GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# All 250 files on Sam's hard drive are infected by either a virus or a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55635
All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

10 Oct 2016, 00:42
2
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:33) correct 30% (02:54) wrong based on 199 sessions

### HideShow timer Statistics

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

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3380
Location: India
GPA: 3.12
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

10 Oct 2016, 02:17
Given data
n(Total) = 250
n(only worm) = 125(50% of total)
n(only worm ) = 2.5 * n(both worm and virus)
So,
n(both worn and virus) = 125/2.5 = 50

n(Total) = n(only worm) + n(both worm and virus) + n(only virus)
n(only virus) = 250-125-50 = 75

Hence, the files not infected by worm is n(Only virus) = 75(Option C)
_________________
You've got what it takes, but it will take everything you've got
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4499
Location: India
GPA: 3.5
All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

10 Oct 2016, 05:26
1
2
Bunuel 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

Let no of files infected by Virus be $$" V "$$ and Number of files infected by Worm be $$"W"$$ and files infected by both a virus and a worm be $$"VW"$$
Quote:
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

Total Infected Files = Files Infected only by Virus + Files Infected only by Worm - Files Infected by both Worm & Virus

$$250 = V + W + VW$$
Quote:
If 50% of the files were not infected by a virus

So, We get $$W = 125$$
Quote:
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.

$$W = \frac{5}{2}VW$$
Or, $$125 = \frac{5}{2}VW$$
So, $$VW = 50$$

We know - $$250 = V + W + VW$$
So, 250 = V + 125 + 50
Or, V = 250 - 125 - 50
$$Or, V = 75$$

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 21 Dec 2015
Posts: 25
WE: Account Management (Commercial Banking)
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

02 Nov 2016, 08:52
Abhishek009 - VW = 50
Only W (i.e. W-VW) = 2.5x = 125
Only V (i.e. V-VW) = V-50

V+VW+W = 250
V-50 + 50 + 125 = 250
Hence, V = 125.

Am i missing something?
Intern
Joined: 23 Oct 2014
Posts: 13
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

29 Dec 2016, 03:30
Let
infected by virus and worm= x
so infected only by worm in 2.5x
as 50% is not infected by virus so 50% is infected by worm
so 125 is infected by worm
as 2.5x=125
x= 50 (infected by both virus and worm.
so lastly infected not by worm means infected only by virus
so 250-125(worm only)-(50 both virus and worm)
75 is correct
Retired Moderator
Joined: 04 Aug 2016
Posts: 482
Location: India
GPA: 4
WE: Engineering (Telecommunications)
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

23 Apr 2017, 20:27
Vishvesh88 wrote:
Abhishek009 - VW = 50
Only W (i.e. W-VW) = 2.5x = 125
Only V (i.e. V-VW) = V-50

V+VW+W = 250
V-50 + 50 + 125 = 250
Hence, V = 125.

Am i missing something?

From your solution, we need to find files not affected by a worm - which should be (V-50). You stopped at finding just V (which includes some common files affected by worm).
Manager
Joined: 27 Aug 2014
Posts: 54
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35
GPA: 3.66
WE: Consulting (Consulting)
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

24 Apr 2017, 20:43
Is my method wrong?

V = 125

now we know that

w = 2.5 (v+w)
= 2.5 v + 2.5 w

1.5 w = 2.5 v

3w = 5v

we know that v=125 so w=75.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: All 250 files on Sam's hard drive are infected by either a virus or a  [#permalink]

### Show Tags

08 Mar 2018, 11:44
Bunuel 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

Letting 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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: All 250 files on Sam's hard drive are infected by either a virus or a   [#permalink] 08 Mar 2018, 11:44
Display posts from previous: Sort by