Modems

[DanaJ]

Source: Veritas Prep

A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?

A) d/800
B) 5d/1000
C) 125d
D) d/1000 + 25
E) 125/1000d

[David@VeritasPrep]

Here is the official Veritas Prep explanation:

Correct answer: (A)

Solution: 1,000 modems cost d dollars, so each modem cost d/1000 dollars. Since the selling price is 25% above the cost, the selling price for each modem is 1.25(d/1000)=5/4(d/1000)=5d/4000=d/800.

[Rahul@gurome]

A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?

• A) d/800
  B) 5d/1000
  C) 125d
  D) d/1000 + 25
  E) 125/1000d

Total original cost of 1000 modems = $ d
Original cost of one modem = $ (d/1000)

Individual selling price of each modem = $ (d/1000) + 25% percent of $ (d/1000) = $ (d/1000)*(1 + 25/100) = $ (d/1000)*(1 + 1/4) = $ (d/1000)*(5/4) = $ (d/800)

The correct answer is A.

[GMATGuruNY]

Source: Veritas Prep

A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?

A) d/800
B) 5d/1000
C) 125d
D) d/1000 + 25
E) 125/1000d

Since there is a variable in the answer choices, we can plug in our own value for d.

Let d= 4000.
Cost per modem = 4000/1000 = 4.
Since 25% of 4 = 1, cost increased by 25% = 4+1 = 5. This is our target answer.

Now we plug d=4000 into all the answer choices to see which yields our target of 5.

Only answer choice A works:
d/800 = 4000/800 = 5.

The correct answer is A.

[Yes.WeCan]

My way
25 percent more, so d is modified by 1.25. This could be written as 1.25d/1000 or d/800.

[Zheni]

The above explanations are certainly correct.

Here is the official Veritas Prep explanation:

Correct answer: (A)

Solution: 1,000 modems cost d dollars, so each modem cost d/1000 dollars. Since the selling price is 25% above the cost, the selling price for each modem is 1.25(d/1000)=5/4(d/1000)=5d/4000=d/800.

Hi! Do we know that all 1000 modems were bought at an equal price each? Isn't that supposed to be mentioned in the problem in order to solve it?Thanks!

[David@VeritasPrep]

Certainly that is important, thanks for mentioning it. I will make sure it gets added.

As a practical matter this is what I always tell my students: For Data Sufficiency of course it is an option that you do not have enough information. BUT FOR PROBLEM SOLVING it is not an option that you do not have enough information. So, for example, if the ONLY way to solve is to assume that you have similar triangles, for example, then don't even worry about proving it to yourself because you must get an answer. So if this happens on test day and the only way to solve is for the modems to each be an equal price then just assume they are...for problem solving. Of course, not for data sufficiency.

[Spidy001]

Answer is A.

[prateek_guy2004]

This is a great answer to put in values...

Let d be 5000. Total cost d/1000 = 5000/1000 = 5

It is sold after an addition of 25%. So 5* 25/100 = 1.25

After adding 5 + 1.25 = 6.25 This is out target now choose from every answer choises..

Only Answer A Yields 6.25

[MBA.Aspirant]

d/800

[shingik]

1) Determine the cost of each modem = d/1000
2) Determine selling price of each modem = d/1000 * 125% or d/1000 * 125/100
3) Check to see if this is an answer choice---if not simplify further (as you need to do in this case)
4) After simplifying you get d/800 which is A

Step three ---I am not sure if GMAT answers are always in their simplest form but I would not put anything past the GMAC

[prashant misra]

oh this was a very easy question but i seem to have done this wrong by picking numbers and did not try for other values.can anyone tell me whether i was right or wrong while substituting values.i supposed d to be 100000 and 1000 items so individual price is 100 but sold for 25% above then each item costs 125 while putting these values i got answer option D but right answer was B when i checked

[LalaB]

Source: Veritas Prep

A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?

A) d/800
B) 5d/1000
C) 125d
D) d/1000 + 25
E) 125/1000d

1000 modems-d$
1 modem -X$
X=d/1000

since the price is 25% more than the original cost,we just multipy 1.25*d/1000=d/800

[vaibhavgupta]

Source: Veritas Prep

A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?

A) d/800
B) 5d/1000
C) 125d
D) d/1000 + 25
E) 125/1000d

d/1000 = original cost
d/1000*5/4= d/800

Hence A

[immaculatesahai]

Cost price of each modem= d/1000

Selling price of each modem= 1.25d/1000
= d/800

A wins.