fitzpratik wrote:

A total of $1200 is deposited in two savings account for one year, part at 5% and the remainder at 7%. If $72 was earned in interest, how much was deposited at 5%?

A. 410

B. 520

C. 600

D. 650

E. 760

Source: Nova -GMAT

AlgebraWe have two different amounts invested at different interest rates.

We can treat this question as we would a mixture problem.

Define one amount in terms of the other.

\(x\) = the amount invested at 5%

\(y\) = the amount invested at 7%

\(x +y=$1200\)

\(y=(1200-x)\)

The

sum of the interest earned on each part is \($72\)

\((.05)(x)+(.07)(y)=72\)

\((.05)(x)+(.07)(1200-x)=72\)

Multiply all terms by \(100\)

\(5x+(7)(1200-x)=7200\)

\(5x+8,400-7x=7200\)

\(1,200=2x\)

\(x=600\)

Answer C

Use the answer choicesStart with C to get a benchmark.*

C) 600 = the amount invested at 5%

The total amount invested is $1,200

The other portion invested at 7% also = $600

Interest earned by $600 at 5%:

\($600 * \frac{5}{100}=$30\)

Interest earned by $600 at 7%

\(($600*\frac{7}{100})=$42\)

Total interest earned? $72

$30 + $42 = $72

That's correct.

Answer C

**Using a benchmark

If C is too great, eliminate D and E. Both are greater than C.

If C is too small, eliminate A and B. Both are smaller than C.

Suppose we had started with E) $760

Interest earned by $760 at 5% ?

10% would be $38. 5% is half that: $38

Other portion = $(1,200 - 760) = $440

Interest earned? $440 * \(\frac{7}{100}\)= ($4.40 * 7) = $30.80

Total interest? $38 + $30.80 = $60.80

Actual total interest earned? $72.00. The theoretical $60.80 earned is a lot less than $72.

$760 at 5% is too great an amount—too much of the original $1,200.

We need the higher interest rate, 7%, to earn more. Make the 7% portion's base amount greater.

To do so, decrease the 5% base amount. Try (C).