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Jackson invested $300,000, dividing it all unequally between

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by Mike@Magoosh » Fri Dec 27, 2013 8:15 am
Jackson invested $300,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
(A) $115,384
(B) $120,000
(C) $121,072
(D) $124,129
(E) $130,000

This is a hard problem without a calculator, and of course you don't get a calculator on the GMAT Q section. It's a good problem on which to use estimation:
https://magoosh.com/gmat/2012/the-power- ... mat-quant/
It's also a good problem on which to use backsolving:
https://magoosh.com/gmat/2013/backsolving-on-gmat-math/
That latter link has the OA & OE for this particular question.

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by theCodeToGMAT » Fri Dec 27, 2013 8:43 am
P = x

Q = 30000 - x

60000 = x * (0.12) + (300000 - x) * 0.25

60000 = 0.12x - 0.25x + 75000

.13x = 15000

If we divide we see 11....

So, [spoiler]{A}[/spoiler]
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by naseem_iqbal » Sat Dec 28, 2013 12:05 pm
Going by Mike's method, we can take 25% as 1/4 and approximate 12% as 1/8.

Then pick a number to backsolve. For simplicity, take 120,000.
(120,000/8)+(180,000/4)
=15,000+45,000
=60,000.
This is exactly what we need. But we approximated 12% as 12.5%. That means our interest with $120,000 in P is slightly lesser than 60,000. For it to be exactly 60,000, P will have a little less than 120,000, Q, little more than 180,000.
Option A.
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