A woman invested $1,000, part at 5% and the rest at 6%. Her total inve

Hi,
a simpler way to do averages/mixtures problems are through weighted averages..

1000 at 5% would give us 50..
and, 1000 at 6% would give us 60..
but we have interest as 53..
so the avg at 5%:6%=60-53:53-50=7:3..
therefore at 5%=1000*7/10=700 and at 6%=300..
C

Answer C by plugging answer choices:

\(7*5 + 3*6 =53\)

Also
\(5x + 6(10-x) =53\)
\(x = 7\)

Her average return is (53/1000) * 100 = 5.3%

Use the standard weighted avg formula:
w1/w2 = (A2 - Aavg)/(Aavg - A1)

w1/w2 = (6% - 5.3%)/(5.3% - 5%) = 7/3

So Amount invested at 5% : Amount invested at 6% = 7:3.

So $700 was invested at 5%.

Answer (C)

Hi All,

This question can be solved by TESTing THE ANSWERS. There's also a logical 'shortcut' built into the prompt that can help to avoid some of the potential 'math work' involved.

We're told that a woman invested $1,000, part at 5% and the rest at 6% and that the total investment with interest at the end of the year was $1,053. We're asked how much of that $1,000 was invested at 5%.

Since the interest is $53, we know that MORE money was invested at 5% than at 6% (since if the two investments were both $500, then the total interest would have been $55). Since $53 is relatively close to $55, the investment at $5 wouldn't be that much more than 1/2 though. This implies that the correct answer is probably B or C. As such you can TEST either one.

Let's TEST Answer B: $600
$600(5%) = $30
$400(6%) = $24
$30+$24 = $54
This is TOO HIGH (but pretty close - the total interest has to be $53). We need there to be LESS interest, so we need MORE money invested at 5%. There's only one answer that's left that logically fits.

Final Answer:
Of course, if you wanted to prove that that was the correct answer, it would not take much additional work.

GMAT assassins aren't born, they're made,
Rich

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