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655-705 (Hard)|   Percent and Interest Problems|                        
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KarishmaB
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A total of $60,000 was invested for one year. Part of this amount earn 25 Apr 2019, 23:13
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VeritasKarishma

I mistakenly read (2) as saying "the amount of interest earned at x" rather than "the amount that earned interest." If it was said in the former way (2) would be sufficient on its own, right? You could find the value of each out of 4080, so you could also determine x% and y% from just (2). Would the GMAT do something tricky like this?

4080/5 = 816
So 2448 at x and 1632 at y.
2448/4080 = .6 and 1632/4080 = .4
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You would still not know the amount invested at x% and the amount invested at y%.

If interest earned is 2448 at x%, what is the amount on which this interest is earned?
You could earn 2448 interest at 10% on 24480.
or you could earn 2448 interest at 5% on 48960.
etc.
x would be different in each case.
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A total of $60,000 was invested for one year. Part of this amount earn Updated on: 13 Jan 2020, 20:44
Originally posted by Probus on 12 Jan 2020, 15:10.
Last edited by Probus on 13 Jan 2020, 20:44, edited 1 time in total.
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here are my two cents for this question

Attachment:
Sample.png
Sample.png [ 9.88 KiB | Viewed 3553 times ]

Avg interest is \( \frac{4080}{60,000} \) =6.8 ( hidden information in Stem)

Using concept of allegations

We have a information that is represented by figure 1 ( From Question Stem)
we can see that we need values of X or Y and 'a' or 'b'. IN this regard if we have any relation in term of X and Y and some relation between 'a' and 'b' .

Now from statement 1:
we have a relation between X and Y but we don't have any relation or values of 'a' and 'b'.

Now from statement 2:

"The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2." This information gives a relation between 'a' and 'b'
But in absence of any information regarding "X" and "Y" we cannot find out the value of "X"

Combining both statements we do have information of "x" and "y" and also information about 'a' and 'b'


Hence Answer C

Avg interest is \( \frac{4080}{60,000} \) =6.8 ( hidden information in Stem)
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A total of $60,000 was invested for one year. Part of this amount earn 11 Sep 2021, 12:59
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Video solution from Quant Reasoning:
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A total of $60,000 was invested for one year. Part of this amount earn 03 Jan 2024, 21:59
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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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A total of $60,000 was invested for one year. Part of this amount earn 15 Oct 2024, 05:21
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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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