Of the 400 employees in a certain office, 260 have been given a watch

Question

Of the 400 employees in a certain office, 260 have been given a watch and 80 have been give a cell phone. If the number of the employees have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone. How many employees have been give a watch but not a cell phone?

A. 90
B. 170
C. 180
D. 200
E. 220

A. 90
B. 170
C. 180
D. 200
E. 220

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Kinshook · Accepted Answer

Given: Of the 400 employees in a certain office, 260 have been given a watch and 80 have been give a cell phone.

Asked: If the number of the employees have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone. How many employees have been give a watch but not a cell phone?

Number of employees given a watch  Number of employees not given a watch  Total number of employees  
  Number of employees given a cell phone  x  80-x=140-2x  80  
  Number of employees not given a cell phone  320-2x=260-x  2x  320  
  Total number of employees   260  140  400

Since 320-2x = 260 - x
x = 60

Number of employees given a watch  Number of employees not given a watch  Total number of employees  
  Number of employees given a cell phone  60  20  80  
  Number of employees not given a cell phone   200   120  320  
  Total number of employees   260  140  400

IMO D

JeffTargetTestPrep · Answer

#W + #C - #W&C + Neither = Total

260 + 80 – (1/2)Neither + Neither = 400

(1/2)Neither = 60

Neither = 120

#W&C = (1/2)120 = 60

#W&NC = #W - #W&C = 260 – 60 = 200

Therefore, 200 employees have been given a watch but not a cell phone.

Answer: D

Archit3110 · Answer

use 2x2 matrix

---Watch---NW----total
CP--x/2 ---140-x ----80
NCP-- 200-- 120---320
total-- 260---140---400
x/2 +140-x=80
solve for x = 120
200 is watch ncp 
option D

Paras96 · Answer

Let no. of people given neither watch nor phone =2n
therefore no. of people given both watch and phone =n
According to given problem

Only watch + only phone + both phone and watch + neither watch nor phone = 400
(260-n)+(80-n)+(n)+(2n)=400
n=60

therefore people given only watch=260-n=260-60=200

Hence Ans is D

kamalsharmam21 · Answer

Posted from my mobile device

DanTheGMATMan · Answer

Standard overlapping sets we all enjoy so much:

https://www.youtube.com/watch?v=an3dI9pHu84

Millionsknives63 · Answer

W 
 Not W

C 
 1/2X 
  
 80 
 
  Not C 
 A 
 X 
 320

260 
 140 
 400

Solve for A (overlap of watches and no cells)

Use column and row to set up system of linear equations to solve for A.

A + X = 320
A+ 1/2X = 260

Use elimination to solve directly for A.
2*(A+ 1/2X = 260)
-(A+X=320)

A = 200

Of the 400 employees in a certain office, 260 have been given a watch

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	Number of employees given a watch	Number of employees not given a watch	Total number of employees
Number of employees given a cell phone	x	80-x=140-2x	80
Number of employees not given a cell phone	320-2x=260-x	2x	320
Total number of employees	260	140	400

GMAT Problem Solving (PS) Questions

Of the 400 employees in a certain office, 260 have been given a watch

Prep Toolkit

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

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