A toy store regularly sells all stock at a discount of 20

Question

A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent 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

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

BrentGMATPrepNow · Accepted Answer

We can save some time by using the fact that the answer choices are spread out nicely (see video below for more on this).

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

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sudhir18n · Answer

the maximum discount offered is 40% on $ 16 ; 60% of 16 = 9.6
additional 25 % = 3/4*9.6 = 7.2

hope this helps

Fluke: Before discount means = 16 Dollars is the CP of the product( assuming no discount is deducted)

vitamingmat · Answer

16*60/100*75/100 = 7.2

fluke · Answer

I understand the answer explanation. But "before any discount" at the end of the question is confusing to me. Shouldn't it be "after discount(s)". I usually don't stumble upon these tricky wordings. But, this one got me. Please explain.

subhashghosh · Answer

Hi

"costing $16 before any discount?" means that $16 is the Cost Price, i.e., no discount has been applied to it yet.

Regards,
Subhash

akkifreaky · Answer

I dont understand the solution. Can someone elaborate ?

puneetj · Answer

B $7.20

Price after 1st discount (40%) = 60/100 * 16 = 48/5

Price after 2nd discount (25%) = 75/100 * 48/5 = $7.20

icaniwill · Answer

I too stumbled with the question wording initially, but I understood the next time.

Cost price is $16. Lowest possible price is when max discount is applied.

So Discount of 40% first and then 25%.

Final price = 16 * (1-40/100) * (1- 25/100) = 16 * 60/100 * 75/100 = 7.2

Ans B

ScottTargetTestPrep · Answer

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

Answer: B

MikeScarn · Answer

If  time  is an issue for you, the quickest way to solve this would be to use fractions. Do  not  waste time solving out the first price and then adding the additional discount.

Do it all at once, use fractions, and cancel.

16 *  \frac{6}{10}  *  \frac{3}{4}  =  \frac{4*4*6*3}{5*2*4}    Now cancel a 4   =  \frac{4*6*3}{5*2}  =  \frac{72}{10}  =   7.20

Kimberly77 · Answer

Hi  BrentGMATPrepNow , thanks for another great post.
A bit confuse with this part "AFTER the additional 25% discount, customers will pay 75% of the original price." Thought it'll be 25% add to 40% = 65% total discount of $16 ? Where is my thinking going wrong? Thanks for your time in advanced.

BrentGMATPrepNow · Answer

A common misconception is that percent increases and decreases are additive.
For example, many believe that a 25% decrease followed by a 30% decrease results in a new decrease of 55% (which is incorrect).

Here's an example that shows the flaw in that theory: 
If the regular price is $4, then if we decrease the price by 50% to get $2, and if we apply another 50% decrease to get $1. 
So, we go from $4 to $1, which is a 75% net decrease. However, if we ADD the percent decreases (50% and 50%), we incorrectly conclude that there's a 100% net decrease (which would mean the new cost = $0), which is false.

Alternatively, a 40% discount means we must pay 60% of the original cost. 
So, if the original cost is x, then we must pay 0.6x

If we apply an additional 25% discount, then we are paying 75% of the cost. 
So, the new price we must pay = 0.75(0.6x)

Does that help?

Kimberly77 · Answer

Brilliant thanks  BrentGMATPrepNow , make sense now. So we need to apply additional discount to the 1st discounted price rather than adding percentage to it again?

BrentGMATPrepNow · Answer

That's correct.

So, for example, if we apply a third discount of 20%, then we will pay 80% of the already discounted price (which is 0.75(0.6x) dollars)
In other words, the final price after the third discount = 0.8(0.75)(0.6x)

ArnauG · Answer

To find the lowest possible price after all discounts, we need to apply the maximum discount of 40% and then deduct an additional 25% from the discounted price.

The toy store offers a discount of 40%, which means the toy will be sold at 60% of its original price.

60% of $16 = 0.60 * $16 = $9.60

Next, we deduct an additional 25% from the discounted price of $9.60:

25% of $9.60 = 0.25 * $9.60 = $2.40

Subtracting $2.40 from $9.60 gives us the lowest possible price:

$9.60 - $2.40 = $7.20

Therefore, the lowest possible price of the toy after all discounts is $7.20.

The answer is (B) $7.20.

Leon685 · Answer

Lowest possible price means we have to  maximize the discount , so we choose 40 %.
After 1st discount 60 % of 16 $ remain and after 2nd discount 75% of that remaining price remain ( no need to calculate the remaining price after 1st discount )

Lowest price x = 16 * 3/5 * 3/4 = 7.2

BadukMagician · Answer

Base Price: $16

Total Discount : 40% plus 25% translated into 60% remaining from the original $16, and then 75% remaining from the reduced price.
Multiply 6/10 -> 3/5ths by 3/4ths to get 9/20

9/20 * 16 -> 9/5 * 4-> 36/5 -> 7.xx

Answer Choice B

A toy store regularly sells all stock at a discount of 20

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A toy store regularly sells all stock at a discount of 20

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