Let A Salary/hour = 15
B salary/hour = 10
Let there are 40hours in 5 days of the week.
40*15 = 600, 40*10 = 400

1) Let say A worked only 6 hours = 30*15 = 450
B worked 5 hours in weedays and 1 saturday = 250+20*5 = 450 [ 1 holds]
2) Yes holds, without a weekend work reaching equal wages is tough..
I havent looked into third as 1 and 2 holds...

ankur.agrawal wrote:Alan's regular hourly wage is 1.5 times Barney's regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

Let's think things through logically:

1) we know that they worked the same number of hours during the week;
2) we know they earned the same total salary for the week;
3) we know that Alan's regular wage is higher; and
4) we know that Barney gets paid double time on Saturdays.

If they only worked Monday-Friday, then there's no way that Barney could earn the same salary for the week as Alan. So, we can quickly conclude that Barney must have worked on Saturday. Accordingly, (II) must be true: eliminate (A) and (D).

Now let's think about the other statements. (I) should be immediately suspect because it talks about Monday through Friday, but doesn't mention Sunday at all. Nowhere does it say that they take Sunday off. Accordingly, there's no way we can draw a definite conclusion about Monday-Friday and (I) isn't a "MUST be true": eliminate (C).

Sadly, we still have two choices left, so we have to think about (III). It's tempting to conclude that (III) is true, but since Alan's wage is the same throughout the week, we can come up with extreme scenarios in which Barney earns less money than Alan on Saturday, rather than more. For example:

A's regular wage is $15/hour, B's is $10/hour, so B's Saturday wage is $20/hour.

A works 10 hours on Saturday, earning $150.
B works 5 hours on Saturday, earning $100, and 5 hours on Friday, earning $150.

Each has worked 10 hours, each has earned $150 total, and A has actually earned more money on Saturday than B.

Accordingly, (III) is not a "MUST be true": choose (B) II only.

* * *

A note to HSPA on picking numbers: when a question asks what MUST be true, picking one set of numbers isn't always good enough. You proved that (I) COULD be true, but not that it's ALWAYS true, which is what this question demands.

In fact, when you pick numbers on a MUST BE TRUE question, your goal should be to pick numbers to show that the statement COULD BE FALSE; as soon as you show that it's not necessarily true, you can eliminate any answers that include that statement.

Very tough, I assumed that since sunday salary is not mentioned it is zero.. Only 6 days are valid in a week.

Hi stuart,
Kindly provide a mathematical equation which proves 'I' as false while holding equal hours and equal wage conditions.

HSPA wrote:Very tough, I assumed that since sunday salary is not mentioned it is zero.. Only 6 days are valid in a week.

Hi stuart,
Kindly provide a mathematical equation which proves 'I' as false while holding equal hours and equal wage conditions.

Hi,

we can't prove (I) is false, but that's not what we need to do to disqualify it - we merely need to show that it COULD be false.

We can certainly pick numbers to show that (I) need not be true, let's just change the days that I used for my counter example to (III):

A's regular wage is $15/hour, B's is $10/hour, so B's Saturday wage is $20/hour.
A works for 10 hours on Monday, earning $150.
B works for 5 hours on Saturday, earning $100, and 5 hours on Friday, earning $50.

They've each earned $150, they've each worked 10 hours total. A worked 10 hours Mon-Fri, B worked 5 hours Mon-Fri, so it's NOT true that A worked fewer Monday-Friday hours than did Barney.

In fact, (I) doesn't really make much sense - for B to earn the same weekly salary as A, B needs to work some of his hours on Saturday, making us think that the opposite of (I) is likely to be the case (actually, now that I look at your solution in more details, even the numbers you pick show that (I) could be false). The whole "what about Sunday" angle just let us quickly eliminate (I) without thinking about it at all.