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  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

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In XYZ Building, a flight of stairs connects each floor to the next, a

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In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 03:01
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Question Stats:

46% (02:35) correct 54% (03:14) wrong based on 170 sessions

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In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


Kudos for a correct solution.

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In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 04:06
1
1
Bunuel wrote:
In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


Kudos for a correct solution.

Given :
S=2L
13S + 12L = 798

Asked:
27S + 26L= ?

Solution:
S-2L =0 ------------> \(1^{st}\)
13S + 12L = 798 ------------> \(2^{nd}\)

Solving \(1^{st}\) && \(2^{nd}\)
L=21 Secs
S=42 Secs

27S + 26L= 1680 = 28mins .

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 20:28
1
suppose , to climb one flight of stairs = x min and to cross one landing = y min
Given x=2y

According to given data ,
13X+12y=13.3
so , 13x+6x=13.3

so x=13.3/19

now to find ,
27x+26y=27x+13x=40x=40*13.3/19 = 28.0 mints

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 24 Apr 2015, 07:55
Time taken to cross one landing = \(t\)
Time taken to cross a flight of stairs = \(2t\)

Time taken to cross \(13\) stairs + \(12\) landings (in between stairs) = \([13\)(\(2t\)) + \(12t]\) = \(38t\) = \(13.3\) mins
Time taken to cross \(27\) stairs + \(26\) landings (in between stairs) = \([27\)(\(2t\)) + \(26t]\) = \(80t\) = \(?\)

\(\frac{80t}{38t}\) = \(\frac{?}{13.3}\) mins

\(?\) = \(\frac{80*13.3}{38}\) = \(28\) mins

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 27 Apr 2015, 01:12
Bunuel wrote:
In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Since it takes Josie twice as long to climb a flight of stairs as it does to cross a landing, let’s start with the smaller time. Let’s take the time to cross 1 landing and call it x. Then the “flight climbing time,” the time to climb 1 flight, is 2x.

Josie takes 13.3 minutes to climb 13 flights of stairs and 13 – 1 = 12 landings between them. (We “subtract one before we’re done” to count the landings between the flights.)

The relationship can now be written:

13.3 = time to climb 13 flights + time to cross 12 landings
13.3 = 13(2x) + 12x
13.3 = 26x + 12x = 38x
x = 13.3/38 = 133/380

380 can be factored easily: 380 = 38 × 10 = 2 × 19 × 2 × 5
133 is tricky; it equals 7 × 19.
So 133/380 reduces (with the 19’s canceling) to 7/20. That’s x.

Now, the quantity we want is the time to climb 27 flights and cross 27 – 1 = 26 landings.

27(2x) + 26x = ?
54x + 26x = ?
80x = ?
80(7/20) = ? Cancel out the 20, leaving 4 × 7 = 28 exactly.

The correct answer is C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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