All 250 files on Sam's hard drive are infected

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

All 250 files on Sam's hard drive are infected

by BTGmoderatorDC » Sat Feb 24, 2018 3:14 am

All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

Can some experts show me how to solve this?

OA C

Quote

Source: Beat The GMAT — Problem Solving | Sat Feb 24, 2018 3:14 am

mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 am; Location: London, UK; Thanked: 2 times; Followed by:4 members; GMAT Score:770

by mbawisdom » Mon Mar 05, 2018 5:37 pm

lheiannie07 wrote:All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

Can some experts show me how to solve this?

OA C

I would set up the following diagram and equations, then solve as shown:

Quote

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Thu Mar 08, 2018 4:36 pm

lheiannie07 wrote:All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

etting b = the number of files infected by both a virus and a worm, we can create the equation:

Total = worm only + virus only + both + neither

250 = 2.5b + [0.5(250) - b] + b + 0

250 = 2.5b + 125

125 = 2.5b

50 = b

The files that were not infected by a worm were those that were infected by a virus only, so there were 0.5(250) - 50 = 125 - 50 = 75 files infected by virus only.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
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