BTGmoderatorDC wrote:If Mary always takes the same route to work, how long did it take Mary to get to work on Friday?

(1) It took Mary 20 minutes to get to work on Thursday.

(2) Mary's average speed on her trip to work was 25 percent greater on Thursday than it was on Friday.

? = time took on Friday (route is fixed)

(1) Insufficient

Mary could have taken 20min on Friday (same as the day before) or 30min (if she got traffic, for instance)

(2) Insufficient

Imagine the distance (route) was 100 km.

> Mary´s speed could have been 100 km/h on Friday (if 125 km/h on Thursday) and in this case ? = 1h
> Mary´s speed could have been 80 km/h on Friday (if 100 km/h on Thursday) and in this case ? = 100/80 h is different from 1h.

(1+2) When distance is fixed, we have (average speed may be considered constant) speed and time inversely proportional, hence

(*) Vthursday = (5/4) Vfriday ==> Tthursday = (4/5) Tfriday.

We have Tthursday (20min) , hence Tfriday is a unique numerical value, hence (1+2) is Sufficient.

(*) We usually prefer "V" for speed (although velocity is a vector, in which speed is only its magnitude), because in many countries "S" is reserved for space ("distance").

The above follows the notations and rationale taught in the GMATH method.

Average speed = distance / time taken
Mary takes the same route to work. Hence, distance is constant.
So, how long did it take Mary to get to work on Friday?
Thus, time taken = distance / average speed
20 mins = distance/(time taken)
If mary's speed for Friday changes, time taken will also change.
$$average\ speed=\frac{dis\tan ce}{20\ \min s}$$
Statement 1 does not provide sufficient information to calculate the average speed. Hence, statement 1 is INSUFFICIENT.
Statement 2; Mary's average speed on her trip to work was 25% greater on Thursday than it was on Friday.
$$\left(average\ speed\ on\ Thursday-Friday\right)=25\%=\frac{dis\tan ce}{20\ \min s}$$
$$25\%=\frac{dis\tan ce}{time},\ and\ time=\frac{dis\tan ce}{25\%}$$
No specific information about the distance covered. Hence, statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together;
Mary's speed on Thursday = distance / 20 minutes

Mary's speed on Friday = distance / (time * 25%)

$$\frac{d}{20}=\frac{d}{t\cdot25\%}$$
$$\frac{d}{20}=\frac{d}{t\cdot0.25}$$
$$\frac{\left(t\cdot0.25\cdot d\right)}{d}=\frac{\left(20\cdot d\right)}{d}$$
$$t=\frac{20}{0.25}=80\min s$$
Neither statement 1 nor statement 2 is SUFFICIENT alone but both statement combined together is SUFFICIENT

Therefore, ANSWER = OPTION C