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If $6,000 invested for one year at x percent simple annual interest

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If $6,000 invested for one year at x percent simple annual interest [#permalink]

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New post 19 Jan 2018, 10:48
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If $6,000 invested for one year at x percent simple annual interest yields $450, what amount must be invested at y percent simple annual interest for one year to yield the same number of dollars?

(1) If $4,500 were invested at y percent simple annual interest for one year, the investment would yield $450.
(2) If $6,000 were invested at y percent simple annual interest for one year, the investment would yield $150 more than if it were invested at x percent simple annual interest.

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Re: If $6,000 invested for one year at x percent simple annual interest [#permalink]

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New post 19 Jan 2018, 12:49
Bunuel wrote:
If $6,000 invested for one year at x percent simple annual interest yields $450, what amount must be invested at y percent simple annual interest for one year to yield the same number of dollars?

(1) If $4,500 were invested at y percent simple annual interest for one year, the investment would yield $450.
(2) If $6,000 were invested at y percent simple annual interest for one year, the investment would yield $150 more than if it were invested at x percent simple annual interest.


I'd recommend avoiding doing math on this one. Instead, think about what you could calculate, if you wanted to. Since it's Data Sufficiency, you don't really have to do the calculations.

The question says that $6000 at x percent interest will give you $450. That's enough info to calculate x. So, x is a known value. (Don't actually calculate it - that's a waste of time.)

It asks how much you'd need to invest at y percent interest to yield $450. To determine that, you'd have to know the value of y.

(1) Does this tell us the value of y? It sure does. We could calculate y from this information if we wanted to. Sufficient.

(2) Does this tell us the value of y? It's not totally obvious, so let's write out some equations to check.

$6000*y/100 is the amount you'd get in interest.

$6000*x/100 is the amount you'd get if you invested at x% instead. Since we could calculate the value of x if we wanted to, we could also calculate this value! So this is just a number.

It breaks down to "$6000*y/100 is $150 greater than some number we could calculate."

There's only one unknown variable there, y. So we could definitely solve for y. Statement 2 is sufficient as well.

The answer is D.
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Re: If $6,000 invested for one year at x percent simple annual interest   [#permalink] 19 Jan 2018, 12:49
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