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18 May 2020, 04:18
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C
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Difficulty:
95%
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Question Stats:
44% (02:38) correct
56%
(02:35)
wrong
based on 183
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The table above shows the research data gathered from a group of rural and urban residents. What is the number of rural residents who own a car?
(1) The number of rural residents in the group is 60% of the number of urban residents in the group.
(2) The difference between the number of urban residents who own a car and the number of rural residents who own a car is one-fifth of the number of rural and urban residents in the group.
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18 May 2020, 07:35
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Let the number of rural residents who own a car = p
STATEMENT 1: The number of rural residents in the group is 60% of the number of urban residents in the group.
Let the number of urban residents = x
Then, number of rural residents = 0.6x
We know that, total number of people = number of people who own a car + number of people who don't own a car = number of urban residents + rural residents
total = (15 + p) + 18 (given in the question) = x + 0.6x
We have two variables x and p but only 1 equation.
Insufficient
STATEMENT 2: The difference between the number of urban residents who own a car and the number of rural residents who own a car is one-fifth of the number of rural and urban residents in the group.
Two equations can be formed here:
1) 15 - p = 1/5(rural + urban) or
2) p-15 = 1/5(rural + urban)
Both will give different answers of p
Insufficient
COMBINING BOTH STATEMENTS:
1) 15 - p = 1/5 (rural + urban)
75 - 5p = rural + urban
75 - 5p = 0.6x + x
75 - 5p = 15 + p + 18 (from statement 1)
42 = 6p
p = 7
2) p - 15 = 1/5 (rural + urban)
5p - 75 = 15 + p + 18
4p = 108
p = 27
We have two values of p.
Let's put it in equation 1 and get the value of x (the number of urban residents)
For p = 7,
15 + p + 18 = 1.6 x
33 + 7 = 1.6x
x = 25
For p = 27,
15 + p + 18 = 1.6 x
33 + 27 = 1.6x
1.6 x = 60
x = 75/2 = 37.5 INVALID
The value of x represents number of people and cannot be a fraction. Therefore, there is only onw unique value of x and that is x = 25 when p = 7
Thus, (C) is sufficient.
STATEMENT 1: The number of rural residents in the group is 60% of the number of urban residents in the group.
Let the number of urban residents = x
Then, number of rural residents = 0.6x
We know that, total number of people = number of people who own a car + number of people who don't own a car = number of urban residents + rural residents
total = (15 + p) + 18 (given in the question) = x + 0.6x
We have two variables x and p but only 1 equation.
Insufficient
STATEMENT 2: The difference between the number of urban residents who own a car and the number of rural residents who own a car is one-fifth of the number of rural and urban residents in the group.
Two equations can be formed here:
1) 15 - p = 1/5(rural + urban) or
2) p-15 = 1/5(rural + urban)
Both will give different answers of p
Insufficient
COMBINING BOTH STATEMENTS:
1) 15 - p = 1/5 (rural + urban)
75 - 5p = rural + urban
75 - 5p = 0.6x + x
75 - 5p = 15 + p + 18 (from statement 1)
42 = 6p
p = 7
2) p - 15 = 1/5 (rural + urban)
5p - 75 = 15 + p + 18
4p = 108
p = 27
We have two values of p.
Let's put it in equation 1 and get the value of x (the number of urban residents)
For p = 7,
15 + p + 18 = 1.6 x
33 + 7 = 1.6x
x = 25
For p = 27,
15 + p + 18 = 1.6 x
33 + 27 = 1.6x
1.6 x = 60
x = 75/2 = 37.5 INVALID
The value of x represents number of people and cannot be a fraction. Therefore, there is only onw unique value of x and that is x = 25 when p = 7
Thus, (C) is sufficient.
Bunuel
25 May 2020, 07:46
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Bunuel
From the 2*2 matrix it is quite clear that either we need the total number of residents or we need total number of residents who own a car.
From1
Total=1.6Y (Not sufficient)
From 2
let the total is T
15-x=T/5
not sufficient
from 1 and 2
15-x=1.6Y/5
15+x+18=1.6Y
two equation and two unknown
C:)
