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A group of cousins has 5 females aged x years, 24 years, 20 years, 18

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A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 30 Jul 2019, 09:12
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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
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 30 Jul 2019, 09:57
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With all the information that is provided to us, we can take 30 to be the largest age in males. Thus, in order to get the range as 17 the value of y should be the least as 30-26=4 which cannot be true. So 30-y=17.
Hence, y=13.
The answer is B.
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 01 Aug 2019, 07:56
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y= 13
Because if, for men, the lowest value is 13 and the highest 30, we do get a range of 30-13=17. However, if for the females 16 is the smallest value then the highest must be 28 because 28-16=12. Then, 30 of the males is still the highest value and 16 of the females the lowest 30-16=14 which does not match with the 18 from the excercise. If, instead, 24 is the highest value for the female, then 12 must be the smallest as 24-12=12. Then, 30 of then men and 12 of the female would be the overall range which equals 30-12=18 which matches
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 05 Aug 2019, 10:04
Aprajita760 wrote:
With all the information that is provided to us, we can take 30 to be the largest age in males. Thus, in order to get the range as 17 the value of y should be the least as 30-26=4 which cannot be true. So 30-y=17.
Hence, y=13.
The answer is B.


Hi! Can you please explain how did you get this i.e. the male should be 30?
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 05 Aug 2019, 10:37
kunalbean wrote:
Aprajita760 wrote:
With all the information that is provided to us, we can take 30 to be the largest age in males. Thus, in order to get the range as 17 the value of y should be the least as 30-26=4 which cannot be true. So 30-y=17.
Hence, y=13.
The answer is B.


Hi! Can you please explain how did you get this i.e. the male should be 30?

30 is given in the question. We then assume that it will be the highest value and use it as such for our calculations
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 24 May 2020, 18:53
mangamma wrote:
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


For option A. 12- If we take y=12, this implies that the range of the ages of all people in the group can be 18 years as the set contains the age "30". However, if we take y=12, the range of the ages of the males in the group cannot be "17" as the set for males' ages will be (12, 26, 30). So, we reject option A

For option B. 13- If we take y=13, this implies that the range of the males in the group can be 17 as the set for males' ages will be (13, 26, 30). Also, if we take y=13, the range of the ages of all people in the group can be 18 years if x becomes 31 as the set will be (13, 16, 18, 20, 24, 26, 30, 31). Thus, y=13 satisfies both the conditions.

I didn't go further for other options.
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18  [#permalink]

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New post 29 Jun 2020, 01:34
mangamma wrote:
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


Took slightly more than 3 mins :
Given: Range of total = 18, range of female = 12 and range of men = 12.

Using respective ranges,
Possible values of x = x,16,18,20,24,x = 12 or 28
Possible values of y = y,26,30,y = 13 or 39

30-12 = 18 - Yes
30 -16 = 12 (not)= 18(given range) - No
39 - 12 = 27 (not)= 18
39-16 = 23 (not)= 18
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Re: A group of cousins has 5 females aged x years, 24 years, 20 years, 18   [#permalink] 29 Jun 2020, 01:34

A group of cousins has 5 females aged x years, 24 years, 20 years, 18

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