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

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

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
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only 18 is a multiple of 6, so C

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
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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) ...

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

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

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.

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.

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.

Bunuel,

I believe Currently word confused me.

Just to clarify, do you think it is normal type of question which can appear in GMAT or because of this sort of confusions, this will not appear in GMAT?

Praveen

can we solve this problem by backtracking? it appears to be easy that way. just feed the value of the no. of men and get number of women as per the ratio then apply condition of subtraction to see which value matches 8/7

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

Where are you coming up with "x=3" in the solution? Thank you.

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.

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

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

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
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