The number of students passing or failing in an exam for a particular subject are presented in the bar chart above (Year 1: Pass 50, Fail 10; Year 2: Pass 60, Fail 5; Year 3: Pass 50, Fail 3). Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt. The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are ______.
Figure (reconstruction)
Options:
(A) 65 and 53
(B) 60 and 50
(C) 55 and 53
(D) 55 and 48
Official Answer Key:
D
Step-by-Step Solution & Explanation
Year 1 is the first year, so all 60 (50 pass + 10 fail) are first-timers. The 10 who failed retake the exam in Year 2 and — since a repeater always passes on the second attempt — all 10 appear in Year 2's PASS count. Year 2 total = 60+5 = 65, of which 10 are guaranteed-pass repeaters, so first-time takers in Year 2 = 65 − 10 = 55. Of these 55 first-timers, 5 fail (matches the Year-2 fail count exactly, since repeaters cannot fail) and 50 pass. Those 5 Year-2 failures repeat in Year 3 and must pass. Year 3 total = 50+3 = 53, of which 5 are repeaters, so first-time takers in Year 3 = 53 − 5 = 48. Answer: 55 and 48 → (D).
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