Q26·CSAT · Prelims 2025
Three primes in arithmetic progression
NumericalPrime NumbersNumber theory● Hard
Question
Three prime numbers p, q and r, each less than 20, are such that p - q = q - r. How many distinct possible values can we get for (p + q + r)?
Options
aAnswer
4
b
5
c
6
d
More than 6
Explanation
The condition p - q = q - r means p, q, r form an Arithmetic Progression (AP). The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, 19. Let's find all sets of three primes in this list that form an AP and calculate their sum:
1Common difference 2: {3, 5, 7} \rightarrow Sum = 15.
2Common difference 4: {3, 7, 11} \rightarrow Sum = 21.
3Common difference 6: {5, 11, 17} \rightarrow Sum = 33.
4Common difference 6: {7, 13, 19} \rightarrow Sum = 39.
5Common difference 8: {3, 11, 19} \rightarrow Sum = 33.
The possible sums are 15, 21, 33, and 39. There are exactly 4 distinct possible values.
When finding combinations of prime numbers under a constraint, quickly list the primes and systematically test common differences rather than random guessing.
Answer: (a).
Question details
Year
2025
Paper
CSAT
Question
Q26
Section
Numerical Ability
Sub-topic
Prime Numbers
Type
Number theory
Difficulty
Hard
Source hint
Number theory
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