Soline put money into two savings accounts

[melguy]

Please suggest some shortcut for this problem.

Thanks for your help!

[GMATGuruNY]

Let c = the amount invested in C and d = the amount invested in D.
Let C's yearly interest rate = x/100 and D's yearly interest rate = (x+2)/100.

Thus:
Yearly interest earned by C = (x/100) * c = xc/100
Yearly interest earned by D = (x+2)/100 * d = (x+2)d/100.

Thus:
C's interest/D's interest =

__xc/100__ =
(x+2)d/100

__xc__
(x+2)d.

Statement 1:
Since C's interest/D's interest = 30/180 = 1/6, we get:
xc / (x+2)d = 1/6.
No way to solve for c.
INSUFFICIENT.

Statement 2:
d = 3c.
No way to solve for c.
INSUFFICIENT.

Statements combined:
Substituting d=3c into xc / (x+2)d = 1/6, we get:
xc / (x+2)(3c) = 1/6
x/(3x + 6) = 1/6
6x = 3x + 6
3x = 6
x = 2.
Thus, C's yearly interest rate = 2%.

Since C's interest over 3 years = $30, C's yearly interest = 10.
Since C's yearly interest rate = 2%, we get:
(2/100)c = 10
c = 500.
SUFFICIENT.

The correct answer is C.

[melguy]

Thanks GMATGuru for your response.

If you don't mind me asking, plz advice the difficulty level of this question (rough idea). Is it 700+ level question. The reason I ask is that I would find it very difficult to complete it in 2 mins .

[Matt@VeritasPrep]

Melguy, I don't think it's that bad just because you don't have to actually SOLVE it: in Data Sufficiency, all you have to do is determine WHETHER you can solve it, and here you can say "not without statements 1 and 2".

Think of it this way. The prompt gives you three variables: C dollars in one account, D dollars in the other, with x% interest on one and (x+2)% interest on the other. Since I have three variables, I probably need at least two equations to solve for any given variable, so the only question is how many equations I can write, given the statements that follow.