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Prep question

by hnature0704 » Tue Nov 09, 2010 4:06 am
Need some Help! thank you :)

Linda put an amount of money into each of two new investment, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1.5 times that of investment A, what amount did Linda put into investment A?

(1) The interest for 1 year is $50 for investment A and $150 for investment B.
(2) The amount that Linda put into investment B is twice the amount that she put into investment A.
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Source: — Data Sufficiency |
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by Dani@MasterGMAT » Tue Nov 09, 2010 9:38 am
Use "number of equations = number of unknowns", but beware of the twist at the end.

form equations: Let A be the investment in A,
B in B,
p be the interest in A.
thus, the interest in B is 1.5p = p*3/2.
Stat. (1):

thus, 2 equations:
A*p = 50
B*p*(3/2)=150.
(technically should be p/100, but that's not important for our purposes).

2 equations with 3 unknowns is insufficient - you cannot isolate A from these equations.

Stat. (2): B=2A. Alone, this is obviously insufficient to find A - again, one equation, 2 unknowns.

Combined:
we now know that
A*p=50
B*p*3/2 = 150
B=2A

looks fine: 3 equations, 3 unknowns, sufficient, right? Take it a few steps down the line: substitute B=2A in eq.2 to get
A*p=50
2A*p*3/2 = 150
the 2s reduce to leave A*p*3=150 - a recycled version of A*p=50.
So it's not really 3 equations, 3 unknowns - we only have 2 different equations with unknowns, which is why the statements combined are still insufficient. Answer is E.
Dr. Dani Noy
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
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