Data Sufficiency

Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?

1) d1 is 30 greater than d2

2) r1 is 30 greater than r2


-----------------my doubt----

I understand the reasoning provided in the OG but please let me know why the below method is flawed.

R--T--D
r1 t1 d1
r2 t2 d2

question - is t1 > t2?

t1 = d1/r1------(eq. 1)
t2 = d2/r2------(eq. 2)

using statements 1) and 2) together we have.

t1 = (d2 + 30)/(r2 + 30) ----(eq. 3)
t2 = (d1 - 30)/(r1 - 30) ----(eq. 4)

using eq. 2 & eq. 3

t1 > t2
= (d2 + 30)/(r2 + 30) > d2/r2
= r2(d2 + 30) > d2(r2 + 30)
= 30*r2 > 30*d2
= 1 > d2/r2
= 1 > t2 ---- (eq. 5)

now using eq. 1 & eq. 4
t1 > t2
= d1/r1 > (d1 - 30)/(r1 - 30)
= d1(r1 - 30) > r1(d1 - 30)
= - 30*d1 > -30*r1
= d1/r1 > 1
= t1 > 1 ----- ---- (eq. 6)

combining eq. 5 and eq. 6
t1 > 1 > t2
t1 > t2

I'm thinking the above is flawed because I'm using the same equation to derive equation 5 and 6. Please help. thank you in advance.

ruwan_s wrote:Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?

1) d1 is 30 greater than d2

2) r1 is 30 greater than r2


-----------------my doubt----

I understand the reasoning provided in the OG but please let me know why the below method is flawed.

R--T--D
r1 t1 d1
r2 t2 d2

question - is t1 > t2?

t1 = d1/r1------(eq. 1)
t2 = d2/r2------(eq. 2)

using statements 1) and 2) together we have.

t1 = (d2 + 30)/(r2 + 30) ----(eq. 3)
t2 = (d1 - 30)/(r1 - 30) ----(eq. 4)

using eq. 2 & eq. 3

t1 > t2
= (d2 + 30)/(r2 + 30) > d2/r2
= r2(d2 + 30) > d2(r2 + 30)
= 30*r2 > 30*d2
= 1 > d2/r2
= 1 > t2 ---- (eq. 5)

now using eq. 1 & eq. 4
t1 > t2
= d1/r1 > (d1 - 30)/(r1 - 30)
= d1(r1 - 30) > r1(d1 - 30)
= - 30*d1 > -30*r1
= d1/r1 > 1
= t1 > 1 ----- ---- (eq. 6)

combining eq. 5 and eq. 6
t1 > 1 > t2
t1 > t2

I'm thinking the above is flawed because I'm using the same equation to derive equation 5 and 6. Please help. thank you in advance.

Your mistake is highlighted by RED part of your explanation.

t1 will not essentially be greater than t2 because you have no idea about the value of ratio d2/r2 whether this is greater than or less than 1

The reasoning is as mentioned below:

1) If a/b >1 and x is a positive number
then (a+x) / (b+x) < (a/b)

2) If a/b <1 and x is a positive number
then (a+x) / (b+x) > (a/b)

3) If a/b =1 and x is a positive number
then (a+x) / (b+x) = (a/b)

Is the number seconds required to travel d� feet at r� feet per second greater than the number of seconds required to travel d₂ feet at r₂ feet per second?

(1) d� is 30 greater than d₂
(2) r� is 30 greater than r₂

Sometimes algebra makes a problem harder rather than easier.
Here, I would test values.

Clearly, neither statement alone is sufficient.

Statements combined:
Since d�=d₂+30 and r�=r₂+30, the question stem can be rephrased as follows:
Is (dâ‚‚ + 30)/(râ‚‚ + 30) > dâ‚‚/râ‚‚?

Case 1: dâ‚‚=1 and râ‚‚=1
(1+30)/(1+30) > 1/1
1 > 1.
NO.

Case 2: dâ‚‚=1 and râ‚‚=2
(1+30)/(2+30) > 1/2
31/32 > 1/2.
YES.

Since in the first case the answer is NO, but in the second case the answer is YES, INSUFFICIENT.

The correct answer is E.