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.

(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:

\(\displaystyle \frac{x-1.5x}{1.5x}=\frac{-.5x}{1.5x}=-\frac{1}{3}\)

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 \(\displaystyle \frac{2}{3}y\).

The percentage of discount is:

\(\displaystyle \frac{\frac{2}{3}y-y}{y}=\frac{-\frac{1}{3}y}{y}=-\frac{1}{3}\)

Statement (2) is sufficient.

Each Statement ALONE is sufficient.

(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.

\(\displaystyle \frac{.5x+.5x+x+x+x}{5}=50000\)

\(\displaystyle 4x=250,000\)

\(\displaystyle x=\frac{250000}{4}=62500\)

Statement(2) Alone is sufficient.

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:

\(\displaystyle \frac{25}{100}\times400=100\)

Jane saved $100 by using the coupon.

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

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

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

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

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

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

Substituting values this is

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

 \(\displaystyle D=1-100\cdot S/P\)

or  \(\displaystyle 1-0.675\cdot 100 = 32.5\%\)

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

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

Inserting values and re-organizing:

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

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

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

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

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

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

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

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

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