Each of the products produced yesterday was checked by x or

Question

Each of the products produced yesterday was checked by x or y. 0.5% of the products checked by x are defective and 0.8% of the products checked by y are defective. If the total defective rate of all the products checked by x and y is 0.75%, what fraction of the products was checked by y?

A. 3/5
B. 5/6
C. 7/11
D. 4/5
E. 5/8

A. 3/5
B. 5/6
C. 7/11
D. 4/5
E. 5/8

SrinathVangala · Accepted Answer

This is a allegation problem.

We can use a shortcut.

See the attachment for the shortcut.Its a simple one

So X/Y = 0.05/0.25 = 1/5

Therefore the fraction of products checked by Y = 5/6

VeritasPrepRon · Answer

The easiest way to do these types of questions is to look at the difference between x and y on a number line. x is at 0.5 and y is at 0.8, and together the average is 0.75. This means that every product checked by x brings down the average by 0.25 and every product checked by y brings up the average by 0.05. To balance these two out, y needs to check 5 products for every time x checks 1 product. Hence 1/6 of total checked by x and 5/6 of total checked by y.

Algebra works too but the number line strategy gets you the correct answer quickly. If you practice doing that, this is a 1-minute question, from starting to read to clicking "next".

Hope this helps!
-Ron

Zarrolou · Answer

You can use alligation to solve this.
Ratio X=0.75-0.5=0.25

Ratio Y=0.8-0.75=0.05
Now the ratio y/x is:
 \frac{Y}{X}=\frac{0.25}{0.05}  or  \frac{5}{1}

So for 6 products there were 5 Y and 1 X. 5/6 is the answer
If you wanna know more about this method check my signature : mixture!

apsForGmat · Answer

Hi, I am not aware of allegation. can you please explain about this or point me to some useful but short source.

Temurkhon · Answer

Differential approach

---50------------75------80----->

25x=5y

x/y=5/25=1/5, so y/x+y=5/6

B

yoysufpolash · Answer

0.5X + 0.8Y = 0.75 ( X + Y )
=> 0.05 Y = 0.25 X 
=> Y / X = 5 / 1

Fraction = 5/6

Answer : B

bumpbot · Answer

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.

Each of the products produced yesterday was checked by x or

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Each of the products produced yesterday was checked by x or

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards