All geologists must pass a written test and a field test to become lic

Question

All geologists must pass a written test and a field test to become licensed. If 70% of geologists pass the written test and 90% of geologists pass the fieldtest, what percent pass both tests?

(1) 10% did not pass either test.

(2) 20% passed only the field test.

pushpitkc · Answer

Assume that there are 100 geologists applying for a license. As per the question stem,
70 pass the written test and 90 pass the field test. We don't know how many people
pass both the tests.

1. 10% did not pass either test -> Neither = 10

Total = P(W) + P(F) - Both + Neither -> 100 = 70 + 90 - Both + 10 -> Both = 70  (Sufficient)

2. 20% passed only the field test -> P(Only F) = 20

We know that P(F) = P(Only F) + Both -> Both = P(F) - P(Only F) = 90 - 20 = 70  (Sufficient - Option D)

CareerGeek · Answer

https://gmatclub.com/forum/download/file.php?mode=view&id=50970 
-->  Sufficient

IMO Option D

siddharthkapoor · Answer

Let, the number of geologists= 100
So, the number geologists who pass the written test=70, and
The number of geologists who pass field test=90

Let, the number of geologist that pass both the tests= x
So, the number geologists who only pass the written test=70-x, and
The number of geologists who only pass field test=90-x

Let, number of geologists who do not pass either test=n

Thus, total number of geologists=70-x+x+90-x+n=100
So, if we can find either n or x, we can find the remaining details.

(1) n=10
Thus, sufficient.

(2) This statement says that 90-x=20
=> x=70
Thus, sufficient.

Therefore, the correct answer is option D.

Bunuel · Answer

Veritas Prep Official Explanation For Data Sufficiency Venn Diagram problems, treat them as problem-solving exercises, but make sure that you don’t carry information or forget about neither. Label what you know from the question in the Venn Diagram and then treat each statement separately: https://gmatclub.com/forum/download/file.php?id=60027 Statement (1) is clearly sufficient, as you could just use the formula to see that it will give you both: 100 = 70 + 90 – B + 10. Statement (2) is also sufficient, because when you plug in “Only P” = 20 in the diagram above, you can see that “Both” must be 70 to sum up to 90 for the whole circle. Answer choice D is correct. 2021-01-12_00-40-53.png

bumpbot · Answer

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All geologists must pass a written test and a field test to become lic

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