Unfold Prep
CAT 2017 · SLOT 1
Passage
Study the following table given below and answer the questions that follow.
A study to look at the early learning of rural kids was carried out in a number of villages 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 types of schools for mothers who dropped out of school before completing primary education:
| State | G | P | O | Total |
|---|---|---|---|---|
| NE | 4200 | 500 | 300 | 5000 |
| W | 4200 | 1900 | 1200 | 7300 |
| S | 5100 | 300 | 300 | 5700 |
| Total | 13500 | 2700 | 1800 | 18000 |
It is also known that:
- 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.
- In NE, among the O kids, 50% had mothers who had dropped out before completing primary education.
- The number of kids in G in NE was the same as the number of kids in G in W.
Q41.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?
### 1. Global Proportions & Totals Find the total surveyed kids in each region and globally. Calculate overall school allocations using the 55% Government (G), 37% Private (P), and 8% Out of School (O) proportions. * **NE Total** = `150 × 50 = 7,500` kids * **W Total** = `250 × 50 = 12,500` kids * **S Total** = `200 × 50 = 10,000` kids * **Grand Total** = `30,000` kids * **Global G** = 55% of 30,000 = `16,500` * **Global P** = 37% of 30,000 = `11,100` * **Global O** = 8% of 30,000 = `2,400`
### 2. Calculate Mother Completed (M-Comp) Margins Subtract the Mother Dropped Out (M-Drop) values from the absolute Global Totals to get the margins of the Mother Completed table. * **Total M-Comp NE** = `7,500 - 5,000 = 2,500` * **Total M-Comp W** = `12,500 - 7,300 = 5,200` * **Total M-Comp S** = `10,000 - 5,700 = 4,300` * **Total M-Comp G** = `16,500 - 13,500 = 3,000` * **Total M-Comp P** = `11,100 - 2,700 = 8,400` * **Total M-Comp O** = `2,400 - 1,800 = 600`
### 3. Clue 1: S Region Demographics In S, 60% of the kids are in G (`6,000` total G). All kids whose mothers completed primary education are in school, meaning M-Comp Out of School (O) is `0`. Calculate P as the remaining value. * **Total G in S** = 60% of 10,000 = `6,000` * **M-Comp G in S** = 6,000 (Total) - 5,100 (M-Drop) = `900` * **M-Comp O in S** = `0` (all in school) * **M-Comp P in S** = 4,300 (Total) - 900 (G) - 0 (O) = `3,400` * **Total O in S** = 0 (M-Comp) + 300 (M-Drop) = `300` * **Total P in S** = 10,000 - 6,000 - 300 = `3,700`
### 4. Clue 2: Out of School (O) Distribution In NE, among O kids, 50% had mothers who dropped out. Since O from M-Drop in NE is `300`, the Total O from NE must be `600`. * **Total O in NE** = 300 × 2 = 600 * **M-Comp O in NE** = 600 - 300 = `300` * **Total O in W** = 2,400 (Global O) - 600 (NE) - 300 (S) = `1,500` * **M-Comp O in W** = 1,500 - 1,200 (M-Drop) = `300`
### 5. Clue 3: Government (G) Distribution The number of kids in G in NE was the same as the number of kids in G in W. Let this number be `x`. * **Total G** = `x + x + 6,000 (S) = 16,500` * **`2x`** = `10,500` * **`x`** = `5,250` * **Total G in NE** = `5,250` * **Total G in W** = `5,250` * **M-Comp G in NE** = 5,250 - 4,200 (M-Drop) = `1,050` * **M-Comp G in W** = 5,250 - 4,200 (M-Drop) = `1,050`
### 6. Finalizing Private (P) Fill in the remaining P values by simple subtraction from the rows' Totals. * **Total P in NE** = 7,500 - 5,250 (G) - 600 (O) = `1,650` * **Total P in W** = 12,500 - 5,250 (G) - 1,500 (O) = `5,750` * **M-Comp P in NE** = 2,500 - 1,050 (G) - 300 (O) = `1,150` * **M-Comp P in W** = 5,200 - 1,050 (G) - 300 (O) = `3,850`
To solve this, we match the percentages (25%, 50%, 100%) to the regions (NE: 600, W: 1500, S: 300) such that the sum is 1200.