The ratio of men to women in the Snyder community choir is 4

Question

The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?

A. 20
B. 24
C. 30
D. 32
E. 34

A. 20
B. 24
C. 30
D. 32
E. 34

Zarrolou · Accepted Answer

\frac{Ms}{Ws}=\frac{4}{5}  and  \frac{Ml}{Wl}=\frac{5}{6}

Ms=Mi+4
Ws=Wi+6

\frac{Ms}{Ws}=\frac{Ml + 4}{Wl+6}=\frac{5x+4}{6x+6}=\frac{4}{5} 
Solve for x and you obtain  x=4

Ws= 6x+6=30

C

To make things clear the  x  is derived from the relation  \frac{5}{6}  that can be seen as  \frac{5x}{6x} . So 5x is the total number of men in L, and 6x is the total number of women if L.

jlgdr · Answer

Use simultaneous equations / By combination 4x = 5y + 4 5x = 6y + 6 Multiply (1) by 6 Multiply (2) by -5 Get rid of y, and x = 6 Then 5x = 30 C is your best friend today Cheers! J

doe007 · Answer

Let's say, 
 number of men in Snyder community choir = Sm
 number of women in Snyder community choir = Sw
 number of men in Leigh community choir = Lm = 5x
 number of women in Leigh community choir = Lw = 6x

We are given that,
 Sm = Lm + 4
 Sw = Lw + 6

\frac{Sm}{Sw} = \frac{4}{5}   ----  ==>  ----   \frac{Lm + 4}{Lw + 6} = \frac{4}{5}   ----  ==>  ----   \frac{5x + 4}{6x + 6} = \frac{4}{5} 
==> 25x + 20 = 24x + 24  ----  ==>  ----  x = 4
==> Sw = Lw + 6 = 6x + 6 = 24 + 6 = 30

Correct answer is C.

AugustAcademy · Answer

Let's look at the Snyder community first:

M:W = 4:5. Thus, the possibilities are: 4 men/5 women | 8 m/10 w | 12 m, 15w | 16m, 20 w | 20m, 25w | 24m, 30w etc.

Similarly, the Lehigh community has men and women in the ratio:

M:W = 5:6. The possibilities are 5 m, 6w | 10m, 12w | 15m, 18w | 20m, 24w, etc.

We now have two conditions: (1) There are 4 more men and 6 more women in the Snyder group than in the Lehigh group. (2) Further, the combined ratio is 22:27.

Consider (1): Add 4 to the possible number of men and 6 to the possible number of women in the Lehigh group to get possibilities for the Snyder group:

Modified Lehigh numbers are then given by: 5+4 m, 6+6 w | 10+4,12+6| 15+4, 18+6 | 20+4, 24+6 => 9m 12w | 14m 18w | 18m 24w | 24m 30w|

Compare these with the Snyder numbers to see which one of these also occurs in the Snyder group. You will see that 24m, 30w occurs both in the original Snyder group and in the modified Lehigh group.

The number of women in the Lehigh group is therefore given by option C: 30.

Check statement (2)

S - M:W = 24:30
L - M:W = 20:24

Combined - M:W = 44:54 = 22:27. This satisfies statement two as well. So we can be sure that this is the required answer.

ButwhY · Answer

S community has M: W =4x:5x
L community has M:W = 5y:6y
After Merging M:W = 4x+5y/5x+6y =22/27
After solving, we get 2x=3y -->y=2x/3 --------(1)
Given, S community women are more than L community women by 6.
i.e, 5x = 6y+6 substitute eq (1), we get x=6 --> 5x(Women in S Community)=30//

brij0811 · Answer

concentrating on women, let’s say there are x participants from Snyder and y from Leigh. then, using the mean ratio, we have the equation, (27/49-5/9)x=(6/11-27/49)y, i.e., ((243-245)/(9*49))x=((294-297)/(11*49))y
so, (-2/9)x=(-3/11)y, i.e. x/y=27/22, meaning that the ratio of participants from snyder and leigh is 27:22. 
Given that, (5/9x-6/11y)=6, hence using the result obtained above, 5/9x-6/11*22/27x=6, i.e., (5/9-4/9)x=6, x=54. So, the required answer is 5/9*54=30. i wonder whether the other condition about snyder having 4 more men is required at all!

EMPOWERgmatRichC · Answer

Hi All,

This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.

We're told that the ratio of the Men to Women in the Snyder choir is 4 to 5, so the number of men MUST be a multiple of 4 and the number of Women MUST be a multiple of 5. The question asks how many WOMEN are in the SNYDER choir, so the answer MUST be a multiple of 5. We can eliminate Answers B, D and E (since they're NOT multiples of 5). That leaves only 2 possibilities...

LET'S TEST Answer C...
If the number of Women in the Snyder choir is 30...
Then the number of Men in the Snyder choir is 24...

We're also given more ratio 'data'....that the ratio of the Men to Women in the Leigh choir is 5 to 6, so the number of men MUST be a multiple of 5 and the number of Women MUST be a multiple of 6. Finally, we're told that if the two choirs merged, the ratio of men to women in the COMBINED choir would be 22 to 27 - so the TOTAL number of men MUST be a multiple of 22 and the TOTAL number of Women MUST be a multiple of 27.

Finally, we're told that the Snyder choir has 4 MORE MEN and 6 MORE WOMEN than the Leigh choir....
With the data from answer C.....
The number of Men in Leigh = 24-4 = 20
The number of Women in Leigh = 30-6 = 24
20:24 = 5:6 which is a MATCH for what we were told

Total Men = 24+20 = 44
Total Women = 30+24 = 54
44:54 = 22:27 which is ALSO a MATCH for what we were told

Thus, this MUST be the answer.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Muqeet · Answer

The two choirs merged statement is not even needed in order to solve this question.

The ratio of men to women in the Snyder community choir is 4

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The ratio of men to women in the Snyder community choir is 4

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards