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29 Jun 2026, 04:19
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This is pretty much exactly how I solved it too. Took roughly a minute. Since we want to get the wages equal we will obviously first subtract the wages from the reimbursement amount, so (d-t). This eliminates 2 of the options.
Then looking at b, it doesnt include anything when person 1 worked x hours more than person 2, so we can eliminate that.
Only 2 left are A and E, the only difference between the 2 being (y-x) and (y+x).
Now, logically speaking, if we wanted to get both of their wages equal to each other, why would we ever add the total hours with the extra hours worked? We would subtract it. Leaving us with A.
Can someone tell me if this thinking is correct?
Then looking at b, it doesnt include anything when person 1 worked x hours more than person 2, so we can eliminate that.
Only 2 left are A and E, the only difference between the 2 being (y-x) and (y+x).
Now, logically speaking, if we wanted to get both of their wages equal to each other, why would we ever add the total hours with the extra hours worked? We would subtract it. Leaving us with A.
Can someone tell me if this thinking is correct?
rak08
30 Jun 2026, 09:14
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Hi architkap,
Your elimination is solid all the way up to the final A-vs-E step, and you landed on the right answer. But the reason you gave for that last cut ("we want equal wages, so we'd subtract, not add") is a bit too loose, and it's worth tightening so it doesn't fail you on a harder variant.
Here's the thing: getting the two hourly rates equal has nothing to do with adding or subtracting x. Both women are paid the same rate, (d-t)/y. The (y-x) vs (y+x) part isn't about equalizing rates at all - it's about whose hours you're multiplying that rate by.
What (y-x) and (y+x) actually mean
From the total/difference setup:
- Jia (worked fewer hours) = (y-x)/2
- Shawna (worked more hours) = (y+x)/2
The question asks how much Shawna gives Jia - i.e., Jia's pay. So you need Jia's hours, which is (y-x)/2. That's exactly the (y-x) in choice A.
Choice E, with (y+x), is Shawna's hours times the rate - it gives Shawna's pay. That's the trap for anyone who solves for the wrong person (a few people in this very thread did exactly that).
So the clean reason to pick A over E isn't "subtract to equalize" - it's "Jia worked the smaller share of the hours, and Jia is who we're paying."
Quick check to lock it in
Let y = 10, x = 2. Then Shawna works 6 hours, Jia works 4.
- (y-x)/2 = 8/2 = 4 - that's Jia ✓
- (y+x)/2 = 12/2 = 6 - that's Shawna
Plus is the bigger person, minus is the smaller one - match it to who the question is asking about, and A vs E decides itself.
Answer: A
Your elimination is solid all the way up to the final A-vs-E step, and you landed on the right answer. But the reason you gave for that last cut ("we want equal wages, so we'd subtract, not add") is a bit too loose, and it's worth tightening so it doesn't fail you on a harder variant.
Here's the thing: getting the two hourly rates equal has nothing to do with adding or subtracting x. Both women are paid the same rate, (d-t)/y. The (y-x) vs (y+x) part isn't about equalizing rates at all - it's about whose hours you're multiplying that rate by.
What (y-x) and (y+x) actually mean
From the total/difference setup:
- Jia (worked fewer hours) = (y-x)/2
- Shawna (worked more hours) = (y+x)/2
The question asks how much Shawna gives Jia - i.e., Jia's pay. So you need Jia's hours, which is (y-x)/2. That's exactly the (y-x) in choice A.
Choice E, with (y+x), is Shawna's hours times the rate - it gives Shawna's pay. That's the trap for anyone who solves for the wrong person (a few people in this very thread did exactly that).
So the clean reason to pick A over E isn't "subtract to equalize" - it's "Jia worked the smaller share of the hours, and Jia is who we're paying."
Quick check to lock it in
Let y = 10, x = 2. Then Shawna works 6 hours, Jia works 4.
- (y-x)/2 = 8/2 = 4 - that's Jia ✓
- (y+x)/2 = 12/2 = 6 - that's Shawna
Plus is the bigger person, minus is the smaller one - match it to who the question is asking about, and A vs E decides itself.
Answer: A
architkap
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