A Watch Which Gains 5 Seconds In 3 Minutes Was Set Right At 7 A.M. GMAT Problem Solving

Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m.

In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

1. 59 7/12 min. past 3
2. 4 p.m.
3. 58 7/11 min. past 3
4. 2 3/11 min. past 4
5. 10 min past 4

“A watch which gains 5 seconds in 3 minutes was set right at 7 a.m.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question was mainly borrowed from the book “GMAT Official Guide Quantitative Review”.

The candidate must possess knowledge of basic qualitative skills to solve GMAT Problem-Solving questions. Proper mathematical skills are required to solve calculative mathematical problems in the problem-solving domain of GMAT Quant topic.

Solution and Explanation:

Approach Solution 1:

The problem statement discloses that:

Given:

• The watch gains 5 seconds in every 3 minutes.
• It was set right at 7 a.m.

Find out:

• In the afternoon, the watch marked a quarter past 4 o’clock, then what is the true time?

The candidate should begin with the simplest number by analyzing the choices given.
From 7 am to 4 pm it is equal to 9 hours.
Every 3 mins, the watch leads to gain 5 seconds
Therefore, 9 hours will lead to 9*60/3*5 = 180*5 = 900 seconds or 900/60 minutes = 15 minutes.

Say, the candidate got a higher value of more than 4:15, the candidate should have discarded the greater values above 4. Therefore, the candidates in left with two options and the opposite it were <4:15.
Option B is hence the correct answer.

Approach Solution 2:

According to the problem statement:
Given:
The watch was set exactly at 7 a.m and leads to gain 5 seconds every 3 minutes.
Find out:
The watch indicated at the afternoon quarter past 4 o’clock, then what is the true time?

The solution would be:
The time duration between 7 am to 4:15 pm = 9 hours 15 minutes = 555 minutes
Let the true time passed be x minutes

The watch gains in x minutes= x/3 * 5 seconds or 5x/180 minutes
Therefore, x+ 5x/180 = 555
185x/180 =555
x= 180*3 = 540minutes or 9 hours
Therefore, 9hours after 7 a.m = 4 pm

Hence option B is the correct answer.

Approach Solution 3:

The problem statement states that:

Given:

• A watch increases by 5 seconds in 3 minutes.
• The time of the watch was set at 7 a.m.

Find out:

• The watch when displayed at a quarter past 4 o’clock in the afternoon, what is the right time?

The time period between 7 a.m to 4: 15 p.m = 9 hours 15 minutes = 37/4
3 minutes and 5 seconds of this watch means 3 minutes of the valid watch.

37/720 hours of this watch= 1/20 hours of the valid watch

37/4 of this watch = 1/20 x 720/37 x 37/4 hours of the valid watch
= 9 hours of the valid watch
Therefore, the right time is 9 hours after 7 am, which is equal to 4 pm

Hence opinion B is the correct answer.

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