Barrons New GRE 19th Edition Possible Inequality Mistake

[barbaadr]

The question presents the following equation:

1/c = 1 + 1/d; c and d are positive.

Which is larger, quantity C or quantity D?




The books answer is posted below (B).




I chose (D), the answer is impossible to determine.

Woudln't the inequality change if c = 1/2 vs. c=2?

Please help!

[apo]

HI,

left side of the equation can not be less than 1, because the right side of equation is already more than 1.
So, 1/c > or = 1. Then 0 < c < = 1.
1. If C=1 then D should be very big number so that right side of equation equals the left side.
2. if 0 < C < 1. let's say C = 1/3. then 1/c = 3. In that case D should equal to 1/2, 1+1/d = 3. So D is always bigger than C.
I hope it helped

[barbaadr]

Yes! Thank you. I got so caught up in in the single variable C, I wasn't making sure the equation was balanced.

[twohundredping]

I think rearranging the equation is the best way to do this problem.

1/c = 1 + 1/d
1 = c * (1 + 1/d) (multiply by c)
d = c * (d + 1 ) (multiply by d)
d / (d + 1) = c

Since d is positive, we know that d / (d + 1) is less than d. So c is less than d.