given d>0 and 0<1-c/d<1>0 C is also > 0
So I must be true
c^2 + d^2 is some thing like 1.01d^2 to 1.81d^2 If d=1/10 we will have a value less than 1. If d is 1 or more we will have a value greater than 1. So it need not be true.
I & II must be true and hence C
number properties from GMAT paper test...hard
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
Chidec is correct.
c has to be less than d in order for c/d to be less than 1. However, if d is a decimal (or some fraction), then c can still be a decimal less than d.
When you square both of them, they get smaller, and do not need to add to 1.
For example
d = 0.5 = 1/2
c = 0.25 = 1/4
c / d = . 5
c^2 = 1/16 d^2 = 1/4 c^2+d^2 = 5/16 < 1
I admit, I got this wrong, so it was a good reminder problem. You just have to always look at different types of answers, namely negative, positive, zero, and fractions when solving questions
In this case, 0 and negative is already ruled out. but I just imagined positives greater than 1, rather than including the fractions.
c has to be less than d in order for c/d to be less than 1. However, if d is a decimal (or some fraction), then c can still be a decimal less than d.
When you square both of them, they get smaller, and do not need to add to 1.
For example
d = 0.5 = 1/2
c = 0.25 = 1/4
c / d = . 5
c^2 = 1/16 d^2 = 1/4 c^2+d^2 = 5/16 < 1
I admit, I got this wrong, so it was a good reminder problem. You just have to always look at different types of answers, namely negative, positive, zero, and fractions when solving questions
In this case, 0 and negative is already ruled out. but I just imagined positives greater than 1, rather than including the fractions.
Last edited by zacharyz on Fri May 30, 2008 8:52 am, edited 1 time in total.
-
getneonow
- Senior | Next Rank: 100 Posts
- Posts: 42
- Joined: Fri Mar 14, 2008 1:56 am
- Location: India
- Thanked: 4 times
- GMAT Score:730
I will go with option B as the answer..only 2 is correct
0 < 1 - c/d <1> -1 < -c/d <1> -1 < c/d <1>0
=> -d < c < d
Thus c can be +ve or -ve
and we clearly see that c/d < 1
nothing can be said abt c^2+ d^2
so B will be the answer
Neo
0 < 1 - c/d <1> -1 < -c/d <1> -1 < c/d <1>0
=> -d < c < d
Thus c can be +ve or -ve
and we clearly see that c/d < 1
nothing can be said abt c^2+ d^2
so B will be the answer
Neo
MBA : My passion and My pursuit
-
gmatinjuly
- Master | Next Rank: 500 Posts
- Posts: 101
- Joined: Tue May 27, 2008 6:03 am
- Thanked: 5 times
getneonow
Here is by your approach I think when u subtracted 1 then you didnt apply it to the 0
0 < 1 -c/d < 1
-1 < -c/d <0> c/d > 0
As d > 0 , for c/d to be betweeen 0 and 1
1. c < d (Fraom c/d <1> 0 (From c/d > 0)
Also that doesnt imply anything about values of C nad D
So we can have c = 2 and d = 4 where c^2+ d^2 > 1
or c = 0.4 and d= 0.5 where c^2+ d^2 < 1
So C is the answer
Here is by your approach I think when u subtracted 1 then you didnt apply it to the 0
0 < 1 -c/d < 1
-1 < -c/d <0> c/d > 0
As d > 0 , for c/d to be betweeen 0 and 1
1. c < d (Fraom c/d <1> 0 (From c/d > 0)
Also that doesnt imply anything about values of C nad D
So we can have c = 2 and d = 4 where c^2+ d^2 > 1
or c = 0.4 and d= 0.5 where c^2+ d^2 < 1
So C is the answer
