If an item that originally sold for z dollars was marked up

Question

If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?

A. (10,000z + 100z(x – y) – xyz)/10,000

B. (10,000z + 100z(y – x) – xyz)/10,000

C. (100z(x – y) – xyz)/10000

D. (100z(y – x) – xyz)/10000

E. 10000 /(x – y)

Actually figured it out as I was typing it in by picking the following numbers:

z=$10, x=20%, y=50% 1.2z*.5= 6

Final price should be $6.

Any other ways?

SaraLotfy · Accepted Answer

Solving algebraically:

Z * (1+(x/100)) * (1-(y/100))
Z* (100+x/100) * (100-y/100)
 (100Z + ZX)/100 * (100-y/100)
  /10,000 
  / 10,000

Choice A

Sumithra · Answer

z dollars was marked up by x percent:

z+(z*x/100)=(100z+zx)/100

This discounted by y%:

{(100z+zx)/100}-{(100z+zx)/100 * (y/100)}

{(100z+zx)/100}-{100yz+xyz/100^2}
 
Solving I get A

ak_idc · Answer

Matt, that is the easier way. Other way is to directly multiply and take the common factors out..but that seems to be time taking in this problem. As you know, whenever its possible, solving by substituting the numbers is the best way to solve problems when we are under time pressure :wink:

Priyah · Answer

If mark-up is x%, new price will be (100+x)/100 times old price. Discounted by y% means new price will be (100-y)/100 times old price. So we have final price =z(100+x)(100-y)/10000 and the terms rearranged give A.

Sumithra · Answer

To me, for some questions, picking nos. and applying those in each ans choice and finding the right choice seems tedious. I guess it depends on the method of practice and the strength of the individual, as I see in many threads, and of course, the time pressure.

monirjewel · Answer

Assume Z=100, x=10, y=10. So final price is 99. Now put these value each option. Only option A will give right answer.

JeffTargetTestPrep · Answer

We are given that an item that originally sold for z dollars was marked up by x percent and then discounted by y percent; thus, the final price of the item is:
 
z(1 + x/100)(1 - y/100)
 
z  
 
z[(10,000 + 100x - 100y - xy)/10,000
 
[(10,000z + 100xz - 100yz - xyz)/10,000
 
[(10,000z + 100z(x - y) - xyz)/10,000
 
Answer: A

sahilvijay · Answer

Ans is A

x% rise and y percent fall
net change formula is (a + b + ab/100 )% if rise +ve and if fall -ve
so x is + and y is -
net change will be x-y - xy/100
and this is % of z
so net change ie rise => z( x-y-xy/100)1/100
and last price was z
so new one is z+ z( x-y - xy/100)1/100
so becomes A

spetznaz · Answer

Use the rule for consecutive percentage changes. If there are consecutive %changes a and b. Then a+b+(ab/100) % is the net change. Substitute for x and y and solve. The answer is option A.

GMATGuruNY · Answer

Let z=1, x=0 and y=100.
Since the final discount = 100%, the final price = 0.

Now plug z=1, x=0 and y=100 into the five numerators to see which yields a final price of 0.
Since xyz = 0, this term can be ignored.
Only the numerator in A yields a value of 0:
10,000z + 100z(x-y) = 10,000*1 + 100*1*(0-100) = 10,000 - 10,000 = 0.

A

Riri15 · Answer

Isn't markup taken on cost price and not selling price? How do we get clarity as to x% of what is taken?

Bunuel · Answer

In the context of this question, "marked up" refers to increasing the original price by a specific percentage.

ManishaPrepMinds · Answer

Growth factors: 
 After markup (x%):  z × (1 + x/100)
 After discount  (y%): × (1 - y/100)
 Final price  = z × (1 + x/100) × (1 - y/100)
= z × (1 + x/100) × (1 - y/100)
= z × (100 + x)/100 × (100 - y)/100
= z(100 + x)(100 - y)/10000
=  /10000

Answer: A

ManishaPrepMinds · Answer

clarification about markup/discount:
 Standard practice: 
Markup (x%) is calculated on COST price
Discount (y%) is calculated on MARKED UP price (selling price)
 In questions: 
If not specified, assume markup is on original/cost price
Discount is ALWAYS on selling price

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If an item that originally sold for z dollars was marked up

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If an item that originally sold for z dollars was marked up

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards