Here is the answer for yesterday’s Workbook Wednesday challenge problem!
Question
Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of 
every 10 minutes (so that after 10 minutes its speed is 
, after 20 minutes its speed is 
, and so forth). Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?
1)
2) 
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
Answer
Since Missile 1′s rate increases by a factor of every 10 minutes, Missile 1 will be traveling at a speed of 
miles per hour after 60 minutes:
| minutes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60+ |
| speed |  |
 |
 |
 |
 |
 |
|
And since Missile 2′s rate doubles every 10 minutes, Missile 2 will be traveling at a speed of 
after 60 minutes:
| minutes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60+ |
| speed |  |
 |
 |
 |
 |
 |
 |
The question then becomes: Is 
?
Statement (1) tells us that . Squaring both sides yields 
. We can substitute for y: Is 
? If we divide both sides by , we get: Is 
? We can further simplify by taking the square root of both sides: Is 
? We still cannot answer this, so statement (1) alone is NOT sufficient to answer the question.
Statement (2) tells us that , which tells us nothing about the relationship between x and y. Statement (2) alone is NOT sufficient to answer the question.
Taking the statements together, we know from statement (1) that the question can be rephrased: Is ? From statement (2) we know certainly that , which is another way of expressing . So using the information from both statements, we can answer definitively that after 1 hour, Missile 1 is traveling faster than Missile 2.
The correct answer is C: Statements (1) and (2) taken together are sufficient to answer the question, but neither statement alone is sufficient. 
