A computer store originally bought 1,000 modems at a total..

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Dec 30, 2017 6:10 am

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)

The OA is A.

I'm really confused with this PS question. Experts, any suggestion? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sat Dec 30, 2017 6:10 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sat Dec 30, 2017 6:23 am

Hello LUANDATO.

Let's take a look at your question.

If the store bought 1,000 modems for d dollars, it implies that the individual price is given by $$p=\frac{d}{1,000}\ \text{dollars}.$$ Since each modem was sold for 25 percent more than its original cost, then the price of each modem sold was $$p+25\%\cdot p=125\%\cdot p=\frac{125}{100}\cdot p=\frac{5}{4}\cdot p=\frac{5}{4}\cdot\frac{d}{1,000}=\frac{5d}{4,000}\ =\frac{d}{800}\ \text{dollars}.$$ This is why the correct answer is the option [spoiler]A=d/800[/spoiler].

I hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Aug 25, 2019 5:47 pm

BTGmoderatorLU wrote: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)

The OA is A.

I'm really confused with this PS question. Experts, any suggestion? Thanks in advance.

The cost of each modem is d/1000 dollars. SInce each modem is sold for 25 percent more than its original cost, the price of a modem is:

1.25 x d/1000 = 125/100 x d/1000 = 1/100 x d/8 = d/800 dollars

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 26, 2019 5:19 am

BTGmoderatorLU wrote: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)

Given: d = total cost of 1000 modems
So, d/1000 = cost of ONE modem

After the 25% increase, the retail price per modem = (d/1000) + 25% of (d/1000)
= (d/1000) + 0.25 (d/1000)
= d/1000 + 0.25d/1000
= 1.25d/1000
Check answer choices . . . . not there!
We need to find an equivalent form of 1.25d/1000 that's among the answer choices.

Take: 1.25d/1000
Divide top and bottom by 1.25 to get: d/800

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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