12 Days of Christmas GMAT Competition - Day 1: A sequence of integers

Manhattan Prep Official Explanation:

Step 1: Understand the Prompt and Question

Glance at the answers. The numbers suggest a Quant-based question. Further, the sequence formula in the prompt indicates that this is a Formulas problem. Finally, read the question stem. The words “jointly consistent” indicate that this problem cannot be solved independently; you will have to solve for the two columns simultaneously.

Next, read the entire prompt. Since the problem involves a sequence and asks specifically about s4 and s6, jot down blank spaces for each term in that portion of the sequence on your scratch paper:



It is also helpful to understand the sequence notation in the prompt. Any given term sn+1 comes directly after the term sn in the sequence. For example, for s4, the fourth term in the sequence, n = 4. In this case, sn+1 would be s4+1, or s5, which is the very next term in the sequence. . With this in mind, sn+1 = sn + 2 can be understood as “the term directly after the current term can be found by adding two to the current term.” Similarly, sn+1 = sn + 3 can be understood as “the term directly after the current term can be found by adding 3 to the current term.”

Step 2: Plan your Approach

The simple integer answer choices point to Working Backwards as a possible strategy. Additionally, the two different sequence rules render algebraic simplification difficult, since the rule in use might change from term to term.

To work backwards, plug in each answer choice for s4. Then, apply the appropriate sequence rule to figure out what s5 would be. Finally, apply the appropriate sequence rule to figure out what s6 would be. Repeat this process until you arrive at a value for s6 that appears among the answer choices.

Step 3: Solve the Problem

Begin by testing s4 = 5, the first possible answer choice.

Find the next term in the sequence. Since the current term 5 is not divisible by 4, add 3. s5 = 8.

Now find the next term. Since the current term 8 is divisible by 4, add 2. s6 = 10.



Since 10 is not among the answer choices, there is no way to make s4 = 5 jointly consistent with any available answer.

Repeat the same process by testing s4 = 8, the first possible answer choice.

Find the next term. Since the current term 8 is divisible by 4, add 2. s5 = 10.

Now find the next term. Since the current term 10 is not divisible by 4, add 3. s6 = 13.



Since 13 is one of the possible answer choices, s4 = 8 and s6 = 13 are jointly consistent answers.

The correct answer is 8 for the first column and 13 for the second column.