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A total of $60,000 was invested for one year. But of this [#permalink]
 22 Mar 2009, 23:18
Question Stats:
75% (03:20) correct
25% (00:00) wrong based on 0 sessions
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.
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Re: DS: Interest rates [#permalink]
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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Re: DS: Interest rates [#permalink]
25 Mar 2009, 04:48
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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Re: DS: Interest rates [#permalink]
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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Re: DS: Interest rates [#permalink]
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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Re: DS: Interest rates [#permalink]
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. Answer C Hope this is helpful.
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Re: DS: Interest rates [#permalink]
05 May 2011, 19:04
2
This post received
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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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Re: DS: Interest rates [#permalink]
05 May 2011, 22:03
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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Re: DS: Interest rates [#permalink]
06 May 2011, 21:54
Karishma Pls can you take a look at this. very-hard-mgmat-97488.html#p917767cheers 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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Re: DS: Interest rates
[#permalink]
06 May 2011, 21:54
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