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03 Jan 2025, 02:20
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carcass
It is simply a mixture problem. Men's concentration last year is 3/5. We don't know men's concentration in new members this year. That will decide the overall concentration and whether it is greater than 3/5.
(1) More than half of the new members are male.
This means C1 can be anywhere as shown in the diagram and accordingly Cavg will be less than / equal to / more than 3/5.
If C1 is very close to 1/2 as shown, Cavg will be less than 3/5. If C1 is more than 3/5, Cavg will be more than 3/5.
This alone is not sufficient.
Attachment:
Screenshot 2025-01-03 at 2.41.47 PM.png [ 40.75 KiB | Viewed 520 times ]
(2) The number of members of the club this year is 6/5 the number of members last year.
Gives us the weights that last year : new members = 5 : 1 but not C1. We cannot find Cavg without C1.
Using both also, we don't have C1. The same diagram is applicable.
Answer (E)
Check these video on weighted averages and mixtures:
https://www.youtube.com/watch?v=_GOAU7moZ2Q
https://www.youtube.com/watch?v=VdBl9Hw0HBg
and these posts:
https://anaprep.com/arithmetic-weighted-averages/
https://anaprep.com/arithmetic-mixtures/
29 May 2026, 04:09
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Can we solve this intuitively?
Last year’s percentage of males is 60%
if the % male for this year has to be greater than 60%, then the # of males from the new members’ lot must be >60%. If they are less than 60%, then the % male for this year will be pulled to less than 60%
s1 says that more than 50% of new members are male, so the # of males could be 51% of new members, and the overall % can be less than 60 % or the # of males from new members could be 80%, and this year’s % males could be greater than 60%
statement 2 says 1/5 additional members are added. This doesn’t help much.
statement 1 and 2 together give us the 50% of 1/5 (new members) are males, the total number of males could be >50 % this year
they can either be <60% or they can be >60%, so we can’t be sure. Hence E.
Last year’s percentage of males is 60%
if the % male for this year has to be greater than 60%, then the # of males from the new members’ lot must be >60%. If they are less than 60%, then the % male for this year will be pulled to less than 60%
s1 says that more than 50% of new members are male, so the # of males could be 51% of new members, and the overall % can be less than 60 % or the # of males from new members could be 80%, and this year’s % males could be greater than 60%
statement 2 says 1/5 additional members are added. This doesn’t help much.
statement 1 and 2 together give us the 50% of 1/5 (new members) are males, the total number of males could be >50 % this year
they can either be <60% or they can be >60%, so we can’t be sure. Hence E.
22 Aug 2026, 11:37
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The original ratio is 3/5 male (60%)
The question is asking if the group we add will increase that fraction.
I) Over half of the new members are male. Over half means anywhere between 50% and 100%.
If the percent is 51% then no.
If the percent is 100% then yes.
Being both yes and no could be true but we can't know. N.S.
II) Knowing how much larger the club is doesn't help us determine the ratio of males to females of the new group added. N.S.
I+II) We still don't know if the males in the group make up more than 60% of the members. N.S.
The question is asking if the group we add will increase that fraction.
I) Over half of the new members are male. Over half means anywhere between 50% and 100%.
If the percent is 51% then no.
If the percent is 100% then yes.
Being both yes and no could be true but we can't know. N.S.
II) Knowing how much larger the club is doesn't help us determine the ratio of males to females of the new group added. N.S.
I+II) We still don't know if the males in the group make up more than 60% of the members. N.S.
Carcass
chetan2u
Hi.. For statement 1, how did you intuitively figure out that if the new ratio is between 1/2 and 3/5, then the net ratio will be less than 3/5. Are you simply saying, to have net average percentage(old case +new case) more than 60, the new percentage has to be more than 60? Am I thinking it right? Thank you
Hi.. For statement 1, how did you intuitively figure out that if the new ratio is between 1/2 and 3/5, then the net ratio will be less than 3/5. Are you simply saying, to have net average percentage(old case +new case) more than 60, the new percentage has to be more than 60? Am I thinking it right? Thank you
chetan2u
