In a survey of 150 persons, how many were smokers and drinkers?

Total number of people surveyed = 150
number of those who both smoke & drink?

stmt-1: INSUFFICIENT
80% of 150 thats - 120 people drinks. no info about smokers.

stmt-2: INSUFFICIENT
40% of smokers. what is the percentage of smokers?

stmt-1 + stmt-2: INSUFFICIENT
1. we dont know the exact number of people who neither smoke nor drink.
2. we dont know the number of smokers.

Option E is the correct answers.

t= 150

d= 80% of 150 = 120
s=30

d and s =?

1) NS

2) 12 = smokers who r drinkers too but wat abt other side ..NS

1+2

still no ans abt drinkers who r smokers too

thus E

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In a survey of 150 persons, how many were both smokers and drinkers?

(1) 80% of the person surveyed were drinkers
(2) 40% of the smokers were drinkers also

This is a '2by2' question, one of the most common type of question in GMAT math


There are 4 variables (a,b,c,d) and an equation (a+b+c+d=15) in the original condition, but only 2 equations are given by the conditions, so there is high chance (E) will be the answer.
Looking at the conditions together,
a+b=150*80%=120, a=40%(a+b), a+b+c+d=150, but we cannot derive an unique value of a, so the conditions are insufficient, and the answer hence becomes (E).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Number of people surveyed 150

10% = 15

Statement 1: 80% of the person surveyed were drinkers

10% = 15
80% = 15 * 8 = 90

So, 90 drink. No info about smokers.
Insufficient

Statement 2: 40% of the smokers were drinkers also

40% of smokers were drinkers. But what percent of 150 are smokers?
Insufficient.

Even when we combine the statements together, we don;t have info on how many are neither smokers or drinkers?

Both together too, are insufficient.

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