CAT 2024 Slot 1 — DILR Question 5
Answer the following questions based on the information given below.
Six web surfers M, N, O, P, X, and Y each had 30 stars which they distributed among four bloggers A, B, C, and D. The number of stars received by A and B from the six web surfers is shown in the figure below.
| Surfer | to A | to B |
|---|---|---|
| M | 10 | 0 |
| N | 25 | 0 |
| O | 0 | 0 |
| P | 5 | 25 |
| X | 0 | 0 |
| Y | 5 | 20 |
The following additional facts are known regarding the number of stars received by the bloggers from the surfers.
- The numbers of stars received by the bloggers from the surfers were all multiples of 5 (including 0).
- The total numbers of stars received by the bloggers were the same.
- Each blogger received a different number of stars from M.
- Two surfers gave all their stars to a single blogger.
- D received more stars than C from Y.
What was the total number of stars received by D?
Answer & solution
Answer: 45
Easy
Total stars are fixed, and Fact 2 forces the four bloggers to share them equally. That single observation pins D’s total without any case-work.
Set-up. Six surfers (M, N, O, P, X, Y) each hold 30 stars. Stars to A and B from the bar chart:
| Surfer | A | B | C+D (=30−A−B) |
|---|---|---|---|
| M | 10 | 0 | 20 |
| N | 25 | 0 | 5 |
| O | 0 | 0 | 30 |
| P | 5 | 25 | 0 |
| X | 0 | 0 | 30 |
| Y | 5 | 20 | 5 |
Facts: all values are multiples of 5; all four blogger totals are equal; M gives a different amount to each blogger; two surfers give all 30 to one blogger; D > C from Y.
Total stars in the system. Six surfers, 30 each.
Apply Fact 2 (equal totals). The 180 stars split equally over the four bloggers.
Cross-check. From the chart, A’s total is and B’s is — consistent with 45 each, so C and D must also total 45 each.