Problem Solving

BTGmoderatorLU wrote:A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?

A. $5.60
B. $7.20
C. $8.80
D. $9.60
E. $15.20

The OA is B.

I get the solution to this PS question as follows,

We will get the Lowest price with maximum discount

So the discount in $16 will be 40% - giving $9.60

Then another discount of 25% on $9.60 to give $7.20. Option B.

Please, can anyone explain another way to solve this question? Thanks!

Your solution is great, but you can save some time by using the fact that the answer choices are spread out nicely.

To get the LOWEST possible price (after the two discounts), we must apply the biggest discount (which is a 40% discount)

So, AFTER the 40% discount, customers will pay 60% of the original price.
60% of $16 = (0.6)($16) = $9.60
So, the discounted price is $9.60

From here, we need to apply an additional 25% discount on $9.60
HOWEVER, before we do this, we should recognize that the answer choices are quite spread apart.
So, we can be somewhat aggressive with our estimation.

AFTER the additional 25% discount, customers will pay 75% of the original price.
So, we need to calculate 75% of $9.60.......yuck!
Let's find 75% of $10.00 instead (close enough, right?)

75% of $10.00 = $7.50

So, if 75% of $10.00 is $7.50, then 75% of $9.60 will be a bit less than $7.50
Only answer choice B works.

Answer: B

Cheers,
Brent

Hi All,

We're told that a toy store regularly sells all stock at a discount of 20% to 40% and an additional 25% were deducted from the discounted price during a special sale. We're asked for the lowest possible price of a toy costing $16 before any discount.

When dealing with these types of 'multiple percent reductions', the basic math involved is almost always multiplication - and since we're multiplying values, we can do that math in ANY order. Thus, we can multiply by 40% and then by 25% OR by 25% and then by 40%. You might find it easier to use the second option...

$16 original price
25% off of $16 = 1/4 of $16 = $4

$16 - $4 = $12
40% off of $12 = (.4)($12) = $4.80
Final price = $12 = $4.80 = $7.20

Final Answer: B

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

BTGmoderatorLU wrote:A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?

A. $5.60
B. $7.20
C. $8.80
D. $9.60
E. $15.20

The lowest possible price of a $16 toy after discounts is 16 x 0.6 x 0.75 = $7.20.

Answer: B