Question

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \text {The number of seconds in 7 hours} & \text {The number of hours in 52 weeks} \end{array}$$ A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Short answer

B. Quantity B is greater.

Step-by-step solution

Find the number of seconds in 7 hours

There are 60 seconds in a minute and 60 minutes in an hour. Therefore, the number of seconds in an hour is: \[ 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} = 3600 \text{ seconds/hour} \]Now, multiply this by 7 to get the total seconds in 7 hours: \[ 3600 \text{ seconds/hour} \times 7 \text{ hours} = 25200 \text{ seconds} \]

Find the number of hours in 52 weeks

There are 24 hours in a day and 7 days in a week. The total number of hours in a week is: \[ 24 \text{ hours/day} \times 7 \text{ days/week} = 168 \text{ hours/week} \]Now, multiply this by 52 to get the total hours in 52 weeks: \[ 168 \text{ hours/week} \times 52 \text{ weeks} = 8736 \text{ hours} \]

Compare the two quantities

Quantity A is 25200 seconds and Quantity B is 8736 hours. Since 1 hour is equivalent to 3600 seconds, we must convert Quantity B to seconds to compare: \[ 8736 \text{ hours} \times 3600 \text{ seconds/hour} = 31449600 \text{ seconds} \]Now compare 25200 seconds (Quantity A) with 31449600 seconds (Quantity B). Clearly, Quantity B is greater.

Key concepts

Unit Conversions

Unit conversions are essential for comparing different types of quantities, especially in GRE Quantitative Comparison problems. Here, we need to convert hours to seconds and weeks to hours. This means using the relationships between units: 60 seconds = 1 minute and 60 minutes = 1 hour.
To find seconds in 7 hours, we start by converting hours to minutes and then minutes to seconds:

• 1 hour = 3600 seconds (since 60 minutes/hour * 60 seconds/minute)
• 7 hours = 7 * 3600 seconds = 25200 seconds

Converting weeks to hours follows a similar pattern, knowing there are 24 hours in a day and 7 days in a week:

• 1 week = 168 hours (since 7 days/week * 24 hours/day)
• 52 weeks = 52 * 168 hours = 8736 hours

Conversions are vital to maintain consistency in units for accurate comparisons.

Time Calculations

Time calculations often require converting larger time units into smaller ones for precise comparisons. In this exercise, calculating seconds in 7 hours involved first determining the seconds in one hour by multiplying:

• 60 seconds/minute by 60 minutes/hour, resulting in 3600 seconds/hour

Then, multiply by 7 hours to achieve a total of 25200 seconds.
Similarly, for the number of hours in 52 weeks, first identify the weekly hours by converting days to hours:

• 24 hours/day by 7 days/week, resulting in 168 hours/week

Finally, multiply by 52 weeks to obtain 8736 hours. Accurate time calculations ensure clarity and precision in quantitative comparisons.

Comparison of Quantities

Comparing quantities in different units requires converting them to a common unit first. After converting both quantities to the same unit (seconds), you can clearly see which is greater.
For Quantity A, we found there are 25200 seconds in 7 hours.
For Quantity B, we needed to convert 8736 hours to seconds using the known conversion of 1 hour = 3600 seconds:

• 8736 hours * 3600 seconds/hour = 31,449,600 seconds

Now, comparing 25200 seconds with 31,449,600 seconds, it's evident that Quantity B is significantly larger. This method ensures a reliable and straightforward comparison of different quantities.