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

Question

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) \(\frac{3}{5}\)

(B) \(\frac{108}{125}\)

(C) 1

(D) \(\frac{125}{108}\)

(E) \(\frac{5}{3}\)

(A)  \frac{3}{5}

(B)  \frac{108}{125}

(C) 1

(D)  \frac{125}{108}

(E)  \frac{5}{3}

Zarrolou · Answer

NewSecond=\frac{1}{10*100*100}  this means 1day/(Hours*Min*Sec)
 OldSecond=\frac{1}{24*60*60}

\frac{NewS}{OldS}=\frac{24*60*60}{10*100*100}=\frac{108}{125}

B

SrinathVangala · Answer

Nice question... Got confused a little bit at the beginning

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 second must take less time when compared to the ordinary one.

So the ration of new second to old second..... 24*60*60/10*100*100

Which is 108/125

atalpanditgmat · Answer

Hi Zarrolou,

my query is about the fraction 1/ 10*100*100. why are u taking fraction instead of 10*100*100?

kindly elaborate the concept.

Zarrolou · Answer

You have to start from a common point: the day.
This then is divided differently by the two metods.

The new one has 10*100*100 seconds in one day, the old one has 24*60*60 seconds.
This means that the day is divided in 10*100*100 seconds in the new method, and in 24*60*60 seconds in the old method.

And here we get the fractions  \frac{1}{10*100*100}  and  \frac{1}{24*60*60} .
If you want the time elapsed you have to divide the day by the total number of seconds.

The number  10*100*100  is the total number of seconds in a day, not the "time elapsed" in each one (as the queston asks)

Hope it's clear, let me know

atalpanditgmat · Answer

Thank you, it is much clear now....

Bunuel · Answer

Other conversion problems to practice: if-an-object-travels-100-feet-in-2-seconds-what-is-the-103364.html the-rear-wheels-of-a-car-crossed-a-certain-line-0-5-second-135753.html a-train-traveling-at-a-constant-speed-down-a-straight-track-87124.html a-welder-received-an-order-to-make-a-1-million-liter-126154.html a-car-traveling-at-a-certain-constant-speed-takes-2-seconds-126658.html if-an-automobile-averaged-22-5-miles-per-gallon-of-gasoline-109083.html if-1-kilometer-is-approximately-0-6-mile-which-of-the-140731.html measuring-standards-conversion-106516.html if-the-speed-of-x-meters-per-second-is-equivalent-to-the-127005.html if-10-millimeters-equal-1-centimeter-how-many-square-48538.html the-speed-of-light-is-approximately-149492.html Hope it helps

JimmyChen · Answer

Zarrolou is exactly right...

When I originally did this question, I overlooked the fact that we're comparing the  time elapsed  for one new-second vs. one ordinary second and not the number of new-seconds vs. the number of ordinary seconds in a day.

To get the time elapsed per second, you need to divide 1 day by the number of seconds in 1 day, hence the fractions in Zarrolou's solution.

PareshGmat · Answer

For a day (with old seconds)

60 Seconds = 1 Minute
60 Minutes = 1 Hr
24Hrs = 1 Day

1 Day = 24 * 60 * 60 Seconds

1 Second = \frac{1}{24*60*60}  ............... (1)

For a day (with new seconds)

100 new-seconds = 1 new-minute
100 new-minute = 1 new hour
10 new Hr = 1 Day

1 New Day = 10 * 100 * 100 New seconds

1 New second = \frac{1}{10*100*100}  ............ (2)

Ratio = \frac{(2)}{(1)} = \frac{1 New second}{1 Second}

= \frac{\frac{1}{10*100*100}}{\frac{1}{24*60*60}}

= \frac{24*60*60}{10*100*100}

= \frac{108}{125}

Answer = B

Bunuel · Answer

Check other  Conversion problems  to practice in  Special Questions Directory .

JeffTargetTestPrep · Answer

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:

/

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

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

108/125 .

Answer: B

balaji4799 · Answer

The key to this question is to start comparing from whats common between the newly constructed metrics to old metrics.
In that sense 1 day remains 1 day in both metrics so we start from there. 
1 day = 24 hrs*60 min*60 sec1 (old metrics), 1day = 10 hrs*100min*100 sec2
now we need sec2/sec1 which can be calculated from above expressions.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards