The ratio of men to women employed by Company X in 1995 was 1 to 2

Question

The ratio of men to women employed by Company X in 1995 was 1 to 2, what is the ratio of men to women employed by Company X in 1996?

(1) Company X employed 20 more women in 1996 than in 1995.

(2) Company X employed 20 more men in 1996 than in 1995.

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kb26 · Answer

We are given only ratio in the question. Not the multiplier or total.

And, even statement 1 and 2 both provide the number of increase in men and women. So, nothing can be deduced about the ratio in 1996. So, ans is E.

Pratidwandi · Answer

I think this is quite straight forward. E. Ratio of men to women is 1:2.

1) No mention of original numbers, and no mention of whether or not they also hired more men. Insufficient.
2) Again, no mention of original numbers and no mention of whether or not they also hired more women. Insufficient.

Now combining 1 and 2, we know that they hired 20 more men and 20 more women. But that still doesn't give us a unique ratio. For example, if there were originally 10 men and 20 women, after the new hires, the new ratio of men to women will be: 10+20/20+20 = 30/40 = 3/4.

But if there were 20 men and 40 women originally, the new ratio of men to women will be: 20+20/40+20 = 40/60 = 2/3. So we cannot get a unique ratio unless we are aware of the original number of men and women employed at the company. Both statements taken together are still unsufficient.

Hope it's clear!

MarkGMATMentor · Answer

When all you know is a ratio, you generally cannot find the new ratio when things are added or subtracted, with one important exception.

If the ratio in 1995 was 1 man : 2 women, then we can say that the actual numbers of men and women are 1x and 2x, respectively.

Statement 1:
 This tells you that the new numbers of men and women are x and 2x + 20, respectively. You can't reduce  \frac{x}{2x+20}  to a single ratio; the ratio will be different depending on the value of x.  Insufficient.

Statement 2:
 The new numbers of men and women are x + 20 and 2x. Similarly, you can't reduce  \frac{x+20}{2x}  to a single ratio.  Insufficient.

Together: 
The new numbers of men and women are x + 20 and 2x + 20. You can't reduce  \frac{x+20}{2x+20}  to a single ratio either; many results are possible.  Insufficient.   The answer is E.

If Statement 1 had said, "Company X employed 40 more women in 1996 than in 1995," the answer would be C because you would know that ratio stays at 1 to 2. Mathematically, this is because the new ratio would be:
 \frac{ x+20}{2x+40}  -->  \frac{x+20}{2(x+20)}  -->  \frac{1}{2}

So, this problem fits the rule of thumb that you can't find a new ratio when numbers are added to or subtracted from a ratio.   The exception to the rule is when numbers are added in the same ratio as the original.

The ratio of men to women employed by Company X in 1995 was 1 to 2

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The ratio of men to women employed by Company X in 1995 was 1 to 2