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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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11 00:00

Difficulty:   95% (hard)

Question Stats: 40% (02:33) correct 60% (02:45) wrong based on 185 sessions

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In a group of 1000 people, each person is either left-handed or right-handed but not both. 80% of the females are left-handed, and 84% of the right-handed people are male. How many people are right-handed?

(1) There are 600 males in the group

(2) There are 180 left-handed males in the group

Kudos for a correct solution.

Source: GMATPrepNow

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Manager  Joined: 15 May 2014
Posts: 62
Re: In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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1
1
Group of 1000 people and each person is either left-handed or right-handed but not both.
80% of the females are left-handed, and 84% of the right-handed people are male.
How many people are right-handed?

male = M
female = F or (1000 - M)
Left-handed = L
Right-handed = R

Statement (1) There are 600 males in the group

Female = 400
Given 84% of the right-handed people are male & 80% of the females are left-handed
16% right handed = 20% of right-handed female
16%*R = 20%*F
16%*R = 20%*400
R = 500

Sufficient

Statement (2) There are 180 left-handed males in the group

84% of the right-handed people are male & 80% of the females are left-handed
L = 180 [male] + 0.8*(1000-M) [female]

84%*R = M-180
R = (M-180)/84%

Total left-handed and right-handed account for the total of 1000
L + R = 1000
{180 + 0.8*(1000-M)} + {(M-180)/84%} = 1000
180 + 800 - 0.8M + {(100M-18000)/84} = 1000
84*980 - 84*(0.8M) + 100M - 18000 = 84000
82320 - 67.2M + 100M - 18000 = 84000
32.8M = 19680
M = 600; same as statement (1)

Sufficient

Senior Manager  B
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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In a group of 1000 people, each person is either left-handed or right-handed but not both. 80% of the females are left-handed, and 84% of the right-handed people are male. How many people are right-handed?

Let 1000-x =#of right hand people
x=# of left hand people
Females left hand=.80x
Males left hand = .20x
Males right hand =.84 (1000-x)

If we can solve for x we can determine # of people who are right handed.

(1) There are 600 males in the group
.84 (1000-x) + .20x = 600
Sufficient

(2) There are 180 left-handed males in the group
.20x=180
Sufficient

Manager  Joined: 15 May 2014
Posts: 62
Re: In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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peachfuzz wrote:
In a group of 1000 people, each person is either left-handed or right-handed but not both. 80% of the females are left-handed, and 84% of the right-handed people are male. How many people are right-handed?

Let 1000-x =#of right hand people
x=# of left hand people
Females left hand=.80x
Males left hand = .20x
Males right hand =.84 (1000-x)

If we can solve for x we can determine # of people who are right handed.

(1) There are 600 males in the group
.84 (1000-x) + .20x = 600
Sufficient

(2) There are 180 left-handed males in the group
.20x=180
Sufficient

peachfuzz

How did you deduce that 20% of male are left-handed?

Moreover, according to your deduction

(1) There are 600 males in the group
.84 (1000-x) + .20x = 600
x = 375

(2) There are 180 left-handed males in the group
.20x=180
x = 900

Statements (1) & (2) give two different values for x.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

In a group of 1000 people, each person is either left-handed or right-handed but not both. 80% of the females are left-handed, and 84% of the right-handed people are male. How many people are right-handed?

(1) There are 600 males in the group

(2) There are 180 left-handed males in the group

From the original condition and the question, we can obtain the below 2by2 table that is common in GMAT math test

Attachment: GC DS Bunuel In a group of 1000 people each(20150917).jpg [ 23.06 KiB | Viewed 1940 times ]

In the above table we have 4 variables (a,b,c,d), 3 equations(a+b+c+d=1000, a=0.8(a+c), b=0.94(a+b)) and thus we need 1 more equation to match the number of variables and equations. Since there is 1 each in 1) and 2), D has high probability of being the answer and it turns out that D actually is the answer.

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
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Joined: 01 Jun 2017
Posts: 19
Re: In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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Bunuel wrote:
In a group of 1000 people, each person is either left-handed or right-handed but not both. 80% of the females are left-handed, and 84% of the right-handed people are male. How many people are right-handed?

(1) There are 600 males in the group

(2) There are 180 left-handed males in the group

Kudos for a correct solution.

Source: GMATPrepNow

All this information is already given in the question. Our aim is to find X

1) 1000-4x/5= 600

we can find x using this information

2) (1000-x)-16x/25= 180

we can find x using this information.

Remember, there is no need to solve these equations.

Ans. D
Attachments WhatsApp Image 2018-08-21 at 9.28.31 PM.jpeg [ 48.81 KiB | Viewed 558 times ]

Intern  B
Joined: 14 Jan 2018
Posts: 49
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q50 V29 GPA: 3.8
WE: Engineering (Manufacturing)
Re: In a group of 1000 people, each person is either left-handed or right-  [#permalink]

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1000=M+F
Left hand -.8F +.16M
Right hand -.2F +.84M

1) 600 =male means female =400 sufficient
2)180 left handed means 820 right hand sufficient

Answer D both are sufficient

Posted from my mobile device Re: In a group of 1000 people, each person is either left-handed or right-   [#permalink] 21 Aug 2018, 09:20
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