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# How many computers did Michael, a salesman for the computer

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Manager
Joined: 21 Sep 2012
Posts: 195
How many computers did Michael, a salesman for the computer  [#permalink]

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01 Nov 2012, 01:12
2
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Difficulty:

55% (hard)

Question Stats:

67% (02:38) correct 33% (02:47) wrong based on 158 sessions

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How many computers did Michael, a salesman for the computer company Digital Electronics Labs, sell this past year that had more than 4GB of RAM and the Microsoft Windows XP operating system? (Michael sold no computers with exactly 4GB of RAM)

(1) 40% of the 200 total computers that Michael sold had XP and less than 4GB of RAM; these computers represent 80% of the total computers that Michael sold with XP.
(2) 50% of the 200 total computers that Michael sold had XP. Of the computers that Michael sold without XP, half had more than 4GB of RAM while the other half had less than 4GB of RAM.
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: How many computers did Michael, a salesman for the computer  [#permalink]

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01 Nov 2012, 08:02
2
How many computers did Michael, a salesman for the computer company Digital Electronics Labs, sell this past year that had more than 4GB of RAM and the Microsoft Windows XP operating system? (Michael sold no computers with exactly 4GB of RAM)

We need to determine the number of computers sold with XP AND more than 4GB of RAM.

(1) 40% of the 200 total computers that Michael sold had XP and less than 4GB of RAM; these computers represent 80% of the total computers that Michael sold with XP.

0.4*200=80 computers had XP and less than 4GB of RAM. Since these 80 computers represent 80% of the computers with XP, then Michael sold 100 computers with XP. Since, we already know that 80 computers had XP and less than 4GB of RAM, then the rest of the computers with XP had more than 4GB of RAM, thus 100-80=20 computers had XP and more than 4GB of RAM. Sufficient.

(2) 50% of the 200 total computers that Michael sold had XP. Of the computers that Michael sold without XP, half had more than 4GB of RAM while the other half had less than 4GB of RAM

0.5*200=100 computers had XP and 100 did not. The second part of the statement gives info only about the computers without XP, thus it's basically useless for us. Not sufficient.

Hope it's clear.
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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: How many computers did Michael, a salesman for the computer  [#permalink]

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23 Dec 2017, 08:03
nelz007 wrote:
How many computers did Michael, a salesman for the computer company Digital Electronics Labs, sell this past year that had more than 4GB of RAM and the Microsoft Windows XP operating system? (Michael sold no computers with exactly 4GB of RAM)

(1) 40% of the 200 total computers that Michael sold had XP and less than 4GB of RAM; these computers represent 80% of the total computers that Michael sold with XP.
(2) 50% of the 200 total computers that Michael sold had XP. Of the computers that Michael sold without XP, half had more than 4GB of RAM while the other half had less than 4GB of RAM.

so we are looking for COMPUTERS sold that had>4GB RAM and XP OS..

(1) 40% of the 200 total computers that Michael sold had XP and less than 4GB of RAM; these computers represent 80% of the total computers that Michael sold with XP.
Total computers sold = 200,
40% of it so $$\frac{40}{100}*200=80$$ had <4GB and XP os
80% of Computers sold with XP os = 80, so computers sold with XP =$$80*\frac{100}{80}=100$$
so BOTH XP and >4GB = 100-80=20
suff

(2) 50% of the 200 total computers that Michael sold had XP. Of the computers that Michael sold without XP, half had more than 4GB of RAM while the other half had less than 4GB of RAM.
clearly insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: How many computers did Michael, a salesman for the computer   [#permalink] 23 Dec 2017, 08:03
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