Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:17

### 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 but 4 of the counselors at a certain summer camp have a sailing ce

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 27 Oct 2017
Posts: 1234
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

21 Jul 2018, 20:33
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:08) correct 38% (01:57) wrong based on 87 sessions

### HideShow timer Statistics

All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid
certification?
A) 7
B) 9
C) 11
D) 13
E) 15

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

21 Jul 2018, 21:16
gmatbusters wrote:
All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid
certification?
A) 7
B) 9
C) 11
D) 13
E) 15

Total =22
All but 4 means neither =4
So people having one or both certification = 22-4=18

twice as many of the counselors have neither certification as have both certifications..... So both * 2 = neither.......both = 4/2=2
People having only sailing certification = 7-both =7-2=5

So people with first aid certification = 18-5=13

D
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3359
Location: India
GPA: 3.12
All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

21 Jul 2018, 23:39
gmatbusters wrote:
All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid
certification?
A) 7
B) 9
C) 11
D) 13
E) 15

Given data: 7 counselors have a sailing certification | P(Sailing C) = 7

Formula used: P(Total having C) = P(Sailing C) + P(First Aid C) - P(Both)

If there are x counselors at the summer camp, x - 4 have either certification.
For 22 counselors at the summer camp, only 18 have either of the 2 certifications.

Since twice as many counselors have neither certifications as have
both certifications, P(Both) = $$\frac{4}{2} = 2$$ (as 4 have neither certification)

Substituting values, we get $$18 = 7 + F - 2$$ -> $$18 = 5 + F$$ -> $$F = 13$$

Therefore, the total number of counselors that have a first aid certification is 13(Option D)
_________________
You've got what it takes, but it will take everything you've got
Manager
Joined: 12 Mar 2018
Posts: 123
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

02 Dec 2018, 06:53
Could anyone explain "All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both." this statement means? I cannot solve out its structure...
Retired Moderator
Joined: 27 Oct 2017
Posts: 1234
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

02 Dec 2018, 06:57
Hi faltan

All but 4 of the counselors at a certain summer camp have a sailing certification: means that except 4 counselors, all remaining counselors have a sailing certifications.

faltan wrote:
Could anyone explain "All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both." this statement means? I cannot solve out its structure...

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

Updated on: 05 Dec 2018, 00:33
Bunuel wrote:
All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid certification?

A. 7
B. 9
C. 11
D. 13
E. 14

solved using 2x2 matrix IMO D...
Attachments

File comment: 2x2
sailor.xlsx [29.77 KiB]

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 04 Dec 2018, 00:20.
Last edited by Archit3110 on 05 Dec 2018, 00:33, edited 2 times in total.
Intern
Joined: 05 Oct 2018
Posts: 11
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 07:22
I would say D

------Fyes --- Fno --- Total
Syes--2--------5-------7
Sno---11-------4------15
Total--13------9------22
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 07:29
stesmit why have you mentioned 4 under no first aid and no sailing certificate? Its given in question first line as both...

Sent from my iPhone using GMAT Club Forum
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 05 Oct 2018
Posts: 11
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 07:36
All but 4 have a certificate. So 4 don't have any certificate. Correct me if I'm wrong..
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 08:49
stesmit wrote:
All but 4 have a certificate. So 4 don't have any certificate. Correct me if I'm wrong..

I think it means that 4 "both" have certificate..

Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 10 Oct 2018
Posts: 3
Location: India
WE: General Management (Non-Profit and Government)
All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 11:41
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

04 Dec 2018, 11:43
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11

Well even I have marked 11, let's wait for the official answer to get publish..

Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Manager
Joined: 14 Jun 2018
Posts: 222
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

05 Dec 2018, 08:07
Given , neither certificate = 4

"twice as many of the counselors have neither certification as have both certifications". This means people with both the certificate is half of neither = 2.

No of people with sailing = 7
Let the no of people with only sailing = x

22 = 7 +x + 4 - 2
x = 11

Total sailing = 11 + 2 = 13
Attachments

Capture.PNG [ 8.66 KiB | Viewed 568 times ]

Manager
Joined: 14 Jun 2018
Posts: 222
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

05 Dec 2018, 08:09
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11

f = only sailing
total no of people with sailing would be 11+2 (people with both certificate)
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: All but 4 of the counselors at a certain summer camp have a sailing ce  [#permalink]

### Show Tags

05 Dec 2018, 08:11
pandeyashwin wrote:
Yamini27 wrote:
Well, I've marked C. Is it right?
Total= S+F -(both)+ neither
22= 7+f - (4) + 2(4)
22= f+11
f=11

f = only sailing
total no of people with sailing would be 11+2 (people with both certificate)

It's D 13 please check my solution 2x2 matrix

Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: All but 4 of the counselors at a certain summer camp have a sailing ce   [#permalink] 05 Dec 2018, 08:11
Display posts from previous: Sort by