Manhattan GMAT CAT Math

[matanyar826]

Here is a question that I have seen on your cat.
I cant understand why E is wrong

The question state that
A. . Both men work an integer number of hours on any given day
B. Alan and Barney each worked for[b] the same total non-zero number of hours last week

C. , and earned the same total in wages


From the above information - Alan and Barney worked the same total number of hours last week and earned the same total in wages, they must have had the same average hourly wage. Alan’s hourly wage is constant, equal to 1.5 times Barney’s regular wage. Therefore, last week, Barney’s average hourly wage must also have been equal to 1.5 times his regular hourly wage. This is only possible if half of Barney’s working hours were at his regular wage, and the other half of his working hours were at twice his regular wage,

E. So if half of Barney’s working hours were at his regular wage, and the other half of his working hours were at twice his regular wage, it means that Barney made more money on Saturday than did Alan.

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?
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
Because Alan and Barney worked the same total number of hours last week and earned the same total in wages, they must have had the same averagehourly wage. Alan’s hourly wage is constant, equal to 1.5 times Barney’s regular wage. Therefore, last week, Barney’s average hourly wage must also have been equal to 1.5 times his regular hourly wage. This is only possible if half of Barney’s working hours were at his regular wage, and the other half of his working hours were at twice his regular wage, i.e., on Saturday. Therefore II is definitely true.

As for the other statements, we cannot tell, because Alan may or may not have worked on Saturday. For example, suppose Barney worked one hour on Monday and one hour on Saturday, for 2 hours total. If Alan worked both of his total of 2 hours on Tuesday, then I is false. If, on the other hand, Alan worked both of his hours on Saturday, then III is false.

[RonPurewal]

i'm sorry, but i can't make sense of this post. i'm going to lock this thread; let's start again.

• per the forum rules, please use the first few words of the problem as the title of the thread.

• please post the problem first.

• if you're quoting from the answer explanation, please indicate this in some way (italics, quote marks, quote tags, etc.)

• please ask at least one specific question.

thanks.