If Nicole worked 20% more this week than she worked last week, how many hours did she work last week?

[BTGmoderatorLU]

Source: Manhattan Prep

If Nicole worked 20% more this week than she worked last week, how many hours did she work last week?

1) Nicole worked 36 hours this week.
2) Nicole worked 6 more hours this week than she worked last week.

The OA is D

[deloitte247]

Let the number of working hours last week = x
no. of working hours this week = (20% of x) + x
Questioning=> How many hours did she work last week? (i.e we want to find the value of x).
Statement 1: Nicole worked 36 hours this week.
$$\left(\frac{20}{100}\cdot x\right)+x=36\ hours$$
$$\frac{x}{5}+x=36\ hours$$
$$\left(\frac{1+5}{5}\right)x=36\ hours$$
$$\frac{6x}{5}=36\ hours$$
$$x=\frac{36\cdot5}{6}=30\ hours$$
Therefore, statement 1 is SUFFICIENT.

Statement 2: Nicole worked 6 more hours this week than she worked last week.
$$\left(20\%\ of\ x\right)+x=\left(x+6\right)\ hours$$
$$\frac{x}{5}+x=\left(x+6\right)\ hours$$
$$\frac{6x}{5}-x=6\ hours$$
$$\frac{6-5}{5}x=6\ hours$$
$$x=30\ hours$$
Statement 2 is also SUFFICIENT.

Answer = option D