GMAT Math : Word Problems

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Example Questions

Example Question #4 : Dsq: Calculating Discounts

How many dollars does Jane save when using a coupon to buy a purse at a local store?

(1) The original price of the purse is $400.

(2) When using the coupon, Jane saves 25%.

Possible Answers:

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

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

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

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

Each Statement ALONE is sufficient.

Correct answer:

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

Explanation:

Note that the question does not ask for the percentage of discount but the amount of money saved.

(1) The original price of the purse is $400.

Statement (1) alone is not sufficient because it only gives the selling price prior to using the coupon.

(2) When using the coupon, Jane saves 25%.

Statement (2) alone is not sufficient. Even though we know the percentage of discount, we do not have the original price.

However, combining both statements, we get the amount of money saved as:

$\frac{25}{100}\times400=100$ $\displaystyle \frac{25}{100}\times400=100$

Jane saved $100 by using the coupon.

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

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Example Question #6 : Dsq: Calculating Discounts

A lawn-mower is initially offerred at $\$250$ $\displaystyle \$250$. Its price is discounted $8\%$ $\displaystyle 8\%$ off the full price. What is the final price?

Possible Answers:

$\$240.00$ $\displaystyle \$240.00$

$\$150.00$ $\displaystyle \$150.00$

$\$172.20$ $\displaystyle \$172.20$

$\$200.00$ $\displaystyle \$200.00$

$\$230.00$ $\displaystyle \$230.00$

Correct answer:

$\$230.00$ $\displaystyle \$230.00$

Explanation:

If the initial price is $P=\$250$ $\displaystyle P=\$250$, and the discount is $d=8\%$ $\displaystyle d=8\%$, the final sale price is

$S=(1-d/100)\cdot P$ $\displaystyle S=(1-d/100)\cdot P$

$\$250\cdot(1-8/100)) = \$230$ $\displaystyle \$250\cdot(1-8/100)) = \$230$

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Example Question #2 : Discount

A lawn-mower is discounted $10\%$ $\displaystyle 10\%$ off the full price. A second discount of $25\%$ $\displaystyle 25\%$ is applied at the register. What is the final discount?

Possible Answers:

$10.5\%$ $\displaystyle 10.5\%$

$32.5\%$ $\displaystyle 32.5\%$

$53.2\%$ $\displaystyle 53.2\%$

$68.3\%$ $\displaystyle 68.3\%$

$25.2\%$ $\displaystyle 25.2\%$

Correct answer:

$32.5\%$ $\displaystyle 32.5\%$

Explanation:

If the initial price is P, and it is discounted twice at rates $d{_{1}}$ $\displaystyle d{_{1}}$ and $d{_{2}}$ $\displaystyle d{_{2}}$, the final price $\displaystyle S$ is

$S=P\cdot(1-d_{1}/100)\cdot (1-d_{2}}/100)%$ $\displaystyle S=P\cdot(1-d_{1}/100)\cdot (1-d_{2}}/100)%$

Substituting values this is

$\frac{S}{P}=(1-10/100)\cdot(1-25/100)%$ $\displaystyle \frac{S}{P}=(1-10/100)\cdot(1-25/100)%$

$D=1-100\cdot S/P$ $\displaystyle D=1-100\cdot S/P$

or $1-0.675\cdot 100 = 32.5\%$ $\displaystyle 1-0.675\cdot 100 = 32.5\%$

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Example Question #2201 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at $\$250$ $\displaystyle \$250$. Its price is discounted off the full price some unknown amount, $\displaystyle D$. An employee uses their $50\%$ $\displaystyle 50\%$ discount at the register and is charged $\$100$ $\displaystyle \$100$.

What is the unknown initial discount,$\displaystyle D$?

Possible Answers:

$10\%$ $\displaystyle 10\%$

$25\%$ $\displaystyle 25\%$

$5\%$ $\displaystyle 5\%$

$15\%$ $\displaystyle 15\%$

$20\%$ $\displaystyle 20\%$

Correct answer:

$20\%$ $\displaystyle 20\%$

Explanation:

The relationship between the list price, $L=\$250$ $\displaystyle L=\$250$, sale price, $\$100$ $\displaystyle \$100$, and the employee's discount, $D=50\%$ $\displaystyle D=50\%$, is

$S =L\cdot (1-E/100) \cdot(1-D/100)$ $\displaystyle S =L\cdot (1-E/100) \cdot(1-D/100)$

Inserting values and re-organizing:

$D = 100\cdot (1-\frac{\$100}{\$250 (1-50/100) })= 20\%$ $\displaystyle D = 100\cdot (1-\frac{\$100}{\$250 (1-50/100) })= 20\%$

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Example Question #9 : Dsq: Calculating Discounts

A lawn-mower is initially listed at $\$600$ $\displaystyle \$600$. Its price is discounted $10\%$ $\displaystyle 10\%$ off the full price. How much does the customer save relative to the initial list price?

Possible Answers:

$\$60.00$ $\displaystyle \$60.00$

$\$405.00$ $\displaystyle \$405.00$

$\$540.00$ $\displaystyle \$540.00$

$\$270.00$ $\displaystyle \$270.00$

$\$30.00$ $\displaystyle \$30.00$

Correct answer:

$\$60.00$ $\displaystyle \$60.00$

Explanation:

If the initial price is $L=\$600$ $\displaystyle L=\$600$, and the discount is $D=10\%$ $\displaystyle D=10\%$, the savings are

$L\cdot D/100 = \$600\cdot (10/100) = \$60$ $\displaystyle L\cdot D/100 = \$600\cdot (10/100) = \$60$

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Example Question #2202 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at $\displaystyle P$. Its price is discounted $D\%$ $\displaystyle D\%$ off the full price.

In terms of $\displaystyle P$, and $\displaystyle D$, with $\displaystyle D$ expressed in percent, what is the formula for the amount charged, $\displaystyle Q$ at the register?

Possible Answers:

$Q=100\cdot P\cdot (1-D)$ $\displaystyle Q=100\cdot P\cdot (1-D)$

$Q= P\cdot D$ $\displaystyle Q= P\cdot D$

$Q=100\cdot P\cdot D$ $\displaystyle Q=100\cdot P\cdot D$

$Q= P\cdot D/100$ $\displaystyle Q= P\cdot D/100$

$Q=P\cdot(1-D/100)$ $\displaystyle Q=P\cdot(1-D/100)$

Correct answer:

$Q=P\cdot(1-D/100)$ $\displaystyle Q=P\cdot(1-D/100)$

Explanation:

The relationship between the list price, $\displaystyle P$, the discount $\displaystyle D$ in $\%$ $\displaystyle \%$, the price charged at the register is

$Q=P\cdot(1-D/100)$ $\displaystyle Q=P\cdot(1-D/100)$.

The factor of 100 $\displaystyle 100$ represents the conversion from $\%$ $\displaystyle \%$ to a decimal value.

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Example Question #91 : Data Sufficiency Questions

A lawn-mower is initially listed at a full price of $\displaystyle P$. Its the ticket lists a discount of $D\%$ $\displaystyle D\%$ off the full price. The item is placed in a 'extra discount' location where all prices are listed as being discounted $E\%$ $\displaystyle E\%$ off the already discounted ticket price.

In terms of $\displaystyle P$, $\displaystyle D$ and $\displaystyle E$, with discounts $\displaystyle D$ and $\displaystyle E$ expressed in percent, what is the formula for the amount, $\displaystyle Q$, charged at the register.

Possible Answers:

$Q= P\cdot D\cdot E$ $\displaystyle Q= P\cdot D\cdot E$

$Q=100\cdot P\cdot (1-D)\cdot (1-E)$ $\displaystyle Q=100\cdot P\cdot (1-D)\cdot (1-E)$

$Q= P\cdot (D+E)/100$ $\displaystyle Q= P\cdot (D+E)/100$

$Q=P\cdot (D/100)\cdot (E/100)$ $\displaystyle Q=P\cdot (D/100)\cdot (E/100)$

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

Correct answer:

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

Explanation:

The relationship between the original list price and the price charged after two discounts is obtained by applying the formula for a discount serially:

$Q=P\cdot (1-D/100) \cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100) \cdot (1-E/100)$

The factors of 100 $\displaystyle 100$ represent the conversion from $\%$ $\displaystyle \%$ to decimal values.

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Example Question #2211 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at $\displaystyle P$. Its price is discounted $D\%$ $\displaystyle D\%$ off the full price. An employee uses their discount, $E\%$ $\displaystyle E\%$, at the register and is charged $\displaystyle Q$.

In terms of $\displaystyle P$, $\displaystyle Q$ in dollars and $\displaystyle D$ in percent, what is the formula for the employee discount, $\displaystyle E$ in percent?

Possible Answers:

$E=\frac{P}{Q} (1-D/100)$ $\displaystyle E=\frac{P}{Q} (1-D/100)$

$E=100\cdot \left(1-\frac{P}{Q\cdot (1-D/100)}\right)$ $\displaystyle E=100\cdot \left(1-\frac{P}{Q\cdot (1-D/100)}\right)$

$E=100\cdot \frac{P}{Q}\cdot (1-D/100)$ $\displaystyle E=100\cdot \frac{P}{Q}\cdot (1-D/100)$

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

$E=\frac{Q}{P}\cdot (1-D/100)$ $\displaystyle E=\frac{Q}{P}\cdot (1-D/100)$

Correct answer:

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

Explanation:

The relationship between the price charged at the register after two discounts is computed by applying the rule for discounts serially.

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

The factor of 100 $\displaystyle 100$ converts $\displaystyle %$ to decimal values.

Rearranging algebraically and solving for $\displaystyle E$, we obtain

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$ $\displaystyle E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

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Example Question #2212 : Gmat Quantitative Reasoning

A sewing machine is initially listed at $\displaystyle P$. Its price is discounted $\displaystyle D$ off the full price. It fails to sell and is placed in a location where all items are discounted $\displaystyle E$ off the already discounted ticket price. A customer carries it to the register and is charged $\displaystyle Q$.

In terms of $\displaystyle P$,$\displaystyle Q$ and dollars and $\displaystyle E$ in percent, what is the formula for the original discount, $\displaystyle D$ in percent?

Possible Answers:

$D= 100\cdot \left(1-\frac{Q}{P\cdot E/100} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot E/100} \right)$

$D= \left(1+\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= \left(1+\frac{Q}{P\cdot (1-E/100)} \right)$

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

$D= \frac{100\cdot Q}{P\cdot (1-E/100)}$ $\displaystyle D= \frac{100\cdot Q}{P\cdot (1-E/100)}$

$D= 100\cdot \left(1+\frac{Q}{P\cdot (1+E/100)} \right)$ $\displaystyle D= 100\cdot \left(1+\frac{Q}{P\cdot (1+E/100)} \right)$

Correct answer:

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

Explanation:

The relationship between list price $\displaystyle P$, the two serial discounts, $\displaystyle D$ and E and the price charged is found by applying the formula for an individual discount serially:

$Q=P\cdot (1-D/100)\cdot (1-E/100)$ $\displaystyle Q=P\cdot (1-D/100)\cdot (1-E/100)$

The 100 $\displaystyle 100$ represents the conversion from percent to decimal.

Rearranging to solve for $\displaystyle D$ results in

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$ $\displaystyle D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

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Example Question #2213 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at $\displaystyle P$. Its the ticket lists a discount of $\displaystyle D$ off the full price. The item is placed in a 'extra discount' location where all prices are listed as being discounted $\displaystyle E$ off the listed ticket price.

The customer wants to know how much she saved, $\displaystyle S$, in dollars. In terms of $\displaystyle P$, $\displaystyle D$ and $\displaystyle E$, with discounts $\displaystyle D$ and $\displaystyle E$ expressed in percent, what is the formula for dollar savings off the initial list price, $\displaystyle P$?

Possible Answers:

$S=P\cdot (D+E)$ $\displaystyle S=P\cdot (D+E)$

$S=P\cdot \left(\frac{D}{100}+\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(\frac{D}{100}+\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}-\frac{E}{100}\right)$ $\displaystyle S=P\cdot \left(1-\frac{D}{100}-\frac{E}{100}\right)$

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Correct answer:

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Explanation:

The price charged at the register, $\displaystyle Q$ after two discounts is computed using the rule for a single discount applied serially.

$Q=P\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$ $\displaystyle Q=P\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

The 100 represents the conversion from % to decimal.

The savings, $\displaystyle S$, is the difference between the price charged and the list price. So,

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$ $\displaystyle S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

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GMAT Math : Word Problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #4 : Dsq: Calculating Discounts

Example Question #6 : Dsq: Calculating Discounts

Example Question #2 : Discount

Example Question #2201 : Gmat Quantitative Reasoning

Example Question #9 : Dsq: Calculating Discounts

Example Question #2202 : Gmat Quantitative Reasoning

Example Question #91 : Data Sufficiency Questions

Example Question #2211 : Gmat Quantitative Reasoning

Example Question #2212 : Gmat Quantitative Reasoning

Example Question #2213 : Gmat Quantitative Reasoning

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