In a certain school, 1/5 of the students own an older c

Question

In a certain school, \frac{1}{5} of the students own an older computer, made more than three years ago; \frac{1}{30} of the students own a newer computer, made in the last three years; and \frac{7}{9} of the students own no computer. What fraction of the students own both an older and a newer computer? A. \frac{1}{180} B. \frac{1}{90} C. \frac{1}{60} D. \frac{1}{45} E. \frac{2}{9} qgemnqhyn99c1.png

chetan2u · Accepted Answer

Let the total number of students be LCM of denominators or LCM(5,30,9) or 90.

Thus,  \frac{2}{9}  of total or  90*\frac{2}{9} , that is 20, have computers. 
 90*\frac{1}{5}  or 18 have old computers. 
 90*\frac{1}{30}   or 3 have new computers. 
Total 18+3 or 21.

This means 21-20 or one has both types of computers. 
As a fraction =  \frac{1}{90}

Archit3110 · Answer

LCM is 90
Make 2x2 
Matrix
------>3------n>3-----
New----1------2-----3
NNew----17----70----87
Total----18----72----90
1/90
Option B

Posted from my mobile device

playthegame · Answer

At first, I could not even understand this was an overlapping sets problem, so I ended up choosing 2/9 which is about 23%. This was towards the end of the test and I did not have much time left....

MBAToronto2024 · Answer

KarishmaB  this question confused me. I recalculated answer cause the first answer was too obvious. How'd you solve it using the matrix-approach?

KarishmaB · Answer

Here is the solution: Assume 90 students, the LCM of 5, 30 and 9. So all values will become integers. Screenshot 2024-11-12 at 4.08.28 PM.png Overlapping sets are discussed here: https://youtu.be/HRnuURqGhmg https://anaprep.com/sets-statistics-thr ... ping-sets/ https://anaprep.com/sets-statistics-min-max-in-sets/ https://anaprep.com/sets-statistics-why ... re-tricky/

KarishmaB · Answer

We cannot use double set matrices here. We use them when we have two non overlapping characteristics such as boys and girls in junior year and senior year. Someone who is in the boy set is not in the girl set and vice versa. Someone who is in junior year is not in the senior year and vice versa. 
Here, we have old set, new set and neither set. Plus there is overlap between old and new. This is a simple Venn diagram (or formula) question.

NEYR0N · Answer

KarishmaB ,

So I take it we only use Double-set matrix when a,b are mutually exclusive ? hm..

How do you distinguish between these? What keywords should make us assume dependence and use The formula A+B - AintersectB , instead of a doubleset matrix ?

I skipped this one, I used a double - set matrix and did not find the correct answer.

thanks

KarishmaB · Answer

We typically use double set matrices when we have 2 sets of variables such as 'Girls and Boy' owning 'Old and New computers' with no overlap in the sets. If there is overlap, even then a double set matrix could help us to view the data as done in this question: https://gmatclub.com/forum/at-a-certain ... l#p3522890 But we may want to use a Venn diagram too in such cases. Here we have a single set of variables - old and new computers - so we do not use double set matrix.

In a certain school, 1/5 of the students own an older c

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

In a certain school, 1/5 of the students own an older c

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