GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jan 2019, 02:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# Every day at noon, a bus leaves for Townville and travels at a speed

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Dec 2015
Posts: 28
Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

Updated on: 26 May 2016, 11:11
2
1
13
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:44) correct 23% (02:40) wrong based on 226 sessions

### HideShow timer Statistics

Every day at noon, a bus leaves for Townville and travels at a speed of $$x$$ kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of $$x$$?

A) 66
B) 72
C) 80
D) 84
E) 90

Originally posted by Sallyzodiac on 26 May 2016, 10:54.
Last edited by Sallyzodiac on 26 May 2016, 11:11, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8804
Location: Pune, India
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

26 May 2016, 19:16
5
4
Sallyzodiac wrote:
Every day at noon, a bus leaves for Townville and travels at a speed of $$x$$ kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of $$x$$?

A) 66
B) 72
C) 80
D) 84
E) 90

You can also use ratios.

If speed becomes 7/6 the original, time taken will become 6/7 the original (since same distance is traveled). The 1/7 th of the time taken is 30 mins so total time taken usually is 7*30 = 210 mins = 210/60 = 7/2 hrs

Usual Speed = 280/(7/2) = 80 mph

_________________

Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Intern
Joined: 19 Dec 2015
Posts: 28
Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

Updated on: 26 May 2016, 11:12
2
I did this algebraically, but I guess you could do it by plugging in numbers as well. My approach:

$$Time = \frac{Distance}{Speed}$$; thus the required time to travel 280 km = $$\frac{280}{s}$$.

However, this lady is running 30 minutes or $$\frac{1}{2}$$ of an hour late, but is at the same time travelling $$\frac{7s}{6}$$ as fast as usual and reaches Townville on time (as if she was travelling at her regular speed $$s$$ and left at her regular time). Thus, we can set up the following equation:

$$\frac{280}{s}$$ = $$\frac{280}{7s/6}$$ + $$\frac{1}{2}$$. Solving for $$s$$, we get $$s = 80$$, answer choice C.

Originally posted by Sallyzodiac on 26 May 2016, 11:10.
Last edited by Sallyzodiac on 26 May 2016, 11:12, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52385
Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

26 May 2016, 11:11
Sallyzodiac wrote:
Every day at noon, a bus leaves for Townville and travels at a speed of x kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of x?

A) 66
B) 72
C) 80
D) 84
E) 90

Distance = Time*Rate

$$280 = Usual \ Time*x$$ --> $$Usual Time = \frac{280}{x}$$;

$$280 = (Usual \ Time - \frac{1}{2})*(\frac{7}{6}*x)$$ (because 30 minutes = 1/2 hours) --> $$Usual \ Time = \frac{40*6}{x} + \frac{1}{2}$$

$$\frac{280}{x} = \frac{40*6}{x} + \frac{1}{2}$$;

$$\frac{40}{x} =\frac{1}{2}$$;

$$x = 80$$.

_________________
VP
Joined: 07 Dec 2014
Posts: 1152
Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

26 May 2016, 13:51
x=normal speed of bus
t=normal time of trip
xt=280 km
(7x/6)(t-1/2)=280 km
xt=(7x/6)(t-1/2)
t=3.5 hours
280/3.5=80 kph
Senior Manager
Joined: 18 Jan 2010
Posts: 251
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

27 May 2016, 03:01
1
Total Distance: 280 Km.
Usual speed: x KM per hour.

Usual time: $$\frac{280}{x}$$

In the revised situation the bus covers the same distance by driving fast. So speed is more and Time taken is less

Our revised equation is:

$$\frac{280}{x}$$ (-) $$\frac{1}{2}$$ = 280/($$\frac{7x}{6}$$)

$$\frac{280}{x}$$ (-) $$\frac{1}{2}$$ =$$\frac{280*6}{7x}$$

$$\frac{280}{x}$$ (-) $$\frac{280*6}{7x}$$ =$$\frac{1}{2}$$

$$\frac{40}{x}$$ =$$\frac{1}{2}$$

x = 80.

Intern
Joined: 05 May 2016
Posts: 20
Location: United States
WE: Web Development (Computer Software)
Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

10 Jun 2016, 11:47
Sallyzodiac wrote:
Every day at noon, a bus leaves for Townville and travels at a speed of $$x$$ kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of $$x$$?

A) 66
B) 72
C) 80
D) 84
E) 90

Algebra / plugging values are two approaches to solve this problem. There is one more approach and I took the road less travelled

The question stem mentions that "the driver drives $$\frac{7}{6}$$ times as fast as usual". Before jumping to algebra / plugging values, take a look at the answer choices. All the options, except (C), are multiples of 6. The distance is 280 kms. Driving at 80 km/hr, it will take 3.5 hours to cover the total distance. To cover the distance in 3 hours, the speed should be $$\frac{280}{3}$$. Multiplying 80 by $$\frac{7}{6}$$, you get $$\frac{280}{3}$$. Therefore, the answer is (C).
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13368
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

16 Mar 2018, 10:08
Hi All,

This question CAN be solved with either algebra or TESTing THE ANSWERS. Either way, this question involves the Distance Formula:

Distance = Rate x Time

We're told that the distance = 280 km, so

280 = R x T

The question also mentions an exact difference of 30 minutes, which is a "round number" (relative to time). It makes me think that the question is probably designed around other round numbers. While I would normally start with answers B or D when TESTing the Answers, here I'm going to start with 80 (since it's a round number)…

So if X the original speed and X = 80, we'd have.

280 = 80 x T
280/80 = T
T = 3.5 hours

Now let's see what happens when we subtract .5 hours (since the bus left 30 minutes late) and increase the speed by 7/6…

80(7/6) x (3) = ???

560/6 x 3

1680/6 = 280

This MATCHES the original distance, so it MUST be the correct answer.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 14 Sep 2017 Posts: 11 Location: India GPA: 3.33 Re: Every day at noon, a bus leaves for Townville and travels at a speed [#permalink] ### Show Tags 19 Mar 2018, 10:18 Bunuel wrote: Sallyzodiac wrote: Every day at noon, a bus leaves for Townville and travels at a speed of x kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of x? A) 66 B) 72 C) 80 D) 84 E) 90 Distance = Time*Rate $$280 = Usual \ Time*x$$ --> $$Usual Time = \frac{280}{x}$$; $$280 = (Usual \ Time - \frac{1}{2})*(\frac{7}{6}*x)$$ (30 minutes = 1/2 hours) --> $$Usual \ Time = \frac{40*6}{x} + \frac{1}{2}$$ $$\frac{280}{x} = \frac{40*6}{x} + \frac{1}{2}$$; $$\frac{40}{x} =\frac{1}{2}$$; $$x = 80$$. Answer: C. My question may sound silly to you since its been a long time I studied math, My question is that, In the second equation, why are you subtracting 30 minutes from usual time? As the question says that she reaches 30 minutes late shouldn't it be " usual time+30 minutes " since she is late or am i missing something? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13368 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Every day at noon, a bus leaves for Townville and travels at a speed [#permalink] ### Show Tags 19 Mar 2018, 10:27 1 Hi utkarshrihand, The prompt states that "the bus LEFT 30 minutes LATE...." and that the bus driver drives FASTER so that "she will arrive in Townville at the REGULAR TIME." Thus, the bus ride took 1/2 an hour LESS, and we have to subtract that half-hour from the total time. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Joined: 14 Sep 2017
Posts: 11
Location: India
GPA: 3.33
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

19 Mar 2018, 10:50
EMPOWERgmatRichC wrote:
Hi utkarshrihand,

The prompt states that "the bus LEFT 30 minutes LATE...." and that the bus driver drives FASTER so that "she will arrive in Townville at the REGULAR TIME."

Thus, the bus ride took 1/2 an hour LESS, and we have to subtract that half-hour from the total time.

GMAT assassins aren't born, they're made,
Rich

Thank you for clarifying. I have one more question. In general if a question states that a person arrive say y minutes late, and usual time is a x minutes, then we would add y with x i.e total time equals x+y minutes, right ?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13368
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

20 Mar 2018, 09:50
Hi utkarshrihand,

Yes - if you 'arrive LATE', then you would ADD time to the total time traveled.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 625
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

09 Nov 2018, 10:32
Sallyzodiac wrote:
Every day at noon, a bus leaves for Townville and travels at a speed of $$x$$ kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of $$x$$?

A) 66
B) 72
C) 80
D) 84
E) 90

$$? = x$$

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

$$\frac{{30\,\,\,{\text{minutes}}\,\,{\text{saved}}}}{{280\,\,{\text{km}}}} = \,\,\frac{{\,\,\frac{3}{{28}}\,\,\,{\text{minutes}}\,\,{\text{saved}}\,}}{{1\,\,\,{\text{km}}}}\,\,\,\,\,\left( * \right)$$

$$\left. \begin{gathered} x\,\,\frac{{{\text{km}}}}{{\text{h}}}\,\,\,\,::\,\,\,1\,{\text{km}}\,\,\left( {\frac{{1\,\,{\text{hour}}}}{{\,x\,\,{\text{km}}\,}}} \right)\left( {\frac{{60\,\,{\text{minutes}}\,}}{{\,1\,\,{\text{hour}}\,}}} \right)\,\,\,\, = \,\,\,\,\frac{{60}}{x}\,\,\,{\text{minutes}} \hfill \\ \frac{{7x}}{6}\,\,\frac{{{\text{km}}}}{{\text{h}}}\,\,\,:\,:\,\,\,1\,{\text{km}}\,\,\left( {\frac{{6\,\,{\text{hour}}}}{{\,7x\,\,{\text{km}}\,}}} \right)\left( {\frac{{60\,\,{\text{minutes}}\,}}{{\,1\,\,{\text{hour}}\,}}} \right)\,\,\,\, = \,\,\,\,\frac{{6 \cdot 60}}{{7x}}\,\,\,{\text{minutes}}\,\,\, \hfill \\ \end{gathered} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{{60}}{x} - \frac{{6 \cdot 60}}{{7x}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{3}{{28}}$$

$$\frac{{60 \cdot \boxed7}}{{x \cdot \boxed7}} - \frac{{6 \cdot 60}}{{7x}}\, = \frac{3}{{28}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\frac{{60}}{{7x}} = \frac{3}{{28}}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,? = x = \frac{{28 \cdot 60}}{{7 \cdot 3}} = 80\,\,\,\,\,\,\left[ {\,\frac{{{\text{km}}}}{{\text{h}}}\,} \right]$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4596
Location: United States (CA)
Re: Every day at noon, a bus leaves for Townville and travels at a speed  [#permalink]

### Show Tags

12 Nov 2018, 07:07
Sallyzodiac wrote:
Every day at noon, a bus leaves for Townville and travels at a speed of $$x$$ kilometers per hour. Today, the bus left 30 minutes late. If the driver drives $$\frac{7}{6}$$ times as fast as usual, she will arrive in Townville at the regular time. If the distance to Townville is 280 kilometers, what is the value of $$x$$?

A) 66
B) 72
C) 80
D) 84
E) 90

Let’s let the normal speed = x. The time for today is:

280/(7x/6) = (280 * 6)/7x = (40 * 6)/x = 240/x

The regular time is 280/x.

Since today the bus left 30 minutes, or ½ hour, late, we can create the equation:

240/x + 1/2 = 280/x

Multiplying by 2x we have:

480 + x = 560

x = 80

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Every day at noon, a bus leaves for Townville and travels at a speed &nbs [#permalink] 12 Nov 2018, 07:07
Display posts from previous: Sort by

# Every day at noon, a bus leaves for Townville and travels at a speed

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.