CAT 2024 Slot 1 · DILR · Question 17

Solving the set

Step 1 – Total stars = 6 × 30 = 180. All four bloggers received the same number (fact 2), so each received 180/4 = 45. From the chart, A got 10 + 25 + 0 + 5 + 0 + 5 = 45 and B got 0 + 0 + 0 + 25 + 0 + 20 = 45, which confirms it.

Step 2 – Find what each surfer had left for C and D.

Surfer	M	N	O	P	X	Y	Total
Total stars	30	30	30	30	30	30	180
Given to A	10	25	0	5	0	5	45
Given to B	0	0	0	25	0	20	45
Left for C + D	20	5	30	0	30	5	90

Step 3 – Fact 4 (two surfers gave all 30 to one blogger). M, N, P and Y each gave stars to A or B and still had some left, or split between A and B, so none of them gave all 30 to one blogger. Hence O and X are the two surfers, and each gave all 30 to C or to D.

Step 4 – O and X cannot both give to the same blogger (that blogger would get 60 > 45). So one of them gave 30 to C and the other 30 to D. Which one went to which cannot be decided.

Step 5 – Surfer M (fact 3). A got 10 and B got 0, so C and D share 20, using values different from 0 and 10 and from each other (multiples of 5). The only possible pair is 15 and 5.

Step 6 – Surfer Y (fact 5). C and D share 5 and D got more, so D = 5 and C = 0.

Step 7 – Totals of C and D. Each needs 45. C already has 30 (from O or X) + 0 (P) + 0 (Y), so C needs 15 from M and N together. D has 30 + 0 + 5 = 35, so D needs 10 from M and N together. N has only 5 for C and D. If C took 5 from M, it would need 10 from N (impossible). So C gets 15 from M and 0 from N, and D gets 5 from M and 5 from N.

Blogger	M	N	O	P	X	Y	Total
A	10	25	0	5	0	5	45
B	0	0	0	25	0	20	45
C	15	0	30 or 0	0	0 or 30	0	45
D	5	5	0 or 30	0	30 or 0	5	45
Bloggers who got stars	3	2	1	2	1	3

This question

From the final table, the number of bloggers who received stars from each surfer is: M 3 (A, C, D), N 2 (A, D), O 1, P 2 (A, B), X 1, Y 3 (A, B, D).

Exactly two bloggers: N and P, i.e., 2 surfers.

Hence, the answer is 2.