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Ayayai, iMe, iMine et al

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by kartikshah » Sun Jul 22, 2012 5:55 am
Ayayai electronics is a company manufacturing MP3 players. Ayayai manufactures only two players: iMe and iMine. Either player is assembled using a LCD screen or an OLED screen. Excluding the expensive OLED-iMine model, Ayayai manufactures 21,000 players per month. Every month, Ayayai manufactures 11,000 players with an OLED screen, and 12,000 iMine models. If Ayayai manufactures 8000 LCD iMe models monthly, how many players (of all models) does Ayayai manufacture per month?

1. 24k
2. 25k
3. 26k
4. 27k
5. 28k

Source: Master GMAT

Open to all who'd like to try. OA to be announced shortly ;-)
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by niketdoshi123 » Sun Jul 22, 2012 6:45 am
kartikshah wrote:Ayayai electronics is a company manufacturing MP3 players. Ayayai manufactures only two players: iMe and iMine. Either player is assembled using a LCD screen or an OLED screen. Excluding the expensive OLED-iMine model, Ayayai manufactures 21,000 players per month. Every month, Ayayai manufactures 11,000 players with an OLED screen, and 12,000 iMine models. If Ayayai manufactures 8000 LCD iMe models monthly, how many players (of all models) does Ayayai manufacture per month?

1. 24k
2. 25k
3. 26k
4. 27k
5. 28k
Given "Excluding the expensive OLED-iMine model, Ayayai manufactures 21,000 players per month"
=> 8000+x+y1 = 21000
=> x+y1 = 13000 -----(1)
From the figure below
x+y2 = 11000 -----(2)
and y1+y2 = 12000 -----(3)

Subtracting (2) from (3)
y1-x = 1000 -----(4)

adding (1) and (4)
2y1 = 14000
=> y1 = 7000

=> z1 = 8000+7000 = 15000
=> [spoiler]z = 15000 + 11000 = 26k[/spoiler]
Hence the correct answer is 3
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by eagleeye » Sun Jul 22, 2012 7:07 am
kartikshah wrote:Ayayai electronics is a company manufacturing MP3 players. Ayayai manufactures only two players: iMe and iMine. Either player is assembled using a LCD screen or an OLED screen. Excluding the expensive OLED-iMine model, Ayayai manufactures 21,000 players per month. Every month, Ayayai manufactures 11,000 players with an OLED screen, and 12,000 iMine models. If Ayayai manufactures 8000 LCD iMe models monthly, how many players (of all models) does Ayayai manufacture per month?

1. 24k
2. 25k
3. 26k
4. 27k
5. 28k

Source: Master GMAT

Open to all who'd like to try. OA to be announced shortly ;-)
Typically you could do those questions by using venn diagrams.
However, we could just use the union of two sets here.
We need to find the total. We are given the data regarding OLED screens and Imine models. Let's use those. (I have disregarded the 1000 factor to make the calculations elegant)

Total = OLED + IMine - (Both OLED and iMine) + (Neither OLED, Nor Imine)
Now Neither OLED, Nor iMine = iMe LCD
Then Total= 11 + 12 -(OLED iMine) + (iMe LCDs) = 11+12 - (OLED iMines) + 8 = 31-OLED iMine
We are told that Total - OLED iMine = 21.

Then equating the two, we get 21 + OLED iMine = 31 - OLED iMine
=> OLED Imine = (31-21)/2 = 5.

Hence Total = 21 + OLED iMine = 21 + 5 = 26.

Hence [spoiler]C = 26k[/spoiler] is correct.
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