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# A total of \$60,000 was invested for one year. But of this

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A total of \$60,000 was invested for one year. But of this [#permalink]

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22 Mar 2009, 23:18
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A total of \$60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the \$60,000 for that year was \$4,080, what is the value of x?

(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-total-of-60-000-was-invested-for-one-year-part-of-this-126655.html
[Reveal] Spoiler: OA

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23 Mar 2009, 21:11
The answer is "E" without knowing the split in the amount x and Y can be anything

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25 Mar 2009, 04:48
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I think the answer is should be "C"...

if
a = amount invested @ x percent
b = amount invested @ y percent

and
a(x%) + b(y%) = 4,080

Statement (1) would give you
a((3/4)y) + b(y) = 4,080

Statement (2) would give you the actual amounts invested, since
a = 60,000-b (given)
a/b = 3/2

So you can solve for the unknowns

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25 Mar 2009, 14:23
kf13 wrote:
I think the answer is should be "C"...

if
a = amount invested @ x percent
b = amount invested @ y percent

and
a(x%) + b(y%) = 4,080

Statement (1) would give you
a((3/4)y) + b(y) = 4,080

Statement (2) would give you the actual amounts invested, since
a = 60,000-b (given)
a/b = 3/2

So you can solve for the unknowns

It is not a/b = 3/2 but the interest earned on a and b is in the ratio 3/2. I think the answer is E
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27 Jul 2009, 03:33
Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual
interest at the rate of x percent per year, and the rest earned simple annual interest at the
rate of y percent per year. If the total interest earned by the \$60,000 for that year was
\$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to
the amount that earned interest at the rate of y percent per year was 3 to 2.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO it should be C

1. Is insuff as we don't about the split.
2. Lets assume that split is a and b ( b=60,000-a)

AX/100 / (60,000-b)Y/100 = 3/2 and We also know that AX/100 + (60,000-A)Y/100 = 4080. We have 2 equations and 3 variables and hence insuff ( I triesd to calculate also just to be sure)

Now we combine 1 and 2, we have 3 equations and 3 variables and hence we can solve it.

I hope this helps !

Cheers

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05 May 2011, 00:23
A total of \$60,000 was invested for one year. But of this amount earned simple annual
interest at the rate of x percent per year, and the rest earned simple annual interest at the
rate of y percent per year. If the total interest earned by the \$60,000 for that year was
\$4,080, what is the value of x?

(1) x = (3/4) y

(2) The ratio of the amount that earned interest at the rate of x percent per year to
the amount that earned interest at the rate of y percent per year was 3 to 2.

----
Let A be the investment with x interest rate and B be the investment with y interest rate. First, let us process the information we are given:

A + B = 60,000
A * x/100 + B * y/100 = 4,080

We are asked what is x? so A * x/100 + (60,000 - A) * y/100 = 4,080. We can stop here and recognize that we need A and y to find x or A per say and a relationship between x and y.

1) We have a relationship between x and y that helps to get rid of y but we still need A. Insuff. A D out

2) Here the GMAT is telling us each of the interest amount of investments A and B. However there are many combinations of A, x and B, y to get the respective splits. Insuff. B out

1+2) We have each investment interest expressed in terms of A and x. We can isolate A * x/100 so A interest in the formula for B interest ( (60,000 - A) * y/100)) after replacing y with x, and replace it with its dollar amount. We end up with an equation with only one variable - x - and solve sufficienty.

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05 May 2011, 19:04
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Expert's post
1
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Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the \$60,000 for that year was \$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Application of weighted average -
Some amount at x% and some at y%. Total interest earned is \$4080. So we can find the average interest earned (4080/60,000).
So weighted average of x and y is (4080/60,000). What is x?
We do not know the ratio of principal (i.e. the weights) and we have two variables x and y.
(1) x = (3/4) y
A variable reduced but the ratio of weights is still not known.

(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Got the ratio of weights but still have 2 variables.

Both together, now I have the ratio of weights and just one variable x, so definitely I will get the value of x using
w1/w2 = (A2 - Aavg)/(Aavg - A1)
3/2 = (4/3x% - 4080/60,000)/(4080/60,000 - x%)

Ofcourse, it is a DS question so I will not try to find it but I could so sufficient. Answer (C).
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05 May 2011, 22:03
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let a be the amount invested in x% return thus 60,000-a is the amount on y% return.

a gives a * x /100 + (60000-a) * (4/3)x / 100 = 4080

a and x are 2 unknowns. Not sufficient.

b a/ (60000-a) = 3/2 gives a = 36000.

but still x and y are unknown. Not sufficient.

a+b
36000 * x/100 + 24000 * (4/3)x/ 100 = 4080

x is the only unknown.Hence can be found out. Thus C.
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06 May 2011, 21:54
Karishma
Pls can you take a look at this.
very-hard-mgmat-97488.html#p917767

cheers
VeritasPrepKarishma wrote:
Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the \$60,000 for that year was \$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Application of weighted average -
Some amount at x% and some at y%. Total interest earned is \$4080. So we can find the average interest earned (4080/60,000).
So weighted average of x and y is (4080/60,000). What is x?
We do not know the ratio of principal (i.e. the weights) and we have two variables x and y.
(1) x = (3/4) y
A variable reduced but the ratio of weights is still not known.

(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Got the ratio of weights but still have 2 variables.

Both together, now I have the ratio of weights and just one variable x, so definitely I will get the value of x using
w1/w2 = (A2 - Aavg)/(Aavg - A1)
3/2 = (4/3x% - 4080/60,000)/(4080/60,000 - x%)

Ofcourse, it is a DS question so I will not try to find it but I could so sufficient. Answer (C).

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04 Aug 2013, 19:52
VeritasPrepKarishma wrote:
Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the \$60,000 for that year was \$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Application of weighted average -
Some amount at x% and some at y%. Total interest earned is \$4080. So we can find the average interest earned (4080/60,000).
So weighted average of x and y is (4080/60,000). What is x?
We do not know the ratio of principal (i.e. the weights) and we have two variables x and y.
(1) x = (3/4) y
A variable reduced but the ratio of weights is still not known.

(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Got the ratio of weights but still have 2 variables.

Both together, now I have the ratio of weights and just one variable x, so definitely I will get the value of x using
w1/w2 = (A2 - Aavg)/(Aavg - A1)
3/2 = (4/3x% - 4080/60,000)/(4080/60,000 - x%)

Ofcourse, it is a DS question so I will not try to find it but I could so sufficient. Answer (C).

Hi Karishma,

I have been following your solutions. They are an eye opener for me. Now I am stuck in this problem with my approach. Request you to kindly help reason out why I can't take this approach.

From statement 1 x=3y/4
so x/y=3/4
hence I can take x=3 and y=4.
since I know the interest which is 4080 and the ratio of interest 3 and 4
can't I apply these 4080/7*3 to calculate x.

If I can't take this approach in this question then under what question can this approach be taken

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05 Aug 2013, 23:58
davidfrank wrote:
VeritasPrepKarishma wrote:
Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the \$60,000 for that year was \$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Application of weighted average -
Some amount at x% and some at y%. Total interest earned is \$4080. So we can find the average interest earned (4080/60,000).
So weighted average of x and y is (4080/60,000). What is x?
We do not know the ratio of principal (i.e. the weights) and we have two variables x and y.
(1) x = (3/4) y
A variable reduced but the ratio of weights is still not known.

(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Got the ratio of weights but still have 2 variables.

Both together, now I have the ratio of weights and just one variable x, so definitely I will get the value of x using
w1/w2 = (A2 - Aavg)/(Aavg - A1)
3/2 = (4/3x% - 4080/60,000)/(4080/60,000 - x%)

Ofcourse, it is a DS question so I will not try to find it but I could so sufficient. Answer (C).

Hi Karishma,

I have been following your solutions. They are an eye opener for me. Now I am stuck in this problem with my approach. Request you to kindly help reason out why I can't take this approach.

From statement 1 x=3y/4
so x/y=3/4
hence I can take x=3 and y=4.
since I know the interest which is 4080 and the ratio of interest 3 and 4
can't I apply these 4080/7*3 to calculate x.

If I can't take this approach in this question then under what question can this approach be taken

Of the 60,000, say I invest 30,000 at x% and 30,000 at y%.
Now if x/y = 3/4, the actual interest earned by two investments will be in the ratio 3:4 so you can calculate interest earned ta x% using 4080/7*3 and hence can get the value of x.

But say, I invest 10,000 at x% and 50,000 at y% (I don't know how the principal is split), will the actual interest earned at x% and at y% be in the ratio 3:4? No. Actual Interest earned at x% will be much less than actual interest earned at y% because amount invested at x% is very little.

Hence, we need the way the principal was split to get the ratio of interest earned.
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Re: A total of \$60,000 was invested for one year. But of this [#permalink]

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07 Aug 2013, 03:23
Economist wrote:
A total of \$60,000 was invested for one year. But of this amount earned simple annual
interest at the rate of x percent per year, and the rest earned simple annual interest at the
rate of y percent per year. If the total interest earned by the \$60,000 for that year was
\$4,080, what is the value of x?
(1) x = (3/4) y
(2) The ratio of the amount that earned interest at the rate of x percent per year to
the amount that earned interest at the rate of y percent per year was 3 to 2.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

................
From question,
P × X% + (60000-p)y%=4080 ..................(1) {P = portion of amount that gained X% interest}

from st(1), x= (3/4)y , put it in equation (1) and we will have a negative value of P. so (1) not sufficient.
[calculate it, because it could be positive, i have seen a lot of these types of problems]

from st(2), we know , 3m+2m=60,000
or, m = 12,000 .

so, 3 × 12,000 X% + 2 × 12,000 Y% = 4080 [st(2) is not sufficient to solve the problem}

Now use the value of y from st(1) and you will have X=6 .
so its only possible by using both statements to evaluate X .

{this is nothing but a problem regarding calculation and within 2 minutes it's possible to calculate and answer this question}
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Re: A total of \$60,000 was invested for one year. But of this [#permalink]

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09 Aug 2013, 03:44
OPEN DISCUSSION OF THIS QUESTION IS HERE: a-total-of-60-000-was-invested-for-one-year-part-of-this-126655.html
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Re: A total of \$60,000 was invested for one year. But of this   [#permalink] 09 Aug 2013, 03:44
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