A certain company assigns ID numbers to its new employees such that ea

Question

A certain company assigns ID numbers to its new employees such that each ID number is an integer. After the first two employees' ID numbers, each ID number is the sum of the ID numbers of the two most recently hired employees. What is the ID number of the employee who was hired sixth?

1. The ID number of the employee who was hired seventh is 49 more than the ID number of the employee who was hired fifth.

2. The sum of the ID numbers of the employee who was hired fifth and the employee who was hired sixth is 80.

fluke · Answer

ID_3=ID_1+ID_2 
 ID_4=ID_2+ID_3 
 ID_5=ID_4+ID_3

Q: What is  ID_6?

ID_6=ID_5+ID_4

1. The ID number of the employee who was hired seventh is 49 more than the ID number of the employee who was hired fifth.

ID_7=ID_5+ID_6 
 ID_7=ID_5+49 
 ID_5+ID_6=ID_5+49 
 ID_6=49 
Sufficient.

2. The sum of the ID numbers of the employee who was hired fifth and the employee who was hired sixth is 80.

ID_7=ID_5+ID_6=80

ID_5+ID_6=80

Not Sufficient.

Ans: "A"

subhashghosh · Answer

Id # 1 = x

Id # 2 = y

Id3 = x + y

Id4 = x + 2y

Id5 = 2x + 3y

Id6 = 3x + 5y = ?

Id7 = 5x + 8y

(1) 5x + 8y = 49 + Id5

So Id6 = 49, sufficient

(2) 5x + 8y = 80

Insufficient

Answer - A

IanStewart · Answer

This is a really suspect question. If I read a question about ID numbers, I'm going to assume two things:

a) ID numbers can't be negative (does any real world company use negative numbers for IDs?)
b) ID numbers are unique - different employees need different IDs (an ID number is not an ID - that is, an identifier - at all if two people can have the same ID)

Notice if b) is true, this would mean that neither of the first IDs can be equal to 0 (because if, say, the first ID is 0 and the second ID is 5, then the third ID would also be 5).

Now if we assume both of the above, the answer to the question is not A; it is D:

Statement 1 is sufficient alone, because ID_7 = ID_6 + ID_5, so if ID_7 = 49 + ID_5, certainly ID_6 is 49.

Now, for Statement 2, let's suppose that our first ID number is f, and our second ID number is s. Then we have:

ID_1 = f
ID_2 = s
ID_3 = f + s
ID_4 = f + 2s
ID_5 = 2f + 3s
ID_6 = 3f + 5s
ID_7 = 5f + 8s

Statement 2 tells us that ID_7 = 80, so

5f + 8s = 80

Now 8s and 80 are both multiples of 8. This means that 5f must be a multiple of 8 (if that isn't clear, rewrite the equation as 5f = 80 - 8s = 8(10 - s), to see that 5f is a multiple of 8). If 5f is a multiple of 8, then f is a multiple of 8. If f and s are positive, as we assumed, then the only value of f which is small enough to work in our equation is f=8, in which case s must be 5. Since we can find f and s, we can find the value of ID_6.

So if you assume the IDs are distinct positive integers, which I consider a pretty reasonable assumption, then Statement 2 is sufficient alone. If instead ID numbers can be zero (and thus two different employees can have the same ID) or negative, then Statement 2 is not sufficient. All in all, a pretty dodgy question, since it is open to different interpretations.

Spidy001 · Answer

Let us assume the employee Id sequence as x1,x2 ... for employee 1,2.....
1. x7 = 49 + x5
=> x6+x5 =49 + x5
=>x6 =49
sufficient.
2. x5+x6 =80
 Not enough to calculate x6.
 Not sufficient.
Answer is A.

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