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12 Days of Christmas GMAT Competition 2025 - Day 9: In a group of 250

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FrozenDragon

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25 Dec 2025, 13:43

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Bunuel

In a group of 250 people, 30% are both smokers and drinkers. If 40% of the smokers do not drink, and 25% of the drinkers do not smoke, what percentage of non-smokers do not drink?

A. 20%
B. 40%
C. 50%
D. 60%
E. 80%

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Let's form a table from question :

	Drink	Non - Drink	Total
Smoker	75	50	125
Non - Smoker	25	100	125
Total	100	150	250

Now question is percent of non - smoker who don't drink :

Non smoker - 125 and out of which 100 don't drink

So,

100/125 * 100 = 80 percent

Ans - E

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25 Dec 2025, 14:00

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Bunuel

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Both smokers and drinkers = 75.

If 40% smokers doesnt drink. 60% of smokers do drink which is 75.

0.60 S= 75

S = 125.

Smokers who doesnt drink = 125 - 75 = 50.

Similiarly...If 25% of drinkers doesnt smoke,,,75% of the drinkers smokes.

0.75 D = 75

D = 100.

Drinkers who doesnt smoke = 100-75 = 25

People who doenst drink and smoke at all = 250 - (75+50+25) = 250 - 150 = 100.

Total Non Smokers = 250 - 125 (total smokers) = 125.

Non-Smokers who doesnt drink = 100/125 x 100 = 80%

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25 Dec 2025, 14:45

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Both is 30% of 250 which equals= 75 people
If 40% of smokers do not drink then it means 60% which equals 75 does drink so 40%/60%x75= 50
Simmilarly if 25% of drinkers do not smoke then 75=75% meaning 25% equals= 25 people
Total smokers equals 50+75= 125 (Non-smokers =250-125= 125)
Of the 125 non-smokers 25 drink meaning 100 do not
This translates to 100/125x100= 80%
Ans E

Bunuel

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25 Dec 2025, 19:15

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Solve simply with double set matrix.

Important to note that since the question is asking for a percentage, the actual quantity of the people does not matter. When setting up double set matrix, just set the total to 100% and continue entering given information like that.

40% of the smokers do not drink means that 60% of the smokers do drink, and if 30% of the total group are both drinkers and smokers it means that 30% is 60% of the total number of smokers, which means that 20% of the smokers do not drink.
That also means 50% of the group does drink and 50% do not drink. From the additional information about one quarter of the drinkers do not smoke, you can infer that three quarters of the drinks do smoke, which leads to the answer 40.

Always clearly read what the question is asking for; there are other potential traps in the answers. The question is asking for what percentage of non smokers specifically.

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25 Dec 2025, 21:50

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Given that total people count is 250. 30% do both smoke and drink. It means 75 people do both smoke and drink.
Let no of people who do only smoke be x. Now it says 40% of the smokers do not drink. It means 0.4*(x+75) is equal to no of people who do only smoke. Wow the line in the question is little bit complex at first to figure this out.

So , 0.4*(x+75) = x

x = 50

Now let no of people who do only drink be y. Now it says 25% of the drinkers do not smoke. It means 0.25*(y+75) is equal to no of people who do only drink.

So , 0.25*(y+75) = y

y = 25

Then no . of people who do nothing (Neither smoke or drink) is 250-50-25-75 = 100

No of non smokers = 100+25 = 125

% of non smokers do not drink , which implies find the ratio of people who do nothing to total non smokers and then multiply with 100.

So % of non smokers do not drink = (100/125)*100 = 80%

So Answer is E

Good question.

Bunuel

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25 Dec 2025, 22:33

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Total number of people = 250
Given that 30% both drink and smoke
Therefore number of people who drink and smoke = 0.3*250 = 75

Let S and D be the number of people who smoke and drink respectively.

Given that 40% of smokers do not drink
60% of smokers drink
0.6S = 75
S = 125
0.4 * 125 = 50 smoke only

Given that 25% of the drinkers do not smoke
75% of drinkers smoke
0.75*D = 75
D = 100
0.25*100 = 25 drink only

Number of people who neither smokes nor drinks = 250 - (75 + 50+25) = 100
Number of non smokers = 250 - 125 = 125
Percentage of non smokers who do not drink = 100/125 = 80%

Bunuel

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25 Dec 2025, 22:41

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Given that 75 people both smoke and drink and if this covers 60% of the smokers and 75% of drinkers, we have 50 people who only smoke and 25 people who only drink. Now this entire portion covers 150 people implying that 100 people neither drink nor smoke.

To get the percentage of non smokers who do not drink, we have total non smokers as 25+100=125 and people who do not drink among them as 100

100/125=0.8 or 80%

Therefore, Option E

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answer is 80%

30% drink and smoke which is 75
40% of smokers do not drink 60% of smokers drink hence 60%s=75
s=125
similarly 25% drinkers don't smoke 75% drinkers smoke 75%d=75 d=100
number of people who smoke only is 50
number of persons who drink only is 25
number of no smoke and drink is 100
number of non smokers is 125
% of people of non smokers who donot drink is 100/125*100=80%

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25 Dec 2025, 23:00

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Total people = 250
Both Smokers and Drinkers = 30%
0.30x250 = 75
Smoker and Drinker= 75

40 % of the smokers do not drink , But smokers who drink =75
60% of smokers = 75
Total Smokers = 75/0.6=125
60% of smokers = 75
Total Smokers = 75/0.6 = 125
Smokers who do not drink = 40% of 125 = 50

25 % of the drinkers do not smoke
so 75% of drinkers do smoke
Drinkers who smoke = 75
75% of drinkers = 75
Total Drinkers = 75/0.75 =100
Thus drinkers who do not smoke = 25% of 100 = 25
Total Non Smokers = 250-125 = 125
Non Smokers who drink = 25
Non smokers who do not drink = 125-25 = 100

Percentage of non smokers do not drink = 100/125= 0.8 = 80% ✅

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26 Dec 2025, 00:38

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Best to use a Venn diagram.
Given 30% of 250 = 75, both smokers and drinkers.
40% of the smokers do not drink, which means 60% drink, which is 75. So 60% of smokers = 75, smokers = 125, smokers alone = 50.
25% of the drinkers do not smoke, which means 75% of smoke, which is 75. So 75% of drinkers = 75, drinkers = 100, drinkers alone = 25.
None = 250 - 50 - 75 - 25 = 100

The required percetange $\frac{non-smokers and non-drinkers}{non-smokers}*100\\
= \frac{100}{125}*100\\
= 80$

Option E

Bunuel

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26 Dec 2025, 01:33

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Bunuel

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Among 250 people,

people who smoke and drink = 0.3 * 250 = 75

40% of smokers don't drink => 60% of smokers drink
Total smokers = 75 * 100 / 60 = 125
Smokers who don't drink = 125 * 0.4 = 50

Similarly, 75% of drinkers smoke, so total drinkers = 100, and drinkers who don't smoke = 25

So, people who either drink or smoke = smokers who don't drink + drinkers who don't smoke + people who do both = 50 + 75 + 20 = 150
=> People who neither drink nor smoke = 250 - 150 = 100

Now, total number of non-smokers = drinkers who don't smoke + people who neither drink nor smoke = 25 + 100 = 125

Therefore, percentage of non-smokers who do not drink = (people who neither drink nor smoke / total non-smokers) * 100 = (100/125) * 100 = 80%

Hence, the answer is E

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26 Dec 2025, 02:00

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Given,
group of 250 = (both smokers and Drinkers) + (only Smokers) + (only drinkers) + (neither smokers nor drinkers)

both smokers and drinkers = 30% of 250 = 0.3 x 250 = 75 ---(1)

40% smokers do not drink => 60% smokers drink = 75
=> 50 smokers do not drink

25% of the drinker do not smoke => 75% of the drinkers smoke = 75
=> 25 drinkers do not smoke

hence 250 = 75 + 50 + 25 + (no smoke no drink)
non smoking non drinkers = 250 - 150 = 100

=> 40% of total

Bunuel

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26 Dec 2025, 02:58

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Both = 30%*250 = 75
40% smokers do not drink => 60% smokers also drink = 75 => All smokers = 125
25% drinkers do not smoke => 75% drinkers also smoke = 75 => All drinkers = 100
Total = 250 = 125+100-75+Neither => Neither = 100
pct of non-smokers do not drink = 100/(250-125)*100% = 80%

Answer: E

Bunuel

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26 Dec 2025, 03:10

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Total ppl=250
both smokers and drinkers=30% off 250=75
S=ttl smokers
D=ttl drinkers
40% S don't drink
60% S do both
25% D don't smoke
75% D do both
0.6S=75, S=125
0.75D=75, D=100
smokers=125 both 75 only smokes=125-75=50
Drinkers=100, both=75, only drink=100-75=25
neither=250-(only smoke+only drink+both)
=250-(50+25+75)=100
non-smokers=250-125=125
drinkers only=25, neither=100
100/25=0.8X100%=80%

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26 Dec 2025, 03:27

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=>s =smokers, d = drinkers
=>s and d = 30%
=>40% of s do not drink => 60% of smokers drink => 0.6s = 30%=> S = 50%
=> 25% of drinkers do not smoke => So 75%of drinkers do smoke=> 0.75D = 30%=> D => 40%

Smokers who drink = 30%
Smokers who do not drink = 50 - 30 = 20%

Drinkers who smoke = 30%
Drinkers who do not smoke => 40 - 30 => 10%

Non smokers = 100 - 50 = 50%
Nom deinkers = 100 - 40 = 60%

People who neither smoke nor drink = 100 - (30+20+10) = 40%

Percent of non - smokers who do not drink = 40%/50% = 80%

Final Answer = 80% => E

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26 Dec 2025, 04:44

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aswer E 80%

SMokers Non Smokers total

drinkers 30% of 250 25% drinkers do not smoker, therefore 75% of drinkers smoke 100
75
so 60% smokers drink 25
60% is 75
Number of smokers is 75/60 x 100 = 125

75% = 75 therer 100% is 100

non drinkers
40% smokers do not drink 100 150
50

TOtal smokers 125 125 250

there percentage is 100/125 = 80%

Bunuel

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Total people = 250
Both S and D = 250 x 30% = 75

40% of S are not D, i.e. 60% of S are D which is given as 75
Total S = 75 x 100/60 = 125

25% of D are not S, i.e. 75% of D are S which is given as 75
Total D = 75 x 100/75 = 100

Non-smokers = 250 - 125 = 125
D who are not S = 25 x 100/100 = 25
Non-smokers who are D = 125 - 25 = 100

% of non-smokers who are not D = 100 * 100/125 = 80%

Answer, Option E

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26 Dec 2025, 05:15

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In a group of 250 people, 30% are both smokers and drinkers. If 40% of the smokers do not drink, and 25% of the drinkers do not smoke, what percentage of non-smokers do not drink?

Let, total number of people are 100%.
Number of smomers and drinkers = 30%
It is given that 40% of smokers do not drink, then we can infer that 60% of smokers drink
So,
0.60* Smokers = 30%
Smokers = 30%/0.60 = 50%
Smokers= 50% & Non-smokers= 50%

It is given that 25% of drinkers do not smoke, then we can infer that 75% of drinkers smoke.
So,
0.75*Drinkers= 30%
Drinkers = 30%/0.75 = 40%
Drinkers=40% & Non-drinkers=60%

Smoke & Drink= 30%
Smoke only= 40% of smokers= 0.40*50= 20
Drink only= 25% of drinkers= 0.25*40= 10
Neither smoke or drink= 100-(30+20+10)= 40%

The percentage of non-smokers (50%) do not drink(40%)= (40/50)*100= 80%

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26 Dec 2025, 05:56

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smokers + drinkers = 100%
Both S & D= 30%
Smokers who dot drik= 40% so 60% do drink
60%=30% : 60% x S + 30%= 50%
Drinkers dot smoke =25% so 75% drinkers do smoke
75%= 30%: 75% X D= 30%= 40%
D=40%
Neither S OR D= 50%+40%-30%=60% ; 100-50% = 40%
Non S= 50%, either 40%
40/50 x 100=80%
Answer 80 %