Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch...

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BTGmoderatorLU: Moderator; Posts: 2575; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Jan 18, 2018 7:24 am

Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

The OA is C.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu Jan 18, 2018 7:24 am

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

by EconomistGMATTutor » Thu Jan 18, 2018 7:46 am

Hello LUANDATO.

Let's take a look at your question.

TV1= x $, TV2= x+200 $, TV3= x+400 $ and TV4= x+600 $.

We now that $$3400=x+\left(x+200\right)+\left(x+400\right)+\left(x+600\right)=4x+1200 $$ $$3400=4x+1200\ \Leftrightarrow\ 4x=2200\ \Leftrightarrow\ x=550.$$ Therefore, the 28 inch Tv cost 750$ and the 30 inch Tv cost 950$.

Hence, if Alan had bought only the 28 inch and 30 inch TVs, he had spent only 750$+950$=1700$.

This is why the correct answer is the option C.

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: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Aug 06, 2019 4:51 pm

BTGmoderatorLU wrote:Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

The OA is C.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

We can let x = the cost of the 26-inch TV; thus, x + 200, x + 400 and x + 600 are the costs of the 28-inch, 30-inch and 32-in TVs, respectively. Since the total cost of the 28-inch and 30-inch TVs is 2x + 600, which is the same as the total cost of the 26-inch and 32-inch TVs, we see that the total cost of the 28-inch and 30-inch TVs must be half of the total cost of $3,400, or $1,700.

Answer: C

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