For a certain retail company, a customer can purchase a membership

Question

For a certain retail company, a customer can purchase a membership and receive a percent discount applied to all purchases made from that company for one year, or the customer can make purchases from the company without buying a membership and pay full price for purchases. There are exactly four membership types:

1. The 1% discount for $100.
2. The 2% discount for $200.
3. The 5% discount for $500.
4. The 10% discount for $1,000.

Provided that a customer expected to spend exactly $2,400 on purchases made from the retail company during a one-year period (before any discounts are applied), select for  Most advantageous  and for  Least advantageous  the membership option that would be most financially advantageous and least financially advantageous, respectively, for the customer based on the information provided. Make only two selections, one in each column.

chetan2u · Accepted Answer

The customer spends 2400 on purchases and would save the % on this amount if he has a membership.
1. The 1% discount for $100....He spends 100$ and saves 1% of 2400 or 24.....Loss of 100-24 or 76
2. The 2% discount for $200....He spends 200$ and saves 2% of 2400 or 48.....Loss of 200-48 or 152
3. The 5% discount for $500.....He spends 500$ and saves 5% of 2400 or 120.....Loss of 500-120 or 380
4. The 10% discount for $1,000.....He spends 1000$ and saves 10% of 2400 or 240.....Loss of 1000-240 or 760.

Each membership results in loss and the maximum loss is for $1000 membership.

Most advantageous: No membership
Least advantageous: $1000 membership

AshwinChadha · Answer

Well, what you may be missing is that with each membership tier, there is a cost associated.

So, for instance, for the:
1% membership, the customer must pay $100 to get the membership. 
2% membership the customer must pay $200 
5% membership at $500
10% membership at $1000

This way, if the customer is to shop for $2400
at the discounts they get:
1% - $24 off
2% - $48 off
5% - $120 off
10% - $240 off but they are also spending 
1% - $100 - $24 (that they get as discount)
and si ib so forth meaning that by not getting a membership the customer only spends $2400
whereas if they got the 1% discount membership, they would be spending 
$2400 + (100-24)= $2476
and so on so forth

sayan640 · Answer

MartyMurray   KarishmaB  Can you please explain this question ? How can 'no membership' be most advantageous ? Am I missing something while reading the stem ?

MartyMurray · Answer

For a certain retail company, a customer can purchase a membership and receive a percent discount applied to all purchases made from that company for one year, or the customer can make purchases from the company without buying a membership and pay full price for purchases. There are exactly four membership types:

1. The 1% discount for $100.
2. The 2% discount for $200.
3. The 5% discount for $500.
4. The 10% discount for $1,000.

Provided that a customer expected to spend exactly $2,400 on purchases made from the retail company during a one-year period (before any discounts are applied), select for Most advantageous and for Least advantageous the membership option that would be most financially advantageous and least financially advantageous, respectively, for the customer based on the information provided. Make only two selections, one in each column.

1% of 2,400 is 24.

Scanning the membership percentages and rates, we see that each percent of discount costs $100.

Thus, for each percent of discount purchased, the customer spends $100 and saves $24. So, for example, if the customer were to buy the 5% membership, the customer would spend $500 and save 5 × $24, which we don't have to calculate to see that it's less than $500.

Since, in each case, the $100 spent to save 1% is greater than the $24 saved, the higher the membership type the customer buys, the more money the customer loses.

Thus, the customer would be best off financially buying no membership at all and thus spending $0 on a membership.

For  Most Advantageous  select  No membership .

The customer would be worst off financially with the 10% discount, losing 10 times the difference between 100 and 24.

For  Least advantageous  select  A 10% discount membership .

nisen20 · Answer

only when the amount of savings from discount is greater than 0, we can say it's advantageous.

now we are expected to spend 2400 in a year.

Savings=2400×\frac{x}{100}-100x=24x-100x

in the given membership rules, x has to be a negative number to be advantageous for us.
to wit: as long as those discount rates are positive numbers, we'll lose money in any way. so we'd rather not to be its member.

what if we are expected to spend 24000 in a year.

Savings=24000×\frac{x}{100}-100x=240x-100x

the greater x is, the more savings we will make.

Niv92 · Answer

Hi so 2400 I'll have to spend.

If i take 1% discount offers

Then for every 100 of 2400 I get 24 Rs off. So instead of 2400 for 24 articles worth 100$ im only paying 24*76 that is 1824.

Why a discount will cause a loss to a customer?

pranjalshah · Answer

1. The 1% discount for $100.
2. The 2% discount for $200.
3. The 5% discount for $500.
4. The 10% discount for $1,000.

One has to pay $100/200/500/1000 extra as a 1-year membership cost to be eligible for 1/2/5/10% discount respectively. It does not mean you get 24 off for every 100 you spend.

hp808 · Answer

Comparing the percentages and the cost, you can notice that:
1% of 10,000 is 100
2% of 10,000 is 200
5% of 10,000 is 500
10% of 10,000 is 1,000

Therefore, with a 10,000 spend the discounts are all net neutral.

When spending less, none are worth it, with 10% being the most costly, so the least worth it. If spending over $10,000, it will result in the most savings.

ManishaPrepMinds · Answer

Net Benefit = Discount Savings - Membership Cost

Total spending = $2400 (as given)

1. No membership: 
Net benefit: 0 (no cost, no savings)
 2. 1% membership: 
Net benefit: (1% of 2400), 24 - 100 =  - $76 
 3. 2% membership: 
Net benefit: (2% of 2400), 48 - 200 =  -$152 
 4. 5% membership: 
Net benefit: ( 5% of 2400), 120 - 500 =  -$380 
 5. 10% membership: 
Net benefit: ( 10% of 2400), 240 - 1,000 =  -$760

No membership: $0 (best) Most Advantageous  
 10% membership: -$760 (worst) Least Advantageous

For a certain retail company, a customer can purchase a membership

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Most advantageous	Least advantageous
		No membership
		A 1% discount membership
		A 2% discount membership
		A 5% discount membership
		A 10% discount membership

GMAT Two-part Analysis (TPA) Questions

For a certain retail company, a customer can purchase a membership

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