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26 Oct 2025, 02:55
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I thought that : the total in the first mixture had to be divisible by 4, and the total in the second mixture had to be divisible by 10. since I knew that the difference between the first and the second mixture was in the number of peanuts (8): I looked at the answer choice for a number that was divisible by 10 when 8 was subtracted from it.
Toma13
17 May 2026, 08:37
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Mixture 1)
Assuming the peanuts % in the total
Peanuts ---- cashews = total
1 * p + 0 * c = 3/4 (t)
Mixture 2)
Assuming the peanuts % in the total
Peanuts ---- cashews = total
1 * (p - 8) + 0 * c = 7/10 (t-8)
Solve mix (2) but substituting p = 3/4 t
Assuming the peanuts % in the total
Peanuts ---- cashews = total
1 * p + 0 * c = 3/4 (t)
Mixture 2)
Assuming the peanuts % in the total
Peanuts ---- cashews = total
1 * (p - 8) + 0 * c = 7/10 (t-8)
Solve mix (2) but substituting p = 3/4 t
27 Jul 2026, 11:24
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Hi onlyPlanA,
I get why that line tripped you up, but let's look at how the sentence is built, because the structure actually points you to the right reading.
The sentence pairs two comparisons, and both are measured against the first mixture:
- "the same number of pounds of cashews as the first mixture" - cashews vs. the first mixture's cashews
- "but 8 fewer pounds of peanuts" - peanuts vs. the first mixture's peanuts
Each half compares like to like: cashews to cashews, peanuts to peanuts. The "8 fewer" attaches to peanuts, so it means 8 fewer than the first mixture's peanuts - not 8 fewer than its cashews. Nothing in the sentence ever compares peanuts to cashews.
That's exactly why the setup in the thread reads:
- First mixture peanuts = 3T/4
- Second mixture peanuts = 3T/4 - 8
and the cashews stay equal in both. Solving gives T = 48, choice C.
A quick way to feel the grammar
Try this simpler sentence -
"Ben has the same number of pens as Ann, but 3 fewer pencils."
Here "3 fewer pencils" clearly means 3 fewer than Ann's pencils, not 3 fewer than Ann's pens. The item right after "fewer" tells you what's being compared, and it's always matched to the same item in the other person's set. Same logic locks in the peanuts-to-peanuts reading here.
Answer: C
I get why that line tripped you up, but let's look at how the sentence is built, because the structure actually points you to the right reading.
The sentence pairs two comparisons, and both are measured against the first mixture:
- "the same number of pounds of cashews as the first mixture" - cashews vs. the first mixture's cashews
- "but 8 fewer pounds of peanuts" - peanuts vs. the first mixture's peanuts
Each half compares like to like: cashews to cashews, peanuts to peanuts. The "8 fewer" attaches to peanuts, so it means 8 fewer than the first mixture's peanuts - not 8 fewer than its cashews. Nothing in the sentence ever compares peanuts to cashews.
That's exactly why the setup in the thread reads:
- First mixture peanuts = 3T/4
- Second mixture peanuts = 3T/4 - 8
and the cashews stay equal in both. Solving gives T = 48, choice C.
A quick way to feel the grammar
Try this simpler sentence -
"Ben has the same number of pens as Ann, but 3 fewer pencils."
Here "3 fewer pencils" clearly means 3 fewer than Ann's pencils, not 3 fewer than Ann's pens. The item right after "fewer" tells you what's being compared, and it's always matched to the same item in the other person's set. Same logic locks in the peanuts-to-peanuts reading here.
Answer: C
onlyPlanA
