Question: What is the probability that it will rain tomorrow?

(1) The probability that it rains today is 40%.
(2) If it rains today, the probability that it will rain tomorrow will increase by 10%.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E
Solution and Explanation:
Approach Solution 1:

The problem statement asks to find the probability that it will rain tomorrow.

Statement 1: The probability that it rains today is 40%.
The probability of rain that can take place today = \(\frac{40}{100}\) = ⅖ ; No rain today = ⅗.

Therefore, there is no information given regarding tomorrow.
Hence, insufficient.

Statement 2: If it rains today, the probability that it will rain tomorrow will increase by 10%.
Let, the probability of rain that can take place today be x.
Then, the probability of rain tomorrow is x+10%.
There is no such information on today's chances of rain
Hence, insufficient.

Combining both statements:

The probability that it rains today = ⅖
If it rains today then the probability of rain tomorrow = ⅖ + 10% of ⅖
If no rain occurs today then the probability of tomorrow's rain= no such information given.
Hence we cannot calculate the probability that it will rain tomorrow.
We only know that today no rain = 3/5.
This cannot be related to tomorrow since it is not mentioned anywhere in the question
Hence, both statements together are insufficient.

Approach Solution 2:

The problem statement asks to find the probability that it will rain tomorrow.
(1) The probability that it rains today is 40%. - Insufficient. There is no information regarding the possibility of rain tomorrow. It could be a 0% chance or 70% chance.

(2) If it rains today, the probability that it will rain tomorrow will increase by 10%.- Insufficient. If it is mentioned that the possibility of rain tomorrow is 50% then if it rains today, the chance of rain tomorrow will be 10% greater than 50%. However, there is no information regarding the possibility of rain tomorrow.

Combining (1)+(2) - Insufficient. Still, there is no information about the possibility of rain tomorrow.

Approach Solution 3:

The problem statement asks to find the probability that it will rain tomorrow.
(1) The probability that it rains today is 40%. - Insufficient. There is no information regarding the possibility of rain tomorrow.
(2) If it rains today, the probability that it will rain tomorrow will increase by 10%.- Insufficient.
This is no information provided regarding the possibility of rain today and rain tomorrow.
Therefore, each statement alone is not sufficient.

It is required to find the probability that it will rain tomorrow.
Combining (1) and (2), we get:
If it rains today, the probability that it will rain tomorrow will increase by 10%.
Therefore, if it rains today, the probability that it will rain tomorrow = 40% + 10% of 40% = 44%.
However, it is not known if it does NOT rain today, what will be the effect of tomorrow's rain. We do not know whether the chance of tomorrow's rain, corresponding to the non-occurrence of today's rain, decreases or increases; by what percent.

Hence, both statements together are insufficient.

“What is the probability that it will rain tomorrow”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from the book “GMAT Official Guide 2019”. GMAT Quant section includes a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement that is followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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