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Bunuel
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 19 Jul 2016, 03:34
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Difficulty:

15% (low)

Question Stats:

84% (01:30) correct 16% (01:29) wrong based on 191 sessions

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Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.
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D
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 19 Jul 2016, 04:06
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Bunuel
Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.
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In Interest problems, if we know any 2 of Interest, Rate, and Principle, we can find what we need.

St-1: Gives the rate for Travis. It is also the rate for Mickey's Loan. With this rate, and 10,000 interest we can find Travis Loan amount. With Travis Loan amount we can find Mickey's Loan Amount. Sufficient.

St-2: Gives the Loan amount Travis Made. So we can find the Mickey's Loan amount. Sufficient.

Answer: D.
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 23 Nov 2016, 04:48
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Bunuel
Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.
Show more


Bunuel Could you please explain 1st statement?
I get that rate of interest is same and the loan amount is double that of Travis
But interest formula is given by (Principle* rate of interest* number of years)/100
Here in statement 1 you are give rate of interest and the interest payable is given in question.
What am I missing??
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 23 Nov 2016, 05:01
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Vinayak Shenoy
Bunuel
Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.


Bunuel Could you please explain 1st statement?
I get that rate of interest is same and the loan amount is double that of Travis
But interest formula is given by (Principle* rate of interest* number of years)/100
Here in statement 1 you are give rate of interest and the interest payable is given in question.
What am I missing??
Show more
I am confused here. Statement 1 Dorene states that whether the interest is compounded quartlery or yearly or it is a simple interest. So how can we state that statement 1 is sufficient to answer.

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Vinayak Shenoy
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 23 Nov 2016, 07:00
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ashishahujasham
Vinayak Shenoy
Bunuel
Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.


Bunuel Could you please explain 1st statement?
I get that rate of interest is same and the loan amount is double that of Travis
But interest formula is given by (Principle* rate of interest* number of years)/100
Here in statement 1 you are give rate of interest and the interest payable is given in question.
What am I missing??
I am confused here. Statement 1 Dorene states that whether the interest is compounded quartlery or yearly or it is a simple interest. So how can we state that statement 1 is sufficient to answer.

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Bunuel need some help here :)
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 23 Nov 2016, 08:58
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Bunuel
Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey's little brother also made a loan, only twice as large as Mickey's but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey's loan?

(1) The rate of interest on the loan that Travis took is 6% annually.
(2) The loan that Travis made was $166,667.
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Loan of Mickey -

Principal = X
Time = t
Rate = r


Loan of Travis -

Principal = 2X
Time = t
Rate = r

FROM STATEMENT - I ( SUFFICIENT )

Principal = 2X
Time = t
Rate = 6

Amount that will pay during t years is = Principal + Total Interest for t years

\(2X + \frac{2X*t*6}{100} = 2X + 10000t\)

\(\frac{2X*t*6}{100} = 10000t\)

Or, 2X*6 = 1000000

Or, x = 83333.33

So, Mickey's Loan amount is 83333.33

FROM STATEMENT - II ( SUFFICIENT )

2X = $166,667

So, x = $83333.5

Thus, EACH statement ALONE is sufficient to answer the question asked, answer will be (D)
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 09 Sep 2024, 17:14
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I'm not sure if this answer is correct. I don't think statement 1 is sufficient because we don't know the time period - can we just assumer t = 1 in this case?
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Mickey made an X dollars loan at the beginning of 1996. Travis, who is 12 Sep 2024, 12:05
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Statement (1):
The rate of interest on the loan that Travis took is 6% annually.

Using the given interest rate for Travis's loan, we know that Travis pays $10,000 annually in interest. The interest formula is:

Interest
=
Loan Amount
×
Interest Rate
Interest=Loan Amount×Interest Rate
Thus, for Travis:

10
,
000
=
2
X
×
0.06
10,000=2X×0.06
Simplifying:

10
,
000
=
0.12
X
10,000=0.12X
Solving for
X
X:

X
=
10
,
000
0.12
=
83
,
333.33
X=
0.12
10,000
​
=83,333.33
This gives us the size of Mickey's loan. Statement (1) alone is sufficient.

Statement (2):
The loan that Travis made was $166,667.

Since Travis’s loan is twice the size of Mickey's, we can express this as:

2
X
=
166
,
667
2X=166,667
Solving for
X
X:

X
=
166
,
667
2
=
83
,
333.50
X=
2
166,667
​
=83,333.50
This also gives us the size of Mickey’s loan. Statement (2) alone is sufficient.

Both statements are independently sufficient to determine the size of Mickey's loan. Thus, the answer is (D): Each statement alone is sufficient.
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