Question #2191 : Gmat Quantitative Reasoning

What quantity of solution is obtained by diluting  liters of pure acid with water?

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

(2)  ml.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Each Statement ALONE is sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

(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.

### Example Question #1 : Dsq: Calculating Profit

An amusement park sells Children and Adult tickets. What was the total revenue for the day?

Statement 1: The amusement park sold 259 Children tickets and 345 Adult tickets.

Statement 2: Children tickets cost $32 and Adult tickets cost$45.

Statements 1 and 2 together are NOT sufficient.

EACH statement ALONE is sufficient.

Statement 2 ALONE is sufficient, but Statement 1 is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement 1 ALONE is sufficient, but Statement 2 is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

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!

### Example Question #81 : Data Sufficiency Questions

How much money did Mary make this week?

Statement 1: Mary worked 40 hours of regular time and an additional 6 hours of overtime.

Statement 2: Mary made $30 an hour during normal working hours and$37 an hour during overtime.

EACH statement ALONE is sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

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.

### Example Question #1 : Dsq: Calculating Profit

Jorge runs a business making picture frames.

I) Jorge made  in gross profit last year,  more than the previous year.

II) Jorge had a profit margin of .

What was Jorge's net profit?

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Either statement alone is sufficient to answer the question.

Both statements are necessary to answer the question.

Both statements are necessary to answer the question.

Explanation:

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.

### Example Question #1 : Profit

An online store sells costum computers. Find the profit the store made on a  sale.

I) The computer cost the store  to build.

II) The store generally makes a  profit.

Both statements are needed to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Explanation:

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.

### Example Question #1 : Dsq: Calculating Discounts

Susan went to a clearance sale and bought various items on sale. She saves 20% on a purse, retailing for $100. She saves 30% on a skirt that was marked down from a retail price of$40. She also bought a jacket that was on sale, and she spent a total of $150 . How much did the jacket retail for? 1. Her overall savings were 25% off the combined retail price of all three items. 2. Her discount on the jacket was$6 more than her savings on the skirt.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Statements 1 and 2 together are not sufficient.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Each statement alone is sufficient.

Explanation:

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.

2. The sale price is $6 less than the original price. Possible Answers: Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question Each statement alone is sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question Correct answer: Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient Explanation: In order to calculate the percent discount, both the original price and the sale price must be known. From statement 1, we know the sale price and with the additional information from statement 2, we can calculate the original price and then overall percent discount. ### Example Question #1 : Dsq: Calculating Discounts A store owner applies a certain percentage of discount on items bought by customers who have a rewards card. What is the percentage of discount applied? (1) A customer without a reward card pays 1.5 times what a customer with a reward card pays on the same articles. (2) A customer with a reward card pays two thirds of any listed price. Possible Answers: Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient. Statements (1) and (2) TOGETHER are not sufficient. Each Statement ALONE is sufficient. Correct answer: Each Statement ALONE is sufficient. Explanation: (1) A customer without a reward card pays 1.5 times what a customer with a reward card pays on the same articles. Let x be the price a customer with a reward card pays, a customer without a reward card pays 1.5x, 1.5x being the original selling price. We can calculate the percentage of discount as: Statement (1) is sufficient. (2) A customer with a reward card pays two thirds of any listed price. Let y be the listed price of a given article. A customer with reward card pays . The percentage of discount is: Statement (2) is sufficient. Each Statement ALONE is sufficient. ### Example Question #1 : Dsq: Calculating Discounts What is the amount of tuition for a MBA degree at University X? (1) Students with a GMAT score above 700 receive a 50% discount on the tuition. (2) The average tuition paid by 5 students is$50,000, if only 2 of these students received a 50% discount.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Each Statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Explanation:

(1) Students with a GMAT score above 700 receive a 50% discount on the tuition.

Statement (1) is not sufficient as we do not know how much half of the tuition is.

(2) The average tuition paid by 5 students is \$50,000, if only 2 of these students received a 50% discount. Let x be the full amount of tuition for the MBA program.

Statement(2) Alone is sufficient.