The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman

Question

The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman drop out of the class and the ratio of men to women after the drop out is 8 to 7, then how many men are currently in the class?

A. 14
B. 16
C. 18 
D. 20
E. 22

Praveengeol · Answer

Equation on the basis of question

6x-2/5x-1=8/7

x=3

Original number of men = 6*3=18 
Original Number of Women = 5*3=15
Current number of men = 18-2=16 (Answer)
Current number of women = 15-1=14 
Ratio = 16/14= 8/7 ( Just to verify)

Ans B

OC2910 · Answer

m:w =6/5
w=6/5m......................(i)

also
m-2/w-1=8/7.....................(ii
putting (i) in (ii) gives
m=18 current number =16. B ans

kamkaul · Answer

since (total men)/(total women) =6/5 (original)
After drop out
(total men -2)/(total women -1) =8/7
Solve these two equations and the value of m (say m stands for total no. of men) = 18 (originally)

Now the question asks for current number = 18-2( after drop out) =16

Skywalker18 · Answer

Let the current number of men = M
and the current number of women = W

M/W = 6/5
=>5M - 6W = 0 
=>20M - 24W = 0 --1
(M-2)/(W-1) = 8/7
=>7M - 14 = 8W - 8
=> 7M - 8W = 6 
=> 21M - 24W = 18 --2

Now , from equations 1 and 2 , we get
M = 18
and W = 15
Answer C

KS15 · Answer

Glad to see that there is some confusion in such a simple question. Bunuel-could you plz clarify what 'currently' means? It could go either way i.e before or after the drop.

Skywalker18 · Answer

Hi  KS15  , 
In my opinion , the question is clear .  If 2 men and 1 woman drop out of the class and the ratio of men to women after the drop out is 8 to 7  . 
The above is a conditional statement which takes a hypothetical situation into account . 
We can't infer that 2 men and 1 women have actually been dropped from the class .
So the number of men currently in the class should be 18 , Answer C

KS15 · Answer

I agree with your point that it is hypothetical-but dont you think it should be clearly mentioned what currently means? Current could mean presently OR after the drop.

davedekoos · Answer

Earth is at war with Mars. Earth has 208 billion megatons of nuclear explosives, Mars has 9/8 the arsenal of Earth. If Mars shoots first, Earth will retaliate and both planets will be completely obliterated. How much nuclear firepower does the Mars currently have?

Clearly the question is asking what Mars's arsenal is BEFORE both planets are obliterated. The question above is the same (without all the death). The question presents a hypothetical situation. Hypothetical situations have not actually happened (yet), so "currently" refers to the current situation BEFORE any hypothetical class (or bomb) dropping.

If the question wanted to know the number of men in the class  after  2 men and 1 woman dropped the class, it would have explicitly said so. e.g. "If 2 men and 1 woman drop out of the class and the ratio of men to women after the drop out is 8 to 7, then how many men   would there be   in the class?" This keeps the question in the hypothetical situation. A perhaps subtle, but VERY important difference.

Temurkhon · Answer

only 18 is a multiple of 6, so C

Arjunarocks · Answer

let men be 6x and women be 5x.
After 2 men and 1 woman leave, the new numbers are:

Men= 6x-2
Women=5x-1

Now, the new ratio is 8:7,

that is, (6x-2)/(5x-1) = 8/7

solving we get x=3

So, total number of men now are 6*3- 2 = 16

sashiim20 · Answer

Let men  = m  , women  = w .

\frac{m}{w} = \frac{6}{5}

w = \frac{5}{6} m  --------- (i)

2 men and 1 woman drop out of the class and the ratio of men to women after the drop out is 8 to 7.

\frac{m - 2}{w - 1} = \frac{8}{7}

7m - 14 = 8w - 8

7m - 8w = 14 - 8

7m - 8w = 6  ------------ (ii)

Substituting value of  w  from (i) in (ii), we get;

7m - 8 (\frac{5}{6}) m = 6

7m - \frac{4*5}{3} m = 6

\frac{21m - 20m}{3} = 6

m = 6 * 3 = 18 . Answer (C) ...

rahulbanerjee1992 · Answer

Current ratio is given as: 6/5
From common sense, we know that men and women always have to be integers.
So, the current number of men, must be a multiple of 6. 
Option C -18, is the only multiple of 6. Hence, answer.

nigina93 · Answer

I used backsolving to solve this question. 
I picked easy number to work with, a multiple of 6, 18 (C)
if the ratio of men to women is 6:5 , then we have 18:15, subtracting 2 men and 1 women, we get, 16:14, which is 8:7, ratio that we need. Answer is C

Kinshook · Answer

Let men be m and women be w in the class

m/w = 6/5
5m = 6w

(m-2)/(w-1) = 8/7
7(m-2) = 8(w-1)
7m - 14 = 8w - 8
7m - 6 = 8(5m/6) = 20m/3
21m - 18 = 20m
m = 18

IMO C

ScottTargetTestPrep · Answer

The ratio 6 : 5 can be re-expressed as 6x : 5x, where 6x is the number of men currently in the class and 5x is the number of women currently in the class.

We can create the equation:

(6x - 2) / (5x - 1) = 8/7

7(6x - 2) = 8(5x - 1)

42x - 14 = 40x - 8

2x = 6

x = 3

So, there are 6 * 3 = 18 men in the class.

Answer: C

elslyknight · Answer

The question stem is not entirely clear on what does  currently  imply there - I believe GMAC would , make it clearer by stating one of
 
 How many men are originally in the class/how many men are in the class before the drop outs etc - C 
 How many men are currently in the class (generally implying after dropouts)/ how many men are in the class after dropouts - B

eb590 · Answer

When applying the changing ratio method I find 16, many others find 16 too yet the answer is 18 can we have an official solution? Thank you!

addy10024 · Answer

"If" does not mean the men and women have actually dropped out. So Ans is 18 only

eb590 · Answer

But that is the whole point of the problem to justify giving a new ratio and use the ratio change formula.

The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman

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The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman

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