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Updated on: 19 Nov 2018, 07:58
2
00:00

Difficulty:

5% (low)

Question Stats:

91% (02:07) correct 9% (02:39) wrong based on 44 sessions

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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

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Chasing the dragon

Originally posted by fitzpratik on 18 Nov 2018, 10:13.
Last edited by fitzpratik on 19 Nov 2018, 07:58, edited 1 time in total.
Manager
Joined: 26 Apr 2011
Posts: 60
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)
Re: A total of $1200 is deposited in two savings account for one year [#permalink] Show Tags 19 Nov 2018, 07:52 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

I got stuck and could not proceed. A simple google search found out the question is put wrongly. Please correct it! Earned should not be in percentage.
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Senior Manager
Joined: 17 Oct 2016
Posts: 260
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Re: A total of $1200 is deposited in two savings account for one year [#permalink] Show Tags 19 Nov 2018, 07:59 MrCleantek wrote: 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

I got stuck and could not proceed. A simple google search found out the question is put wrongly. Please correct it! Earned should not be in percentage.

Hi MrCleantek

Thanks for bringing the error to my notice. I have corrected it.

Apologies for the error.
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Chasing the dragon
Director
Joined: 20 Sep 2016
Posts: 637
Location: India
Concentration: Strategy, Operations
GPA: 3.95
WE: Operations (Real Estate)

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25 Nov 2018, 19:20
2
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

Algebra
We 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 $$100$$
$$5x+(7)(1200-x)=7200$$
$$5x+8,400-7x=7200$$
$$1,200=2x$$
$$x=600$$

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.

**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). _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. VP Joined: 09 Mar 2016 Posts: 1283 A total of$1200 is deposited in two savings account for one year  [#permalink]

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26 Nov 2018, 07:43
1
let $$x$$ be sum invested @ 5%

let $$(1200-x)$$ be the remainder invested @ 7%

$$1272 = 1.05x+(1200-x)(1.07)$$

$$1272 = 1.05x+1284-1.07x$$

$$1272 = 1284 - 0.02x$$

$$0.02x =12$$

$$x = 600$$