Reasoning question from Social Forest Worker exam, 2026 by JKSSB
In a research facility, there are 122 scientists. Some specialize in Quantum Physics (Q), Molecular Biology (M), and Organic Chemistry (O), while a few have no specialization in any of these fields. There are 65 in Q, 45 in M, and 42 in O. The intersection of Q and M is 20, Q and O is 25, and M and O is 15. The number of scientists in all three fields is exactly half the number of scientists who have no specialization in any of these three fields. How many scientists are specialized only in Organic Chemistry?
Last updated Jul 21, 2026
Correct Answer:
Option B —
12
Here is the complete solution for the 122 scientists problem explained without using any math symbols:
Step-by-Step Breakdown
1. Understand the Overlaps
Total scientists in the facility: 122
Scientists in Quantum Physics: 65
Scientists in Molecular Biology: 45
Scientists in Organic Chemistry: 42
Scientists in both Quantum Physics and Molecular Biology: 20
Scientists in both Quantum Physics and Organic Chemistry: 25
Scientists in both Molecular Biology and Organic Chemistry: 15
2. Find the Number of Scientists in All Three Fields
Adding the three individual groups together gives sixty-five plus forty-five plus forty-two, which equals 152.
Adding the three two-field overlaps together gives twenty plus twenty-five plus fifteen, which equals 60.
Subtracting the two-field overlaps from the individual total gives one hundred fifty-two minus sixty, which equals 92.
This value of ninety-two accounts for everyone in at least one field, except that the group in all three fields has been removed one extra time. Therefore, the total number of scientists in at least one field is ninety-two plus the number of scientists in all three fields.
Since the total number of scientists (122) is equal to those in at least one field plus those in no field:
One hundred twenty-two equals ninety-two plus the number in all three fields plus the number in no field.
The problem states that the number in no field is double the number in all three fields.
Combining these means ninety-two plus three times the number in all three fields equals one hundred twenty-two.
Subtracting ninety-two from one hundred twenty-two leaves 30.
Dividing thirty by three gives 10.
So, exactly 10 scientists specialize in all three fields.
3. Calculate Scientists Specialized ONLY in Organic Chemistry
To find those specialized solely in Organic Chemistry:
Start with the total in Organic Chemistry: 42.
Subtract those who also do Quantum Physics: forty-two minus twenty-five leaves 17.
Subtract those who also do Molecular Biology: seventeen minus fifteen leaves 2.
Add back the scientists who do all three fields (since they were subtracted twice): two plus ten equals 12.
The correct option is B) 12.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
