MI3 wrote:Q: Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack' hourly wage was how many dollars per hour more than Mark's?
(1) Before the wage increases, Jack's hourly wage is $5 per hour more than Mark's
(2) Before the wage increases, the ratio of the Jack's hourly wage to Mark's hourly wage is 4 to 3.
Ans - A
If you increase two quantities by 6%, you'll increase the difference between them by 6% as well, which makes Statement 1 sufficient here. To see this, say that before their wage increase, Jack earned J dollars per hour, and Mark earned M dollars per hour. If their wages increase by 6%, they are multiplied by 1.06, so after their wage increase, Jack earns 1.06J dollars per hour and Mark earns 1.06M dollars per hour. If you look at the new difference in their wages:
1.06J - 1.06M = 1.06(J - M)
you can see that this new difference is 1.06 times, or 6% greater than, the old difference in their wages. So if Jack earned $5 more per hour than Mark before the 6% increase, he will earn (1.06)(5) = 5.30 dollars per hour more after they each receive a 6% pay jump.
Statement 2 is not sufficient. You can just imagine any two scenarios to see this, though I tend to find it easiest to imagine two extremes. Perhaps before the increase, Jack earns $4 per hour and Mark earns $3 per hour, or perhaps Jack earns $4,000,000 per hour and Mark earns $3,000,000 per hour. After a 6% increase, the difference in their wages is going to be much bigger in the second case than in the first.
