M22-18

Question

If 50% of a factory's workers are 30 years old or younger, what percentage of the factory workers are under 40 years old?

(1) 30% of the factory workers are older than 30 but younger than 40 years old
 
(2) 20% of the factory workers are 40 years old or older

Bunuel · Answer

Official Solution:

If 50% of a factory's workers are 30 years old or younger, what percentage of the factory workers are under 40 years old? 
 
(1) 30% of the factory workers are older than 30 but younger than 40 years old
 
Since 50% of the workers are 30 years old or younger, and 30% of the workers are older than 30 but younger than 40 years old, adding these two percentages will give us the percentage of workers who are under 40 years old. So, 50% + 30% = 80%. Statement (1) is sufficient.
 
(2) 20% of the factory workers are 40 years old or older
 
Since the percentage of workers 40 years old or older and those younger than 40 years old must add up to 100%, we can find the percentage of workers younger than 40 years old by subtracting the given percentage from 100%. So, 100% - 20% = 80%. Statement (2) is also sufficient.

Answer: D

seemachandran · Answer

Dear Bunuel /others

Just one doubt-
Second statement says 20% is atleast 40 so the rest of people can be 40 or >40 right.. or it can be <30 as well so how are we doing 100-20 percent?

chetan2u · Answer

Hi,
 the statement says 20% are atleast 40..
this means these 20% are 40 or>40...

this would be the case, if the statement read..
 atleast 20% are 40 years or more

hope it helps

Mbawarrior01 · Answer

Why did we add up in Statement 1? Please check my matrix and let me know where I am going wrong ?

susheelh · Answer

The tricky thing here is the wording of the problem. I too got foxed in the first attempt. But, if we organize the data correctly - It becomes easier to "See" the answer. Please see the snapshot for details.

Attachment:

M22-18.png [ 20.8 KiB | Viewed 39877 times ]

Both statements are suff. Answer choice D

PrayasT · Answer

I think this is a  high-quality  question and I agree with explanation.

energetics · Answer

Hope it helps... very confusing to do quickly with double matrix

https://i.imgur.com/W646ims.png

Shobith · Answer

I think this is a  high-quality  question and I agree with explanation.

kaladin123 · Answer

I think this is a high-quality question and I agree with explanation.

*Assuming 99 to be the max. age of a factory worker.

		0-29	30-99*
		Not >30	>30	Total
40-99*	Not <40	0
0-39	<40	50%		?
	Total	50%	50%	100%

From S1:

		0-29	30-99*
		Not >30	>30	Total
40-99*	Not <40	0
0-39	<40	50%	30%	?=80%
	Total	50%	50%	100%

From S2:

		0-29	30-99*
		Not >30	>30	Total
40-99*	Not <40	0		20%
0-39	<40	50%		?=80%
	Total	50%	50%	100%

joe123x · Answer

I have found that drawing a line and plotting all the information is the most efficient and fastest way to solve this question for people who struggle with the wording.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

bumpbot · Answer

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M22-18

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