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.

Answer: E.

Hope it helps.
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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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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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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

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



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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Bunuel Can you please share your number picking approach? would be really helpful.

3/5 = 60%. So, There are 60% males in the group.

The fraction or the percentage of the male this year will be greater only when there will be more than 60% male in the new group.

St 1: Says more than 50%. But we are not sure whether it is more than 60%. NS

St 2: Tell nothing about the new male member. NS

Combining we are not getting anything new. NS

Ans E

The fraction of male members this year would be the weighted average of old Male ratio and the Male ratio of new member,

Statement 1) the male ratio in new members > 1/2,

But 1) if the male ratio in new members is more than 3/5, the new ratio would be more than 3/5.
2) if the male ratio in new members is less than 3/5, the new ratio would be less than 3/5.
3)if the male ratio in new members is equal to 3/5, the new ratio would be equal to 3/5.

So, Not Sufficient

Statement2: The number of members of the club this year is \(\frac{6}{5}\) the number of members last year.
Number of new total members/ new members is inconclusive without the Male ratio in new members.
NOT Sufficient.

Now, after combining St1 & 2, we cant be sure of the new ratio, as we dont know the male ratio in new members as explained above.
Hence, the answer is E

if where
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OFFICIAL GMAT EXPLANATION

Arithmetic Operations with fractions

Let L represent the number of members last year; N the number of new members added this year; and x the number of members added this year who are males. It is given that 35 of the members last year were males. It follows that the number of members who are male this year is 35L + x. Also, the total number of members this year is L + N. Determine if [(3/5)*L + x]/[L + N] > 35, or equivalently, determine if 3L + 5x > 3L + 3N or simply if x > (3/5)*N.

(1) This indicates that x > (1/2)*N. If, for example, N = 20 and x = 11, then 11>12(20)=10, but 11≯35(20)=12. On the other hand, if N = 20 and x = 16, then 16>12(20)=10, and 16>35(20)=12; NOT sufficient.

(2) This indicates that L + N = (6/5)*L. It follows that N = (1/5)*L. If, for example, L = 100, then N = 15(100) = 20. If x = 11, then 11≯35(20)=12. On the other hand, if x = 16, then 16>12(20)=10, and 16>35(20)=12; NOT sufficient.

Taking (1) and (2) together is of no more help than (1) and (2) taken separately since the same examples were used to show that neither (1) nor (2) is sufficient.

Both statements together are still not sufficient.

Solution:

We need to determine whether the fraction of the members of the club who are males this year is greater than that of last year. Since last year 3/5 of the members were males, the fraction of new members who are males must be greater than 3/5 in order for the fraction of the members who are males this year to be greater than 3/5.

Statement One Alone:

More than half of the new members are male does not necessarily mean more than 3/5 of the new members are male. Statement one alone is not sufficient.

Statement Two Alone:

With statement two, we see that 1/5 of the members this year are new members. However, since we don’t know whether more than 3/5 of the new members are males, statement two alone is not sufficient.

Statements One and Two Together:

Even with the two statements, we can’t tell whether more than 3/5 of the new members are males. Both statements together are still not sufficient.

Answer: E
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We can solve using weighted average concept
When we are adding new male members to the existing members, the fraction of males this year in the overall group depends on the how many males in the new members or fraction of males in the new group

Last year we had 3/5 males in the group
This year the fraction of males in the new member will affect the 3/5 value (3/5 will be higher or lower)

Case 1: If no. of males are greater than 3/5 of the new members, the average of new and old males will be greater than 3/5

Case 2: If no. of males are less than 3/5 of the new members, the average of new and old males will be less than 3/5

This can be solved very intuitively:

The question is simply mentioning that males were 60% last year. Are they greater than that this year?

This year includes all the previous year's members plus new members, so 60% males from the last year are still accounting for the same share of the old members. For this year members to have more than 60% males, the male members of the new members must be more than 60%.

Statement one mentions they are more than 50%; so both yes and no are possible

Statement two mentions about total addition of new members over the last year but we needed the split

Combined as well, we have no better idea about the split