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

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.

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

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

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

Hi Bunuel,

Can you please explain how statement 1 is not sufficient?

Thanks in advance.

Last year 60% of the members of the club were males. (1) says that more than 50% of the new members are male. The percentage of male members this year will fall between 60% and the percentage of new male members. To clarify, if the percentage of new male members is equal to or less than 60%, then the overall percentage of male members in the club this year will also be equal to or less than 60%. On the other hand, if the percentage of new male members exceeds 60%, then the overall percentage of male members in the club this year will be greater than 60%. Therefore, the firs statement is not sufficient.

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.

Last year 60% of the members of the club were males. (1) says that more than 50% of the new members are male. The percentage of male members this year will fall between 60% and the percentage of new male members. To clarify, if the percentage of new male members is equal to or less than 60%, then the overall percentage of male members in the club this year will also be equal to or less than 60%. On the other hand, if the percentage of new male members exceeds 60%, then the overall percentage of male members in the club this year will be greater than 60%. Therefore, the firs statement is not sufficient.

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

(1)+(2) From (2) it follows that the number of members in the club increased by 20%. However, we still don't know the percentage of male members in the new members, so we cannot answer the question definitively. If the percentage of male members in the new members is 60% or less, then the answer to the question will be no. If the percentage of male members in the new members is greater than 60%, then the answer to the question will be yes. Not sufficient.

Answer: E.

I think most of us once learned such a theory in elementary school: there's a cup of saline solution (solution A) with a specified salinity level, say 60%, and we're going to add another saline solution (solution B) into it.
For the new solution to maintain or surpass the original salinity level, the salinity level of solution B must be no less than 60%.
Note that the volume of solution B added is irrelevant to our goal. To wit, as long as solution B has a lower salinity level, solution A will be inevitably diluted, no matter how much is added—a single drop or a million gallons.

If statement (1) is EQUAL or LESS than half of the new members are male. Statement (1) will sufficient right?

Posted from my mobile device

If statement (1) were "Less than or equal to half of the new members are male. ", then it would indeed be sufficient to conclude that the fraction of male members this year is not greater than last year. This is because adding a group with 50% or fewer males to a group that is 60% male would decrease the overall percentage of males.

Thank you so much Bunuel!

­Say last year total number of members be = Old
Given, # of males = 3Old/53𝑂𝑙𝑑/5

This year, new members are added, say New𝑁𝑒𝑤 and let the number of males within the new group be x𝑥.

Question stem asks, if (x+3Old/5)/(New+Old)>35(𝑥+3𝑂𝑙𝑑/5)/(𝑁𝑒𝑤+𝑂𝑙𝑑)>35
Simplifying this, we get, if x>35New𝑥>35𝑁𝑒𝑤 or x>0.6New𝑥>0.6𝑁𝑒𝑤

Stmt1: Gives us x>0.5New𝑥>0.5𝑁𝑒𝑤 but we are not sure if x𝑥 is greater than 0.6New0.6𝑁𝑒𝑤. Hence this statement is insufficient.
Stmt2: Gives New=15Old𝑁𝑒𝑤=15𝑂𝑙𝑑. This gives us nothing about x𝑥 and New𝑁𝑒𝑤 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.