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A day is divided into 10 new-hours, each new hour is divided

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by AAPL » Thu Mar 29, 2018 5:49 am
A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

A. 3/5
B. 108/125
C. 1
D. 125/108
E. 5/3

The OA is B.

I get the solution of the following way,

Number of seconds in an ordinary day = 24*60*60

Number of seconds in the new day = 10*100*100

Clearly, new day has more number of seconds than the ordinary day.

So, new seconds must take less time when compared to the ordinary one.

So, the ration of new seconds to old seconds... (24*60*60) / (10*100*100) = 108/125.

Has anyone another strategic approach to solve this PS question? Regards!
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by deloitte247 » Sat Mar 31, 2018 1:13 pm
Time in seconds = $$hours\cdot\min utes\cdot\sec onds$$
$$New\ \sec ond=\frac{1}{10\cdot100\cdot100}$$
$$old\sec ond=\frac{1}{24\cdot60\cdot60}$$
$$Ratio\ of\ new\ \sec ond\ to\ ordinary\ \sec ond,\ we\ have,\ \frac{\left(new\ \sec ond\right)}{\left(old\ \sec ond\right)}=\frac{\left(24\cdot60\cdot60\right)}{\left(10\cdot100\cdot100\right)}$$
$$=\frac{108}{125}\ \ \left(option\ B\right)$$
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by ErikaPrepScholar » Sat Mar 31, 2018 3:22 pm
This is a solid approach. If we're concerned about keeping track of units, dimensional analysis can help:

$$1\ new\sec\left(\frac{1\ new\ \min}{100\ new\ \sec}\right)\left(\frac{1\ new\ hour}{100\ new\ \min}\right)\left(\frac{1\ day}{10\ new\ hours}\right)\left(\frac{24\ hours}{1\ day}\right)\left(\frac{60\ \min}{1\ hour}\right)\left(\frac{60\ \sec}{1\ \min}\right)$$ $$\frac{24\cdot60\cdot60\ \sec}{10\cdot100\cdot100}$$ Then reduce from there.
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by Jeff@TargetTestPrep » Thu Apr 05, 2018 10:17 am
AAPL wrote:A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

A. 3/5
B. 108/125
C. 1
D. 125/108
E. 5/3
In an ordinary day, there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Thus in an ordinary day, there are 24 x 60 x 60 ordinary seconds.

In a new-day, there are 10 hours in a day, 100 minutes in an hour, and 100 seconds in a minute. Thus in a new-day, there are 10 x 100 x 100 new-seconds.

Since the time elapsed of a day (regardless it's an ordinary day or a new-day) has to be the same, a new-second is 1/(10 x 100 x 100) of a day and an ordinary second is 1/(24 x 60 x 60) of a day. Thus, the ratio of a new-second to an ordinary second is:

[1/(10 x 100 x 100)]/[1/(24 x 60 x 60)]

(24 x 60 x 60)/(10 x 100 x 100)

(12 x 3 x 3)/(5 x 5 x 5)

108/125 .

Answer: B

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