Ms. Morris invested in Fund A and Fund B. The total amount

Question

Ms. Morris invested in Fund A and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A?
(A) $32,000
(B) $36,000
(C) $40,000
(D) $44,000
(E) $45,000

For this question, one could do an algebraic solution, but would it be faster to backsolve from the answers? I would argue for the latter, though I imagine there will be a difference of opinions on this question.

My argument, along with a discussion of backsolving in general and a complete solution to this problem, is here:
https://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/

Perhaps other experts would also like to chime in on the issue of when to solve algebraically vs. when to backsolve.

Mike :-)

EvaJager · Answer

The correct answer should be 42,000, and it is not listed neither above, nor in the question you published on your blog. 
It just appears in the solution you posted.

mikemcgarry · Answer

Yes, you're right --- a mistake on my part --- the OA is $42,000, and I just corrected the question above & the blog. Thank you very much. Mike :-)

chibimoon · Answer

Could someone post the algebraic way please

Amateur · Answer

A+B=100k
0.17B=0.23A+200=> -23A+17B=20000

from first equation 23A+23B=2300K
add above and eq2
40B=2320K
B=58K

A=100k-58k=42k

FullFathomFive · Answer

A+B=100,000

0.17B=0.23A+200

You now have two equations, so you can either substitute or eliminate. In the explanation above, elimination is used, here I use substitution (elimination  is  easier in this case)

Take away decimals first: 17B=23A+20,000

Isolate first equation to solve for A (your goal): B=100,000-A

Plug in for B: 
17(100,000-A)=23A+20,000
1,700,000-17A=23A+20,000
1,680,000=40A
1,680,000/40=A
 A=42,000=Answer Choice D

mikemcgarry · Answer

Here's another problem from that same article, one that's even less amenable to algebraic treatment.

If the sequence a(n) is defined as a(n) = $n^2 + n + \sqrt{n+3}$, then which of the following values of n represents the first terms such that a(n) > 500?
(A) 13
(B) 22
(C) 33
(D) 46
(E) 78

Show Spoiler

OA = (B)

A full solution is shown at that that article:
https://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/

Mike :-)

mvictor · Answer

took some time as the numbers were high...
0.17B-0.23A = 200 | * 100
17B-23A=20,000
A+B=100,000
B=100,000 - A

17(100,000 - A) - 23A = 20,000
1,700,000 - 17A - 23A = 20,000
1,680,000 = 40A
divide by 40
first two digits: 42...so answer is D.

0ld · Answer

A + B = 100,000

0.17B = 0.23A + 200 ==> -23A + 17B = 20,000

For making our calculation easy, we can divide constant by factor of 1000 and get the result.

A + B = 100  
 ==>  17A + 17B = 1700  --{i)  
 ==>  -23A + 17B = 20  --(ii)

Subtract (ii) from (i)

17A - (-23A) = 1700-20

40A = 1680

A = \frac{168}{4} = 42.

A = 42,000

bumpbot · Answer

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Ms. Morris invested in Fund A and Fund B. The total amount

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Ms. Morris invested in Fund A and Fund B. The total amount

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