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Is the probability that Patty will answer all of the

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Is the probability that Patty will answer all of the

by AAPL » Sat Aug 03, 2019 7:09 am

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Is the probability that Patty will answer all of the questions on her chemistry exam correctly greater than 50%?

1) For each question on the chemistry exam, Patty has a 90% chance of answering the question correctly.
2) There are fewer than 10 questions on Patty's chemistry exam.

OA E
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Source: — Data Sufficiency |

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by Ian Stewart » Sat Aug 03, 2019 9:54 am

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Statement 1 is not sufficient, because if the exam contains only one question, she has a 90% chance to get every question right, and if the exam contains a trillion questions, she will almost certainly get something wrong. Statement 2 alone is clearly insufficient.

Using both Statements, if the exam is very short, she will have a greater than 50% chance of answering everything correctly. For the information to be sufficient, we'd need to be sure she also has a 50% chance of answering everything correctly if the test is as long as possible, so if the test contains 9 questions. The probability she answers everything correctly is then (0.9)^9, so if (0.9)^9 > 0.5, the answer is C, and if (0.9)^9 < 0.5, the answer is E.

There are many ways to estimate the value of (0.9)^9 -- for example:

0.9^9 = (0.9^3)^3 = (0.729)^3 < (0.75)^3 = (3/4)^3 = 27/64 < 1/2

so 0.9^9 is less than 0.5, and the answer is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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