In a group of 1000 people, each person is either left-handed or right-

Question

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

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Source: GMATPrepNow

sudh · Answer

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   + 0.8*(1000-M)

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

Answer D

peachfuzz · Answer

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

Answer: D

sudh · Answer

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.

MathRevolution · Answer

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 5283 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.

gupta335 · Answer

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

Loser94 · Answer

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

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bumpbot · Answer

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