A woman invested $1000, part at %5 and the rest at %6.
Her total investment with interest at the end of the year
was $1053. How much did she invest at %5.
1) 500
2) 600
3) 700
4) 900
5) 950
OA is C
money
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Interest earned = 53.grandh01 wrote:A woman invested $1000, part at %5 and the rest at %6.
Her total investment with interest at the end of the year
was $1053. How much did she invest at %5.
1) 500
2) 600
3) 700
4) 900
5) 950
OA is C
We can plug in the answers, which represent the amount invested at 5% interest, with the balance invested at 6% interest.
Answer choice C: 700
.05(700) + .06(300) = 35+18 = 53.
Success!
The correct answer is C.
An alternate approach:
Combined interest rate = 53/1000 * 100 = 5.3%.
At its core, this is a MIXTURE problem: an interest rate of 5% is MIXED with an interest rate of 6% to earn a combined interest rate of 5.3%.
To determine (amount invested at 5%) : (amount invested at 6%), we can use alligation.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (5% and 6%) on the ends and the combined percentage (5.3%) in the middle.
5%-----------5.3%-------------------6%
Step 2: Calculate the distances between the percentages.
5%-----.3----5.3%---------.7---------6%
Step 3: Determine the ratio in the mixture.
The ratio in the mixture is the RECIPROCAL of the distances in red.
(amount invested at 5%) : (amount invested at 6%)= .7 : .3 = 700:300.
Thus, the amount invested at 5% interest = 700.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
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For this one you can try and plug in the options.
I always start with the middle one so hit the jackpot here.
Say $700 was at 5%
So at the end of the year the woman will get = 735
Remaining $300 was at 6%. So end of the year the woman will get = 318.
Add the two and you will get $ 1053.
So answer is $ 700. You can try this for all options and check.
I always start with the middle one so hit the jackpot here.
Say $700 was at 5%
So at the end of the year the woman will get = 735
Remaining $300 was at 6%. So end of the year the woman will get = 318.
Add the two and you will get $ 1053.
So answer is $ 700. You can try this for all options and check.
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Thous options work well. For me I like algebraic approaches (everyone's different). For an algebraic approach:grandh01 wrote:A woman invested $1000, part at %5 and the rest at %6.
Her total investment with interest at the end of the year
was $1053. How much did she invest at %5.
1) 500
2) 600
3) 700
4) 900
5) 950
OA is C
Original Amount =1000
New Amount = 1053
So there was 53 in interest (1053-1000)
Now set up an unknown variable. We want to know how much earned 5%, so lets say that is x
Our Equation:
.05x+.06(1000-x) = 53. Do you understand how I came up with this equation?
-.01x=60=53
-.01x=-7
x=700
The correct answer is C
A useful website I found that has every quant OG video explanation:
https://www.beatthegmat.com/useful-websi ... tml#475231
https://www.beatthegmat.com/useful-websi ... tml#475231
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Assume she invested x$ at 5% and (1000 - x)$ at 6%. It then follows that:
0.05(x) + 0.06(1000 - x) = 53
60 - 0.01(x) = 53
x = $700 at 5%.
0.05(x) + 0.06(1000 - x) = 53
60 - 0.01(x) = 53
x = $700 at 5%.