A cash register in a certain clothing store is at the same distance fr

Question

A cash register in a certain clothing store is at the same distance from two dressing rooms in the store. The distance between the two dressing rooms is 16 feet, which of the following could be the distance between the cash register and either dressing room?

I. 6 feet
II. 12 feet
III. 24 feet

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

I. 6 feet
II. 12 feet
III. 24 feet

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

JeffTargetTestPrep · Accepted Answer

We see that we have an isosceles triangle with its base equal to 16 feet. The other two sides must be equal. We can use the triangle inequality theorem to determine the possible lengths of those two equal sides. The theorem states that the sum of the lengths of the two shortest sides is greater than the length of the longest side.

I. 6 feet

The resulting triangle would have sides of 6, 6, and 16. The two other sides cannot be 6 since 6 + 6 is not greater than 16.

II. 12 feet

The resulting triangle would have sides of 12, 12, and 16. The two other sides can be 12 since 12 + 12 is greater than 16.

III. 24 feet

The resulting triangle would have sides of 24, 24, and 16. The two other sides can be 24 feet since 16 + 24 is greater than 24. (Note in this case that the two shortest sides are 16 and 24.)

Answer: E

GMATinsight · Answer

basically the cash register location alongwith the two dressing rooms with make an isosceles triangle

Property: For a triangle to exist Sum of the two shorter sides must be greater than the longest side

I. 6 feet --- i.e. 6+6 is NOT greater than 16 hence  INCORRECT 
II. 12 feet --- i.e. 12+12 is greater than 16 hence  CORRECT 
III. 24 feet --- i.e. 16+24 is greater than 24 hence  CORRECT

Answer: option E

Stunnz · Answer

Why can't the placement be in a straight line? Is there something in the statement that makes it a triangle?

vicky2019 · Answer

How can both dressing rooms be of equal distance from register if they are in vertical line?

the second dressing room in line will be much farther than the original one.

paikyang · Answer

Could this also be solved using the Triangle property of : The length of any side of a triangle MUST BE LARGER than the positive difference of the other 2 sides, but SMALLER than the sum of the other 2 sides? I ) 6-6<16< 6+6 => 0<16<12 (NOT POSSIBLE) II) 12-12 <16<12+12 => 0<16<24 (POSSIBLE) III) 24-24 < 16 < 24+24 => 0<16>48 (POSSIBLE) Is my understanding of this property correct?

Gmatboat · Answer

Hi  Bunuel , writing to share that this is a GMAT PREP question.

Bunuel · Answer

______________________
Thank you. Added the tag.

kriswati · Answer

If both dressing rooms and the register are in a straight line, then the only way the register is equidistant from each room is when it is in the mid point of the line which is 16 ft/2 = 8ft. There would be only a single value 8 ft for the answer choice, which is not the case in this question which has options 6 ft, 12 ft and 24 ft.

Another way to think of this scenario is that the line discussed above   is also a form of triangle with angles 0 degree. Hence using the properties of the triangle: sum of 2 sides is greater than the other, the min value of each of the other sides of the triangle is 8 ft (since 8ft + 8 ft = 16 ft, sum of two side is greater than or equal to the third side)

Fdambro294 · Answer

Drawing a Straight Line from Dressing Room 1 (Point A) to Dressing Room 2 (Point B) = 16 feet

For the Cash Register to be Equidistant from each Room it must lie on the Vertical Line that is Perpendicular to this 16 foot line connecting the 2 dressing Rooms and Bisect it -----> Call this Point R

Extreme Case: All 3 Points lie on the Same Line: AR = RB = 8 feet - and the Cash Register is 8 feet away from each Room

As the Cash Register moves up the Vertical Line starting at Point R to maintain the Equidistance from each Changing Room, an Isosceles Triangle will start to form in which Sides AR and BR will be the Equal Sides.

The Non-Equal Side will be the Straight Horizontal Line from Dressing Room to Dressing Room = AB = 16 ft

Given the Isosceles Triangle ARB with NON-Equal Side of 16 ft, the Distance from the Register to each Room (the Equal Sides) can be what length?

Rule: A triangle can only be formed if the SUM of the Lengths of the 2 Shorter Sides is GREATER than the Length of the Longest Side

I. 6

If the Register is 6 feet away from each dressing room, this would form an Isosceles Triangle with Sides of: 6 - 6 - 16

However: 6 + 6 is NOT greater than 16 feet, failing the Triangle Formation Theorem

I is eliminated

II. 12

Triangle ARB would have side Lengths 12 - 12 - 16

12 + 12 > 16 --------> Valid Triangle. II is possible

III. 24

16 + 24 > 24 --------> Valid Triangle. III is possible.

II and III

(E)

achloes · Answer

KarishmaB   EMPOWERgmatRichC   avigutman

This is how I approached the question - where did I go wrong?

I also don't understand why the cash register and dressing rooms cannot be along a straight line.

Many thanks in advance!

avigutman · Answer

Hi  achloes . You made an assumption that the triangle is a right triangle. There's a degree of freedom here (which is implied by the words "which of the following could be" in the question stem). The concept tested here is the following:
 Any side of any triangle must be shorter than the sum of the other two sides. 
This is a direct result of the definition of a straight line: the shortest distance between two points.
 
Because of this:
 A cash register in a certain clothing store is  at the same distance  from two dressing rooms in the store.

EMPOWERgmatRichC · Answer

Hi achloes,

The prompt uses the phrase "which of the following COULD be the distance..." (NOT "which of the following IS the distance"). This implies that there are multiple answers that fit everything that is described by the prompt (and since this is a Roman Numeral question, that's not too surprising).

You found a possible distances between the cash register and the two dressing rooms (by assuming that the layout was a right triangle) - but that's clearly not one of the options. IF the cash register was right in the middle between the two changing rooms, then the answer would be 8 feet. Moving any equivalent distance away from the dressing rooms would INCREASE that distance - so we're looking for any answers that are greater than 8.

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

Contact Rich at: [email protected]

nosaj · Answer

You are right in Case 1 - but is it also possible to interpret that the cash register has some width? I guess this should be given in the question and the learning for me here is to not apply my own assumptions.

bumpbot · Answer

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A cash register in a certain clothing store is at the same distance fr

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