Imo C
whats the OA?
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Source: Beat The GMAT — Problem Solving |
raunekk wrote:i more for C
if v take C=1/2
D= 2/3
Hi raunekk,
if we consider c=1/2 and d = 2/3
then c/d = (1/2 * 3/2) = 3/4
now c= 3 and d = 4
so c^2 + d^2 > 1
please correct me if I am wrong.
thanks,
Ket
.
0 < 1 - c/d < 1
subtract 1 from all sides
-1 < -c/d < 0
multiply all sides by d............as we know d>0, it wont affect the signs or inequality
-d < -c < 0
multiply all sides by -1...........as you do that the signs would change
d > c > 0
this means c > 0 and c< d
you can see I and II will always be true..a direct deduction from ineuality
for III you can prove it wrong by using any two +ve fractions, whose sum is less than or equal to 1
0 < 1 - c/d < 1
subtract 1 from all sides
-1 < -c/d < 0
multiply all sides by d............as we know d>0, it wont affect the signs or inequality
-d < -c < 0
multiply all sides by -1...........as you do that the signs would change
d > c > 0
this means c > 0 and c< d
you can see I and II will always be true..a direct deduction from ineuality
for III you can prove it wrong by using any two +ve fractions, whose sum is less than or equal to 1
ket_gmat wrote:raunekk wrote:i more for C
if v take C=1/2
D= 2/3
Hi raunekk,
if we consider c=1/2 and d = 2/3
then c/d = (1/2 * 3/2) = 3/4
now c= 3 and d = 4
so c^2 + d^2 > 1
please correct me if I am wrong.
thanks,
Ket
hi Ket..
if we once take C=1/2 and D=2/3
then we cant change d values of C and D again as 3 and 4 respectively(ie if we simplify)
the values will remain the same,,,
thus 1/4 + 4/9 = 25/36 <1
correct me if i m wrong,,,
Given d > 0 and 0 < 1 - c / d < 1
I) c > 0 - This (I) must be true because if either c is o and c is negative then the inequality would be false.
Eg: c=0
0 < 1 - 0 / d < 1 i.e 0<1<1 - Not possible
c= -ve
0<1+somevalue<1 - Not possible
2) 0 < 1 - c / d < 1
Add c/d to all sides of the inequality
c/d<1<1+c/d
II must be true (proved above)
3)Consider fractional values for c and d
Let c=1/4 d=1/2
0<1- (1/4) / (1/2) < 1
0< 1/2<1
c^2+d^2 < 1 and not > 1
Therefore C) Hope this helps!
OA?
I) c > 0 - This (I) must be true because if either c is o and c is negative then the inequality would be false.
Eg: c=0
0 < 1 - 0 / d < 1 i.e 0<1<1 - Not possible
c= -ve
0<1+somevalue<1 - Not possible
2) 0 < 1 - c / d < 1
Add c/d to all sides of the inequality
c/d<1<1+c/d
II must be true (proved above)
3)Consider fractional values for c and d
Let c=1/4 d=1/2
0<1- (1/4) / (1/2) < 1
0< 1/2<1
c^2+d^2 < 1 and not > 1
Therefore C) Hope this helps!
OA?
