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07 Oct 2021, 08:15
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B
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70% (02:21) correct
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A group of cousins has 5 females aged x years, 24 years, 20 years, 18 years and 16 years respectively, and 3 males aged y years, 30 years and 26 years respectively. If the range of the ages of all the people in the group is 18 years, the range of ages of the females in the group is 12 years and the range of the ages of the males in the group is 17 years, what is the value of y?
A. 12
B. 13
C. 28
D. 43
E. Cannot Be Determined
A. 12
B. 13
C. 28
D. 43
E. Cannot Be Determined
07 Oct 2021, 12:40
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Bunuel
Females : 16,18,20,24 and x
Males : 26,30 and Y
Range of males = 17 => Y can be 13 or 43
Range of females = 12 => x can be 12 or 28
Range of group = 18 :
=> if x =12 , then maximum age possible is 30 => y =13
Also , if x = 28, maximum age possible is 16+18=34 => y =13
In both cases y=13
Hence B
08 Oct 2021, 14:49
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Age of female cousins = x, 24, 20, 18, 16
Range of age of female = 12
Hence possible values of x:
if 16 is lowest => 16+12 = 28
if x is lowest i.e. 24 is highest=> 24 - 12 = 12
Hence, age of female cousins can be: 28, 24, 20, 18, 16 or 24, 20, 18, 16, 12
Age of male cousins = y, 30, 26
Range of age of male = 17
Hence possible values of y :
if 26 is lowest => 26+17 = 43
if y is lowest i.e. 30 is highest=> 30 - 17 = 13
Hence, age of female cousins can be: 43, 30, 26 or 30, 26, 13
Possible value of ranges of all people in group:
(x=28 , y =43) 43 - 16 = 27
(x=12 , y =43) 43 - 12 = 31
(x=28 , y =13) 30 - 13 = 17
(x=12 , y =13)30 - 12 = 18
It is given that overall range = 18
Hence the value of x= 12 and y = 13
Ans: B
Range of age of female = 12
Hence possible values of x:
if 16 is lowest => 16+12 = 28
if x is lowest i.e. 24 is highest=> 24 - 12 = 12
Hence, age of female cousins can be: 28, 24, 20, 18, 16 or 24, 20, 18, 16, 12
Age of male cousins = y, 30, 26
Range of age of male = 17
Hence possible values of y :
if 26 is lowest => 26+17 = 43
if y is lowest i.e. 30 is highest=> 30 - 17 = 13
Hence, age of female cousins can be: 43, 30, 26 or 30, 26, 13
Possible value of ranges of all people in group:
(x=28 , y =43) 43 - 16 = 27
(x=12 , y =43) 43 - 12 = 31
(x=28 , y =13) 30 - 13 = 17
(x=12 , y =13)30 - 12 = 18
It is given that overall range = 18
Hence the value of x= 12 and y = 13
Ans: B
