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# Last year 3/5 of the members of a certain club were males.

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Last year 3/5 of the members of a certain club were males. [#permalink]

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27 Jul 2017, 08:17
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Last year $$\frac{3}{5}$$ of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?

(1) More than half of the new members are male.

(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year.
[Reveal] Spoiler: OA

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Last year 3/5 of the members of a certain club were males. [#permalink]

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27 Jul 2017, 08:55
2
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Expert's post
carcass wrote:
Last year $$\frac{3}{5}$$ of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?

(1) More than half of the new members are male.

(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year.

Hi..
total =T
Male = M
so $$\frac{3}{5}*T=M$$
new member = x..
Ratio of M will be GREATER if the male in new group >$$\frac{3}{5}*x$$ otherwise No

lets see the statements
(1) More than half of the new members are male.
as can be seen slightly more than the 3/5 of new members should be male..
here if new males are between $$\frac{1}{2}..&..\frac{3}{5}$$ including ans is NO
if > $$\frac{3}{5}$$, ans is YES
Insuff

(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year.
Nothing about the number of males in new addition
Insuff

combined..
nothing new

E
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Posts: 260
Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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02 Aug 2017, 08:48
1
KUDOS
this is hard
suppose there are 50 member, 30 of them are male.

1. not sufficient
2. not sufficient

combined
total number is 60
new member is 10
more than half is men, so, there are more than 6 is men
if 6 are men
we have 30+6=36
fraction of men is 36/60=3/5
if 7 are men
we have 30+7=37 men

fraction is 37/60>3/5

so not sufficient.

E
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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07 Aug 2017, 07:09
this question can very well explained by considering it to be like adding 2 solutions, a solution with 3/5 male concentration and another one with 1/2 male concentration
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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12 Aug 2017, 13:06
My 2 cents:
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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14 Aug 2017, 05:18
carcass wrote:
Last year $$\frac{3}{5}$$ of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?

Last Year
Total Members -> T
Male Members -> $$\frac{3}{5}$$*T => In other words M : T = 3 : 5

This Year
Total Members -> T + N
New Male Members -> m

Is $$\frac{(M + m)}{(T+N)}$$ > $$\frac{3}{5}$$ ?

Quote:
(1) More than half of the new members are male.
(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year.

1) m > 0.5N
N = 10, m = 6,7,8..
Ratio will change according to the number of males added
=> Let's say T = 10 => M = 6
and N = 10 => m = 6,7,8..
If m = 6
=> $$\frac{(M + m)}{(T+N)}$$ = $$\frac{3}{5}$$ (Ratio is the same)

If m = 7
=> $$\frac{(M + m)}{(T+N)}$$ = $$\frac{7}{10}$$ (Ratio is greater)

Hence, Insufficient.

2) T + N = 1.2T
=> N = 0.2T
We don't know the value of N or T. Plus, we cannot derive the values of M and m.
Insufficient.

1+2)
We gain no additional information, so we still don't know the value of N,T,M or m.
Insufficient.

E is the answer.
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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15 Aug 2017, 20:38
3
KUDOS
Say last year total number of members be = Old
Given, # of males = $$3Old/5$$

This year, new members are added, say $$New$$ and let the number of males within the new group be $$x$$.

Question stem asks, if $$(x+3Old/5)/(New+Old) > \frac{3}{5}$$
Simplifying this, we get, if $$x > \frac{3}{5}New$$ or $$x > 0.6 New$$

Stmt1: Gives us $$x>0.5 New$$ but we are not sure if $$x$$ is greater than $$0.6 New$$. Hence this statement is insufficient.
Stmt2: Gives $$New = \frac{1}{5} Old$$. This gives us nothing about $$x$$ and $$New$$ relationship. Hence it is insufficient as well.

Combining 1 and 2, we get nothing fresh about the relationship of x and new members 'New' and hence E is the answer.

Hope this helps.
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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15 Aug 2017, 22:16
The answer is E for sure

Explanation : let there be 100 members in the club at starting
So as given 3/5 of them are male
So 60 would be male

Now new members get in and no of males in the new members is more than 1/2

Now 2 bf statement says that now the no of members after addition of new members is 6/5 of the earlier
Earlier there were 100 members
Now 6/5 *100 = 120
So the no of new members who have joined is

120-100=20

Given more than half are male so no of males >10

It can be 11,12,13 ......20

So
Now if the no of males are 11 then this time males are less in fraction
If 12 men are there then fraction of males would remain the same
If the no is 13 or greater than 13 the fraction will we greater this time

So we don't the actual no of males in the new members

So the answers is E

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Last year 3/5 of the members of a certain club were males. [#permalink]

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13 Dec 2017, 20:52
Honestly, i found this problem to be confusing because of 2) The number of members of the club this year is 3/5 the number of members last year.
Why? Because it contradicts this statement: "This year the members of the club include all the members from last year plus some new members".
How can it be? If all members of the last year are still in the club and we have an addition of new members, why the then the total number of members is less than the total number of last year? How it could be?

I would appreciate your comment chetan2u
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Joined: 02 Sep 2009
Posts: 44656
Last year 3/5 of the members of a certain club were males. [#permalink]

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13 Dec 2017, 21:16
Erjan_S wrote:
Honestly, i found this problem to be confusing because of 2) The number of members of the club this year is 3/5 the number of members last year.
Why? Because it contradicts this statement: "This year the members of the club include all the members from last year plus some new members".
How can it be? If all members of the last year are still in the club and we have an addition of new members, why the then the total number of members is less than the total number of last year? How it could be?

I would appreciate your comment chetan2u

(2) says: The number of members of the club this year is 6/5 the number of members last year, NOT 3/5.
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Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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13 Dec 2017, 21:41
Bunuel wrote:
Erjan_S wrote:
Honestly, i found this problem to be confusing because of 2) The number of members of the club this year is 3/5 the number of members last year.
Why? Because it contradicts this statement: "This year the members of the club include all the members from last year plus some new members".
How can it be? If all members of the last year are still in the club and we have an addition of new members, why the then the total number of members is less than the total number of last year? How it could be?

I would appreciate your comment chetan2u

(2) says: The number of members of the club this year is 6/5 the number of members last year, NOT 3/5.

That is what I have in my official quant online version of Wiley!
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Math Expert
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Posts: 44656
Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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13 Dec 2017, 21:44
1
KUDOS
Expert's post
Erjan_S wrote:
Bunuel wrote:
Erjan_S wrote:
Honestly, i found this problem to be confusing because of 2) The number of members of the club this year is 3/5 the number of members last year.
Why? Because it contradicts this statement: "This year the members of the club include all the members from last year plus some new members".
How can it be? If all members of the last year are still in the club and we have an addition of new members, why the then the total number of members is less than the total number of last year? How it could be?

I would appreciate your comment chetan2u

(2) says: The number of members of the club this year is 6/5 the number of members last year, NOT 3/5.

That is what I have in my official quant online version of Wiley!

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It's a typo.
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Posts: 60
Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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17 Dec 2017, 22:05
Bunuel Can you please share your number picking approach? would be really helpful.
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Joined: 02 Sep 2009
Posts: 44656
Re: Last year 3/5 of the members of a certain club were males. [#permalink]

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17 Dec 2017, 23:08
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Bunuel Can you please share your number picking approach? would be really helpful.

Last year $$\frac{3}{5}$$ of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?

(1) More than half of the new members are male. Not sufficient.

(2) The number of members of the club this year is $$\frac{6}{5}$$ the number of members last year. Not sufficient.

(1)+(2):
The number of the members last year = 100 (assume).
The number of males last year = 3/5*100 = 60 (from the stem).
The number of the members this year = 100*6/5 = 120 (from 2). So, 20 new members joined this year.
More than 10, out of those 20, are males (from 1).

The question asks whether the number of males this year is more than 3/5*120 = 72. So, basically whether more than 72 - 60 = 12 males joined this year.

We know that the number of males who joined this year was more than 10, so 11, 12, 13, ..., 20. If that number is 11 or 12, the answer would be NO but of that number is more than 12 the answer would be YES. Not sufficient.

Hope it helps.
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Re: Last year 3/5 of the members of a certain club were males.   [#permalink] 17 Dec 2017, 23:08
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# Last year 3/5 of the members of a certain club were males.

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