In each quarter of 1998, Company M earned more money than in the

We know range of a set= Highest value-Lowest value
Here the set={\({Q_1,Q_2,Q_3,Q_4}\)}, so range=Q_4-Q_1 (where \(Q_1<Q_2<Q_3<Q_4\) is given.)------------(1)

St1:- \(Q_2<Q_3\)
But we need \(Q_1\) and \(Q_4\) in order to determine range.
Not sufficient to determine range.

St2:- Exactly the value of \(Q_1\) and \(Q_4\) is provided.
We can definitely determine range by substituting the values in (1).
Sufficient.

Ans. (B)

Since we are asked to find out the range of the earnings question is asking diff of 4th and 1st quarter earnings
St1: provide 2nd and 3rd qtr earnings hence NS
St2: provide 1st and 4th qtr earning hence SUFFICIENT.

Ans choice B

Isn't 1 statement 1 also sufficient to answer this?

if we take the earnings as x for 1st quarter and add M for second and 2 M for third and 3 M for fourth, giving us x, x+M, x+2M and x+3M

And hence subtracting 2nd and 3rd quarter earnings to get the value of X and M to get the range???

I get what others have posted regarding the range but how is my approach wrong?

\(Range = Greatest - Smallest \)

\(Given, \)

\(First \ Quarter < Second \ Quarter < Third \ Quarter < Fourth \ Quarter \)

So, the Range = Fourth Quarter - First Quarter

(1) We don't about the First and Fourth Quarter; Insufficient.

(2) Sufficient.

The answer is B

Question Stem Analysis:

Remember that the range of a set is defined to be the difference between the largest and the smallest values in that set. Since we are told that the company earned more many than the previous quarter in each quarter of 1998, the company earned the smallest amount of money in the first quarter and the largest amount of money in the fourth quarter. So, the question really is asking for the difference between the earnings in the fourth quarter and the first quarter.

Statement One Alone:

\(\Rightarrow\) In the 2nd and 3rd quarters of 1998, Company M earned $4.0 million and $4.6 million, respectively.

Assuming this statement, the only thing we can say about the earnings in the first quarter is that it was less than $4 million, and the only thing we can say about the earnings in the fourth quarter is that it was greater than $4.6 million. There are many possibilities for the first and fourth quarter earnings that would result in a different range. For instance, if the first quarter earnings were $3 million and the fourth quarter earnings were $5 million, then the range of Company M's quarterly earnings in 1998 is 5 - 3 = $2 million. On the other hand, if the first quarter earnings were $3.9 million and the fourth quarter earnings were $4.7 million, then the range is 4.7 - 3.9 = $0.8 million. Since there are more than one possibilities for the range, assuming statement one alone is not sufficient to answer the question.

Eliminate answer choices A and D.

Statement Two Alone:

\(\Rightarrow\) In the 1st and 4th quarters of 1998, Company M earned $3.8 million and $4.9 million, respectively.

In the question stem analysis, we determined that the range is the difference between the fourth quarter earnings and the first quarter earnings. Thus, the range of Company M's quarterly earnings in 1998 was 4.9 - 3.8 = $1.1 million. Statement two alone is sufficient.

Answer: B

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