Alan Barney hourly wage

[brij.jhu]

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 worked the same total 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.

The correct answer given is II. But there's nothing in the question that disqualifies the case where both Alan and Barney worked 0(zero) hours for the entire week, in which case II is also false.

[amitganguly2k12]

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 worked the same total number of hours last week, and earned the same total in wages, which of the following must be true?

Assume daily working hours = 5 (Monday-Friday) for both Alan and Barney.
Assume Per hour Wage for Barney = $10.
Therefore Per hour wage for Allan = $15.

Let Allan work for x number of hours on Saturday,so that the Weekly total wages for Allan and Barney are equal.

that means 15 * 6 * 5 hrs (Allan's weekly wage Mon - Sat ) = (10 * 5 (days) * 5 hrs) + (10 * 2 * x)

By solving you get x = 10hrs.

So you can observe :

1.Barney has to work at-least an Hour on Saturday for the wages to be 'closer numerically but not equal'.

2.'Barney made more money on Saturday than did Alan' - that will be clearly case sensitive as it will depend upon the numerical difference between the wages till Friday.

[esledge]

The correct answer given is II. But there's nothing in the question that disqualifies the case where both Alan and Barney worked 0(zero) hours for the entire week, in which case II is also false.

You may have a valid concern here. On the one hand, the use of the past tense verbs "worked" and "earned" implies that both did in fact work at least 1 hour and both earned some money. On the other hand, in common speech, unemployed people may say "I earned $0 last week" or "I worked 0 hours last week." I still think you'd be more likely to hear the verb in the negative: "I did not earn any money last week" or "I did not work last week" but a math question probably shouldn't split hairs like this.

I'm going to refer this one to our curriculum group for review. Thanks for the critical thinking!

[gauragar]

III Barney made more money on Saturday than did Alan.

Seems to be also true. As if both Alen and Barney worked for some hours, then for wages to be equal, Barney has to definitely earn more on Saturday the Alen.

[mschwrtz]

.

[mschwrtz]

"III Barney made more money on Saturday than did Alan.

Seems to be also true. As if both Alen and Barney worked for some hours, then for wages to be equal, Barney has to definitely earn more on Saturday the Alen."

No. Suppose that Alan worked 12 hours Saturday, all at $15/hr, while Barney worked 6 hours M-F at $10/hr, and 6 hours Saturday at $20/hr. That satisfies all the conditions, but Alan earned more on Saturday than does Barney.

[rajatsureka]

I have a small doubt to clarify

the question says "Both men work an integer number of hours on any given day". Doesn't it mean that both of them worked equal number of hours on any day. Or, does it mean that the cumulative number of hours on any given day is equal?

[jnelson0612]

I have a small doubt to clarify

the question says "Both men work an integer number of hours on any given day". Doesn't it mean that both of them worked equal number of hours on any day. Or, does it mean that the cumulative number of hours on any given day is equal?

To me it means that each man works an integer number of hours. Each man may work a different number of hours from the number the other works, but neither works a non-integer number of hours (for example, neither works 3.5 hours).

[sabyasachi.nayak8]

A small doubt, may be a silly one:
Is it possible that the previous week Allan worked 6 hrs a day Monday through Friday and Barney worked for 9 hrs a day Monday to Friday?
If this scenario is possible then both of them will end up earning the same amount without B having to work on a Saturday.

[tim]

But then they're not working the same number of hours. Check the constraints of the problem.

[RonPurewal]

you can actually solve this problem without doing any math. in fact you needn't realize anything beyond the following:

• B's usual wage is lower than A's.

• for the week under discussion, B's average wage is the same as A's.

• therefore, B must have gotten 'bonus' wages.

• B only gets 'bonus' wages on saturdays.

there you go.

[RonPurewal]

here, you can make further realizations, too.

let's say that B's usual wage (paid on non-saturdays) is 'x' dollars/hour.
then, on saturdays, B makes 2x dollars/hour.

B's average wage for the whole week is 1.5x dollars/hour (since it's the same as A's average wage).

this is exactly halfway between x and 2x. thus we have a weighted average with equal 'weights'.

...in other words, B must have worked as many hours on saturday alone as he worked for the entire rest of the week combined.

that's one heck of a saturday... O:

--

of course, this is WAY too much reasoning for the problem at hand. for the current problem there's little point in going beyond what i wrote in the previous post.

however, in reviewing this problem it's useful to delve further into what's happening, since whatever you discover might help you on future problems.

[RonPurewal]

oh, and, finally—no, you do not need to worry about 'zero hours worked'. 'tricky' cases will NEVER matter on the exam.

i wrote about this here:
https://www.manhattanprep.com/gmat/foru ... ml#p116154

[tim]

...in other words, B must have worked as many hours on saturday alone as he worked for the entire rest of the week combined.

that's one heck of a saturday... O:

Sounds like the life of a math tutor. I look forward to Mondays because I do the vast majority of my work on the weekends.

[RonPurewal]

...in other words, B must have worked as many hours on saturday alone as he worked for the entire rest of the week combined.

that's one heck of a saturday... O:

Sounds like the life of a math tutor. I look forward to Mondays because I do the vast majority of my work on the weekends.

i actually look forward to my work.

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