mastvita wrote:

Got this in the practice test. Please help.

Q. Two bookworms, Alpha and Beta, start eating at opposite ends of a 42-volume encyclopedia set (numbered 1 to 42), each working directly towards the other. Alpha starts in vol 1 and Beta starts in vol 42. If each volume is the same thickness, where in the set will they be when they meet?

(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.

(2) Alpha eats two volumes more than Beta every 4 days.

Hi!

This is a classic ratio question. Here's the big rule to remember:

if you multiple or divide the parts, you can solve the ratio; if you add or subtract, you can't.

We know the distance travelled before they worms meet (42), so we need either their individual speeds or their relative speeds.

(1) we know their relative rates (a:b = 3x:5x = 3:5), so we can figure out how much each will eat before they meet: sufficient.

(2) with addition or subtraction, you can't figure out the ratio. We can set up:

a:b = 4x+2:4x

but without knowing the value of x, there's no way to figure out where they'll meet.

For example, if worm a eats 2 volumes per day, then in 4 days worm a eats 8 volumes and worm b eats 6 volumes - our ratio is 8:6 = 4:3.

However, if worm a eats 1 volume per day, then in 4 days worm a eats 4 volumes and worm b eats 2 volumes - our ratio is 4:2 = 2:1.

Since we can get different ratios, (2) is insufficient.

(1) is sufficient, (2) isn't: choose (A).