Bunuel
In a sequence of numbers, if the first number is a positive integer and if each number thereafter is the least prime number greater than the preceding number, what is the value of the fifth number in the sequence?
(1) The sum of the first two numbers in the sequence is equal to the third number in the sequence.
(2) The sum of the third and fourth numbers in the sequence is 8.
DS20395
Given: In a sequence of numbers, if the first number is a positive integer and if each number thereafter is the least prime number greater than the preceding number Let's take a moment to understand what does sequence looks like.
The first term is ANY positive integer, and all terms after that are primes
For example one possible sequence could be {10, 11, 13, 17, 19, ....}
Another one could be: {3, 5, 7, 11, etc}
Target question: What is the value of the fifth number in the sequence? Statement 1: The sum of the first two numbers in the sequence is equal to the third number in the sequence. This statement is not sufficient. Consider these two possible cases:
Case a: The sequence is {1, 2, 3, 5,
7, ...}. This meets the condition that term3 = term1 + term2. In this case, the answer to the target question is
term5 = 7Case b: The sequence is {2, 3, 5, 7,
11, ...}. This meets the condition that term3 = term1 + term2. In this case, the answer to the target question is
term5 = 11Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The sum of the third and fourth numbers in the sequence is 8.We already know that term3 and term4 are PRIME numbers.
Since 3 and 5 are the ONLY prime numbers that add to 8, we can be certain that term3 = 3 and term4 = 5, which means
term5 = 7 (since 7 is the next prime after 5)
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent