Free Quiz 1 - linear equation and probability doubts

[gmat04]

Mary spent her summer holidays either by practicing tennis in the morning or by watching movies in the evening. She did not do both the activities on any single day. However, there were some days when she did neither. If there were 22 mornings when she did nothing and 32 evenings when she did nothing. At the end of the summer holidays, she reckoned that she had either played tennis or watched a movie on 26 days. How long was her summer holiday?

Can you please explain how to solve this problem? Thanks!

[ksb]

Let t be the number of days Mary spent holidaying.

She practiced tennis in the mornings. And we know that she did not do anything on 22 mornings.

Therefore, she practiced tennis on t - 22 days.

Similarly, she watched movies in the evenings. And we know that she did not do anything on 32 evenings.

Therefore, she watched movies on t - 32 days.

As on any given day she did not more than one of the two activities, the intersection set of playing tennis and watching movies will be 0.

Therefore, number of days that she had activities = 26 = t - 22 + t - 32
i.e., 2t = 26 + 22 + 32 = 80 or t = 40.

Shortcut

Go from answer choices.

Let the number of days she spent holidaying be 40.

Then 40 - 22 = 18 days she played tennis and
40 - 32 = 8 days she watched movies.

Therefore, 18 + 8 = 26 days she did one of the two activities (concurs with the information given in the question.

KSB

[gmat04]

Thanks for the detailed explanation! That was very helpful.

Can you also explain Q8?
The probability of an anti-aircraft gun hitting its target in a single fire is 0.6. What is the probability that the gun will bring down its next target in 3 fires?

Thanks!

[ksb]

The anti aircraft gun will succeed as long as it can hit the target in at least one of the three trials.

The probability that it will hit the target in a single trial is 0.6
Therefore, the probability that it will not hit the target in a given trial is 0.4

The converse of what we need to find is that the anti aircraft gun does not hit the target in all the three trials.

The probability of it not hitting the target in all three trials = 0.4*0.4*.4 = 0.064.

Therefore, the probability that it will hit the target in at least one of the 3 trials = 1 - 0.064 = 0.936

KSB

[gmat04]

Thanks got it