Last visit was: 26 Apr 2026, 12:30 It is currently 26 Apr 2026, 12:30
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
saintforlife
User avatar
Joined: 09 Nov 2012
Last visit: 27 Feb 2015
Posts: 61
Own Kudos:
661
 [10]
Given Kudos: 40
Posts: 61
Kudos: 661
 [10]
The probability that a brand A widget is defective is x 07 Oct 2013, 23:19
1
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

66% (02:50) correct 34% (02:50) wrong based on 300 sessions

History

Date
Time
Result
Not Attempted Yet
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?

0.03
0.04
0.048
0.05
0.12
ShowHide Answer
Official Answer
A
User avatar
Qoofi
User avatar
Joined: 18 Dec 2012
Last visit: 23 Feb 2024
Posts: 64
Own Kudos:
206
 [2]
Given Kudos: 56
Location: India
Concentration: General Management, Strategy
GMAT 1: 530 Q37 V25
GMAT 2: 660 Q49 V32
GPA: 3.32
WE:Manufacturing and Production (Manufacturing)
GMAT 2: 660 Q49 V32
Posts: 64
Kudos: 206
 [2]
The probability that a brand A widget is defective is x Updated on: 08 Oct 2013, 02:17
Originally posted by Qoofi on 07 Oct 2013, 23:55.
Last edited by Qoofi on 08 Oct 2013, 02:17, edited 1 time in total.
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
saintforlife
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?

0.03
0.04
0.048
0.05
0.12
Show more
Hi

Probability of Brand A defective is x

Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12

Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25

Total = 40 + 25 + 25 = 100

Probability of having defective piece in a lot of 100 ( All brands ) = 0.053
Hence 5.3 defective piece out 100 lot.

So 40x + 2.12 + 2 = 5.3
x = 0.03

Opt A.
User avatar
kusena
User avatar
Joined: 14 Aug 2013
Last visit: 30 Dec 2014
Posts: 23
Own Kudos:
167
 [4]
Given Kudos: 4
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE:Consulting (Consumer Electronics)
Posts: 23
Kudos: 167
 [4]
The probability that a brand A widget is defective is x 08 Oct 2013, 00:09
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
saintforlife
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?

0.03
0.04
0.048
0.05
0.12
Show more

Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.08*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.053=(x*40+0.06*35+0.08*25)/100
=> 40x+2.1+2=5.3
=>40x=1.2
>x=1.2/40=0.03

Ans A..Hope its clear
User avatar
tuanle
User avatar
Joined: 05 Oct 2013
Last visit: 07 Dec 2016
Posts: 14
Own Kudos:
28
Posts: 14
Kudos: 28
The probability that a brand A widget is defective is x 26 Oct 2013, 07:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
saintforlife
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?

0.03
0.04
0.048
0.05
0.12
Show more
The expectation value of defectiveness is 100*0.053 = 5.3 which also is equal to (40x + 35*0.06 + 25* 0.08) = 40x + 2.1 + 2. Hence 40x=1.2, or x=0.03.
User avatar
1991sehwag
User avatar
Joined: 16 Jan 2015
Last visit: 11 Jan 2017
Posts: 36
Own Kudos:
91
Given Kudos: 44
Location: United States
Schools: ISB '17 Kellogg '17
GMAT Date: 05-20-2015
GPA: 3.06
WE:Business Development (Commercial Banking)
Schools: ISB '17 Kellogg '17
Posts: 36
Kudos: 91
The probability that a brand A widget is defective is x 17 Jan 2015, 04:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good qsn ; Option A for me !!
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,052
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,052
 [2]
The probability that a brand A widget is defective is x 17 Jan 2015, 13:01
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi All,

Behind the "thick" wording (and slightly "scary" language) of this prompt, we're really just dealing with a "weighted average" question. The math approaches/calculations shown are spot-on, so I won't rehash any of that here. Instead, I want to show you how you can answer this question without doing much math at all. The specific numbers used in the prompt (and the ones listed in the answers) provide a 'concept shortcut' that you can use to your advantage. You'll still have to take notes and stay organized, but here's how to do it:

We're given info on 3 types of widgets: the number of each, and their respective likelihood of being defective:

Widget:
Brand A: 40 widgets, X% chance of defective
Brand B: 35 widgets, 6% chance of defective
Brand C: 25 widgets, 8% chance of defective

Total: 100 widgets, 5.3% chance of defective.

That 5.3% is interesting....since most of the widgets (35+25 = 60; more than half) have a GREATER % chance of being defective, the Brand A widgets must REALLY "bring down" the average.

If we focus on the Brand B and C widgets, we have 60 widgets and the average chance of defective is a little less than 7% (since there are more Brand B widgets, the weighted average would be slightly closer to 6% than 8%, thus < 7%).

So we have 60 widgets at just below 7% and we need to factor in 40 additional widgets to bring THAT average down to 5.3%....

IF....we had 60 Brand A widgets, then the chance of defective in A would be "balanced" around 5.3% (60 widgets near 7%, the 60 Brand A widgets near 3.5%). HOWEVER, we DON'T have 60 Brand A widgets - we have FAR FEWER - only 40 Brand A widgets that bring down the average. That means these Brand A widgets MUST have a chance of defective that is even LOWER than 3.5%. There's only one answer that fits.

Final Answer:
Show Spoiler
A

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,991
Own Kudos:
1,118
Posts: 38,991
Kudos: 1,118
The probability that a brand A widget is defective is x 09 May 2024, 17:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
109860 posts
Krunaal
Tuck School Moderator
852 posts