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655-705 (Hard)|   Percent and Interest Problems|                        
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KarishmaB
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Full Playlist (DS "Hards" — OG 2024): https://www.youtube.com/playlist?list=P ... xuFStg_I4s

Key Habit for Speed on Data Sufficiency:

We often don't need to actually solve.

We just need to know that we CAN answer the question.

This can save a lot of time on problems with harder calculations.

With 3 UNIQUE LINEAR equations and 3 variables (or 1 equation & 1 variable, 2 equations and 2 variables etc.), we can solve.

Caveats:
⚠️Watch out when it's asking for a "Combo" of two variables. For example, if the question asks for the ratio "X/Y", we can solve with the one equation 2x = 3y. We get "two birds with one stone."
⚠️The equations must be UNIQUE. A common trap is where one equation is just a multiple of the other. For example, x + 2y = 3 and 3x + 6y = 9 are really just the same equation!
⚠️Quadratics often have 2 different solutions for 1 equation. For example, x^2 = 9 has 2 different solutions: x=3 OR x=-3.
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Hi, I think I might know where I got wrong for choosing Statement (1) alone is sufficient but I can't fully explain my logical fallacy in my weighted average technique. Could you please help? Thank you
- Under my thinking about weighted average concept, we have the ratio of x/y (3/4) then we can have the ratio for the amount invested (4/3), from which we can determine the exact amount of each part invested from the total 60k: $60,000x4/7 for x% & $60,000x3/7 for y%
- Now, we can determine the variable x% under the weighted average (WA) of total interests earned $4,080

I've also tried to calculate the exact x% from the above "flip ratio" assumption of the WA. I got exactly 5.95%. Thank you for help.

KarishmaB
gauravk
VeritasPrepKarishma - I was trying to use weighted average with statement 1, can you pls help.

We are given that x/y = 3/4 and we can calculate the overall rate by using the 60,000 and the interest earned 4,080. using this won't we be able to get the ratio in which 60,000 would be invested at X and Y%?

Won't we enough data with equation 1 itself to solve it for X%?

TIA

Using weighted averages,

4080/60,000 = 6.8%

Using stmnt 1:
w1/w2 = (4x/3 - 6.8)/(6.8 - x)
Now here is the problem: We don't know w1/w2 using stmnt 1 alone. So we cannot calculate the value of x.

Using stmnt 2, we get the value of w1/w2 which is 3/2. But here we don't have the ratio of x and y.

So you need both statements to get

3/2 = (4x/3 - 6.8)/(6.8 - x)

And now you can get a unique value of x.

Answer (C)
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