The sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is:

Let the three prime numbers be p
1
​
,p
2
​
, and p
3
​
.
Given that their sum is 90 (an even number):

p
1
​
+p
2
​
+p
3
​
=90
Since the sum of three numbers is even, either all three numbers must be even, or one must be even and two must be odd.
Since 2 is the only even prime number, one of the primes must be 2. Let p
1
​
=2.

2+p
2
​
+p
3
​
=90⟹p
2
​
+p
3
​
=88
We are also given that one prime number exceeds another by 30. Let p
3
​
−p
2
​
=30.
Now we have a linear system of equations:

p
3
​
+p
2
​
=88

p
3
​
−p
2
​
=30

Adding the two equations:

2p
3
​
=118⟹p
3
​
=59
Subtracting the equations:

2p
2
​
=58⟹p
2
​
=29
Check if 29 and 59 are prime: Yes, both are prime.
Thus, the three prime numbers are 2,29, and 59.
Comparing with the options, 59 is present.