Problem Solving

if d>0 and 0<1-c/d<1, which of the following must be true?

I. c>0
II. c/d<1
III. c^2 + d^2 > 1

a. I only
b. II only
c. I and II only
d. II and III only
e. I, II, and III

Answer is C

IMO E

Are u sure its C??

ST wrote:if d>0 and 0<1-c/d<1, which of the following must be true?

I. c>0
II. c/d<1
III. c^2 + d^2 > 1

a. I only
b. II only
c. I and II only
d. II and III only
e. I, II, and III

Answer is C

Answer should be (C).

A) If d > 0, c should also be (+) b/c 1-(-c/d) will give you something greater than 1, which does not follow the requirement 0<1-c/d<1.

B) c/d should be < 1 b/c if they are greater than 1: 1-(c/d) will result in a negative number which does not follow the requirement 0<1-c/d<1.

C) does not have to be necessarily true: suppose c = 1/4, d = 1/2

c/d = 1/2 which is in b/w 0<1-c/d<1.

But (1/4)^2 + (1/2)^2 = 1/16 + 1/4 = 5/16 < 1

Therefore C does not hold true.

I am still confused....

ST wrote:I am still confused....

Ok lets try to deconfuse you:)

d>0 and 0<1-c/d<1

0<1-c/d<1
here I am sure you would agree that 0<c/d<1, because if you subtract something from 1 and the result is between 0 and 1, the subtracted part must be between 0 and 1
in other words,
0<1-c/d<1
subtract 1 from all the terms
-1<-c/d<0
or, 1>c/d>0

d>0
so c must be >0
so I and II are true
now C and D are >0 but not necessarily >1
so if they are fractions then C^2+D^2 is not always >1
take the example of c=1/888080808080 and d=1/23728378787

Thank you. Got it.