CAT DI LR section has become increasingly tough beginning from 2015. However, Understanding the basics of Bar graphs, Pie Charts, Multiple graphs, Line Graphs etc forms an integral part of solving tougher CAT level DI LR questions for the CAT Exam. This question is from CAT 2017 Slot 1 CAT DILR.

>A study to look at the early learning of rural kids was carried out in a number of village spanning three states, chosen from the North East (NE), the West (W) and the South (S). 50 four-year old kids each were sampled from each of the 150 villages from NE, 250 villages from W and 200 villages from S. It was found that of the 30000 surveyed kids 55% studied in primary schools run by government (G), 37% in private schools (P) while the remaining 8% did not go to school (O).

The kids surveyed were further divided into two groups based on whether their mothers dropped out of school before completing primary education or not. The table below gives the number of kids in different type of schools for mothers who dropped out of school before completing primary education:

It is also known that:

1.In S, 60% of the surveyed kids were in G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school.

2.In NE, among the O kids, 50% had mothers who had dropped out before completing primary education.

3.The number of kids in G in NE was the same as the number of kids in G in W.

Question 3: In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools.

What number of the surveyed kids now were in G in W?

- 6000
- 5250
- 6750
- 6300

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**General Solution**

We know that the break up for the kids by Government School, Private School and Other for mothers who dropped out before completing Primary. If we can complete a similar table for mothers who did complete primary, that should be very useful. We know the overall numbers and so can fill the gaps for the remaining.

Let us just recap the overall numbers

We know that the break up for the kids by Government School, Private School and Other for mothers who dropped out before completing Primary. If we can complete a similar table for mothers who did complete primary, that should be very useful. Since we know the overall numbers, this part should be easy.

In S, 6000 students overall were in G. Of this, 5100 are from mothers who had dropped out. So, mothers who finished and student in G should be 900. And O in second table should be 0.

This gives us private school in S in the second table as well. That should be 4300-900 = 3400

NE-O box should be identical for “Mother Drop-Out” and “Mother Finished” tables. Or, NE-O in second box should be 300. This also gives us W-O for second table

G in NE and G in W both in Mother Drop-out have 4200 each. So, G in NE and G in W should also both be identical. These two cells should be 1050

Post this we can fill the last two cells.

2400 kids have now joined school. Now, overall 50% joined G, and in one specific region also 50% joined G. What does this tell us?

> The remaining two regions put together should also have had exactly 50% in G. In one of the regions 25% went to G, in the other 100% went to G.

What does this tell us?

25% and 100% mix to give us 50%. Or they should be mixed in the ratio 2 : 1.

Total numbers that don’t go to schools are 600, 1500 and 300.

Where does the 2: 1 fit in?

NE: S ratio is 2 :1. Or, in NE, 25% go to G, in W 50% go to G and in S all 100% go to G.

G should get 25% of 600 + 50% of 1500 + 100% of 300 = 1200.

In W, total G would be 4200 + 1050 + 750 (Half of 1500) = 6000.

The question is **"What number of the surveyed kids now were in G in W?"**

Choice A is the correct answer.

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