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

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Bunuel

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25 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

We are told that 30% of the total 250 people are both smokers and drinkers, which means 75 people are both smokers and drinkers: {Smokers and Drinkers} = 75.

We are told that, 40% of the smokers do not drink, meaning 60% of the smokers do drink. So:

0.6 * {Smokers} = 75
{Smokers} = 125

Next, we are also told that, 25% of the drinkers do not smoke, meaning 75% of the drinkers do smokers. So:
0.75 * {Drinkers} = 75
{Drinkers} = 100

Now, let’s summarize:

We are asked to find the percentage of non-smokers (125) who do not drink (100), which is 100/125 = 0.8.

Answer: E.

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25 Dec 2025, 09:29

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Bunuel

30% are both smokers and drinkers.

Number of smokers and drinkers = 0.3 * 250 = 75

40% smokers don't drink, indicates 60% drink. This 60% represents the 75 number above.

0.6x = 75

x = 75/0.6 = 125

Hence, the number of smokers = 125
Number of non smokers = 250 - 125 - 125

25% of drinkers don't smoke, indicates 75% smoke. This 75% represents both smokers and drinkers which is 75 people.

0.75y = 75

y = Drinkers = 100

Drinkers but not smokers = 25

Not drinkers and not smokers = 125 - 25 = 100

% = 100 /125 = 80%

Option E

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25 Dec 2025, 09:33

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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?

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

use 2x2 matrix
30% are both smokers & drinkers ; 75
40% of smokers do not drink ; 60% are both so 75/.6 = 125 ( all smokers)
similarly
25% drinkers do not smoke ; 75% are both 75/.75 = 100

fill the values in 2x2 matrix

-------S----NS--- Total
D-----75---25---100
ND---50----100---150
total--125---125---250

100/125 ; 80%
option E ;

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25 Dec 2025, 09:37

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	S	No S	Total
D	=30% * 250 = 75	0.25D	D
No D	0.4S	A
Total	S	B	250

A/B = ?

75 = 0.6S
S = 125
0.4 * 125 = 50

0.75D = 75
D=100
0.25D = 25

	S	No S	Total
D	75	25	100
No D	50	=150-50=100	=250-100=150
Total	125	=250-125 = 125	250

A/B = 100/125 * 100 = 80%

Answer E

Bunuel

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25 Dec 2025, 09:43

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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 ?

	Drinkers	Non Drinkers	Total
Smokers	30%*250=75 =.6x=.75y	.4x	x
Non smokers	.25y		250-x
Total	y		250

.6x = 75
x = 75/.6 = 750/6 = 125

.75y = 75
y = 100

	Drinkers	Non Drinkers	Total
Smokers	75	50	125
Non smokers	25	100	125
Total	100	150	250

Total non-smokers = 125
Non-smokers who don't drink = 100

The percentage of non-smokers who don't drink = 100/125 = 4/5 = 80%

IMO E

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25 Dec 2025, 10:20

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Drinkers | Non Drinkers
Smokers> 30 0.4x x

Non Smokers>. .25y y

y 60 100

Ignored 250 (considered 100), because % is asked, for convenience
Upon solving ans 80% E

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25 Dec 2025, 10:22

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smokers and drinker= 75
total smokers= p
smokers but not drinkers 0.40*p
we can find p
75+ 0.40p = p
p = 125
so smokers who dont drink= 50

total drinker = m
told that drinker but not smoker are are 25%= 0.25m

so we can find the value of m.
75+ 0.25m = m
m= 100
so total drinker = 100
and drinker who dont smoke- 25

find total non smoker= p + non smoker = 250
non smoker= 125

then find non drinker who do not smoke= drinker who dont smoke + niether smoke nor drink= total non smoker
25+ neither = 125
neither= 100

now final = 100/125
80%

Bunuel

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25 Dec 2025, 10:28

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Bunuel

	smokers	smoker not
drinker	75	75/3 =25
drinker not	75 * 2/3 = 50	125 -25 = 100
	125	125	250

answer is 100/125 = 80%

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25 Dec 2025, 10:31

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Total=250
Both S&D= 30%*250=75
40% Smokers don’t drink, 60% smokers drink.
Total smokers= 75/60%=125
75% drinkers smoke. Total drinkers= 75/75%=100
Smoke only= Total smokers- Both = 125-75=50
Drink only= Toral drinkers- both= 100-75=25
Neither= 250-(50+25+75)=100
There are total 125 non-smokers and of these 100 don’t drink = 100/125=0.8 or 80%

E

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25 Dec 2025, 11:07

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Bunuel

Let’s consider a two set venn diagram.

Where 250 denotes the total number of persons.

Let a denote the smokers only group, and b denote the number of people who drink only.

C denote the combination of both smokers and drinkers.

d denote the number of people who do not drink or smoke.

250 = a + b + c + d

c = 30%*(250)

c = 75

40% of smokers Do not drink.

40% * (a+75) = a

2*(a+75) = 5*a

3*a = 150

a =50

25% of drinkers do not smoke.

25% * (75+b) =b

3b = 75

b = 25

What percentage of Non Smokers do not drink ?

Non smokers = 25+100 = 125

Amongst 125 people, 100 do not drink.

= (100/125) *100

= (4/5)*100

= 80%

Option E

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25 Dec 2025, 11:15

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S = smokers
D = drinkers
Total = 250

the question asks to find the fraction: Neither / (Total - Smokers)

SandD = 0.3*250 = 75
0.4*S = onlyS -> (1-0.4)*S also drink -> 0.6*S = 75 -> S=125
0.25*D = onlyD -> (1-0.25)*D also smoke -> 0.75*D=75 -> D=100

OnlyS = 125-75 = 50
OnlyD = 100-75 = 25

Total = OnlyS + SandD + OnlyD + Neither
250 = 50 + 75 + 25 + Neither
Neither = 100

Answer = 100/(250-125) = 100/125 = 4/5 = 80%

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25 Dec 2025, 11:15

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Both= 0.3*250=75
only Smoke= 0.4*(75/0.6)=50
only drink=0.25*(75/0.75)=25

so none = 250-(100+25+75)=100
non smoke = 250-125 =125

reqd % = 100/125 =0.8...80%

Ans E

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25 Dec 2025, 11:17

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Bunuel

These are easiest to do with a table. Since we're dealing with percentages anyway we can do away with the 250 number - that's just going to add calculations that we don't need to do. We can assume a total population of 100 and just work with the percentages.

Let y= # of drinkers and x= # of smokers. We can fill in the table with what we know so far.

	Drinkers	Non-Drinkers	Total
Smokers	30	0.4x	x
Non-Smokers	0.25y	Quantity Needed
Total	y		100

Row 2 and Column 2 both give us equations that we can solve for the respective variables in.
$30+0.25y=y$ therefore $y=40$.
$30+0.4x=x$ therefore $x=50$.

We can update our table now.

	Drinkers	Non-Drinkers	Total
Smokers	30	20	50
Non-Smokers	10	Quantity Needed	50
Total	40		100

Looking down Row 3 we can see that the quantity needed equals 40. But note that the question asks what percent of non-smokers don't drink. So we're looking for the value of $\frac{40}{50}=0.8$. 0.8 is 80%, thus E is the answer.

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25 Dec 2025, 11:26

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S and D = 30%
S and D = 60% of S
S and not D = 40% of S = (30 * 40) / 60 =20%

D and not S = 25% of D
D and S = 75% of D = 30%
D and not S = 10%
not D and not S = 40%

Therefore,
S and D = 30%
S and not D = 20%
D and not S = 10%
not D and not S = 40%
S = 50%
not S = 50%
D = 40%
not D = 60%

(not D and not S)/ not S = 40/50 = 80%
ans: E

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25 Dec 2025, 11:26

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	smokers	non smokers
drinkers	75	0.25d	d
non drinkers	0.4s	??
	s	125	250

30% are both smokers and drinkers=0.3*250=75

40% of smokers don't drink, so 0.6s=75 or s=125 and 0.4s=50

25% of drinkers don't smoke, so 0.75d=75 or d=100 and 0.25d=25

so % of non smokers who don't drink=100/125=4/5=80%

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25 Dec 2025, 11:34

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Bunuel

Let S=smoker, D=drinkers, total =250
Given 30% are both: |S intersection D| = 0.30(250) = 75

40% of smokers do not drink, means 60% of smokers do drink,
so |S intersection D| = 0.60|S| => |S| = 75/0.6 = 125

25% of drinkers do not smoke means that 75% of drinkers do smoke,
so |S intersection D| = 0.75|D| => |D| = 75/0.75 = 100

Non smokers = 250-125=125 and non smokers who dont drink = neither = 250 - (|S| + |D| - |S instersection D|) = 250 - (125 + 100 - 75) = 100

so % of non smokers who do not drink = 100/125 = 80%

Option E

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25 Dec 2025, 11:37

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Both smokers & drinkers are 30% * 250 = 75. Since 40% of smokers don't drink so 60% drink therefore total smokers = 75/(60%) = 125 So Only Smoke = 125-75 = 50.
25% of drinkers don't smoke hence 75% smoke therfore total drinkers = 75/(75%) = 100 So only drink = 100-75 = 25.

Total given = 250 so who don't drink & don't smoke = 250-50-25-75 = 100.

% of non smokers who don't drink = Who don't drink don't smoke/Smokers = 100/125 = 80%.

Ans- E

Bunuel