Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1 1/2 times that of investment A, what amount did Linda put into investment A

The rate of investment A = r;
The rate of investment B = 1.5r.

(1) The interest for 1 year is $50 for investment A and $150 for investment B --> A*r = 50 and B*(1.5r) = 150 --> A*r = 50 and B*r = 100 --> B = 2A. Not sufficient.

(2) The amount that Linda put into investment B is twice the amount that she put into investment A --> B = 2A. Not sufficient.

(1)+(2) We have the same info from (1) and (2). Not sufficient.

Answer: E.

Hope it's clear.
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I'm getting E

(I'm assuming the bold portion refers to the amount of interest received from investment A and B and not the rate)

From 1) We are not told anything about the actual interest rates so she could have put 1000 into each and respective interest rates could have been 5% and 15% or if she'd only put in 100 then interest rates would be 50% and 150%. INSUFF

From 2) This tells us nothing about the interest rates either. So she could have put 100 in A and 200 in B with respective interest rates being 50% and 75% or she could have put 1000 in A and 2000 in B with respective interest rates equalling 5% and 7.5% INSUFF

Taking both together she still could have put 100 in A and 200 in B with interest rates equalling 50% and 75% or 1000 in A and 2000 in B with interest rates equalling 5% and 7.5% INSUFF

Well, I chose A as my answer and would like to get your comment on what's wrong with my approach:

Amount invested in plan A= A
Amount invested in plan B= B
Interest rate for plan A= x/100
Interest rate for plan B= 1.5x/100


Plan A: Ax/100
Plan B: 1.5Bx/100


Statement 1:

\((Ax)/100=50\) and \((1.5Bx)/100=150\)

So, \(x=5,000/A\) and \(x=15,000/1.5B\) ---> \(x=10,000/B\)

Since both the fractions equal to x, make them equal to each other:

\(5,000/A = 10,000/B\) ----> \(5,000/10,000 = A/B\)

Doesn't that answer the question? Amount invested in plan A is 5,000


What's wrong with this approach?

Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1 1/2 times of investment A, what amount did Linda put into investment A?

(1) The interest for 1 year is $50 for investment A and $150 for investment B.

(2) The amount that Linda put into investment B is twice the amount that she put into investment A.

Okay lets start again
I = PTR/100

What we have is Rb = 3/2 Ra and T = 1

Statement 1 :
Ia = 50
Ib = 150
Statement 2 :
Pb = 2 Pa

Using Statement 1
PaRa/100 = 50
PaRa = 5000

PbRb/100 = 150
PbRb = 15000

Using Rb = 3/2 Ra, still can't help us solve the problem because there are 3 Unknowns( Pa, Pb and Ra or Rb)

So, based on statement 1, we can't really solve the problem.

Lets use Statement 2

Pb = 2 Pa
Rb = 3/2 Ra

We don't have any correlation between A and B, so can't really solve the problem.


Now, when we combine statement 1 and 2,
we will still be left with atleast 2 unknowns

So, the answer has to be E

I am not sure if this is what you were thinking, but
x/y = 5/4 does not mean that x = 5 and y =4, because
x/y = 5/4 = 20/16 = 50/40 etc

Is that what you were thinking ?

since (1) and (2) are insuff, proceeding to (1)&(2):

inv A: X*(1+a/100)^1=50 --> a=(5000-100x)/x
inv B: 2X*(1+3a/100)^1=150 --> a=(15000-200x)/6x

a=a --> (5000-100x)/x=(15000-200x)/6x --> x=150/4

i agree that the result (150/4) has no logic but anyway didnt i get (C) rather than (E)

Whats wrong with this solution?

Equations in red are not correct. We are told that "the interest for 1 year is $50", not the balance after 1 year. So, it should be x*a/100 and x*1.5a/100=150, which are basically the same equations, which cannot be solved.
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Question
Investment A: \(A*\frac{r}{100}\)
Investment B: \(B*\frac{1.5r}{100}=B*\frac{3r}{200}\)
Investment A ?

Statement 1
\(A*\frac{r}{100}=50\) and \(B*\frac{3r}{200}=75\); This information is not sufficient, as we need info about rates

Statement 2
\(B=2A\) is clearly not sufficient

(St1)+(St2)
\(A*\frac{r}{100}=50\) --> \(A=\frac{5000}{r}\) and \(2A*\frac{3r}{200}=75\) --> \(A=\frac{30,000}{6r}=\frac{5000}{r}\); So we have here twice the same information. No info about the rate, so it's not possible to calculate the amount for investment A. Not sufficient

Answer E

Let us assume that Linda put $a into investment A and $b into investment B.
Also assume that the annual rate of interest of A is 2r%.
Hence, the annual rate of interest of B is 3r%.

Statement 1: 2ar/100 = 50 and 3br/100 = 150
Hence, ar = 2500 and br = 5000
Hence, b = 2a

Not sufficient

Statement 2: b = 2a --> Same as statement 1

Not sufficient

1 & 2 Together No new information

Not sufficient

The correct answer is E
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To interpret this question on Interest, I would take the help of ratios instead of the more common approach of using decimals or fractions.
From the question data, we know that the annual rate of interest of investment B is 1 ½ times that of investment A. Let x be the annual rate of interest of A and y be the corresponding value for B.

From the data given, y = \(\frac{3}{2}\) x or in other words, \(\frac{x}{y}\) = \(\frac{2}{3}\). Since x and y are in the ratio of 2:3, we can assume x = 2k and y = 3k. Doing this is actually going to help us during the later stages of the solution.

From statement I alone, the interest for 1 year is $50 and $150 for investments A and B respectively. Since we know that SI = P*T*R/100, we can formulate equations for the 2 investments.
If we say the investment in A is a and the investment in B is b, we can say,

50 = \(\frac{a*2k}{100}\) and 150 = \(\frac{b*3k}{100}\). Solving the equations, we have,

a*k = 2500 and b*k = 5000. Since we do not know the value of k, we will not be able to calculate the value of a.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, the amount put into investment B is twice the amount put in investment A.
This is insufficient to find a unique value for the investment in A.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining the data given in statements I and II, we have the following:

From statement II, we know that the investment in B is twice the investment in A. Using this along with the data given in statement I, we can say b=2a.
Because of the above relationships, the equations will now become,
a*k = 2500 and 2a*k = 5000. These are a pair of dependent equations and insufficient to find out the unique value of a. (this is where the ratio method actually helped us because we were able to develop equations in terms of k)
The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!
Arvind
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R = rate of simple annual interest for investment A
M = Amount put into investment A
N = Amount put into investment B

Given: Rate of simple annual interest for investment B = 3R/2.

We are asked to determine the value of M.

(1) The interest for 1 year is $50 for investment A and $150 for investment B

RM/100 = 50 and 3RN/200 =150

Three unknown variables and two equations. INSUFFICIENT


(2) The amount that Linda put into investment B is twice the amount that she put into investment A

N = 2M

We do not know the values of any of the variables R, M, N.

INSUFFICIENT

Statements (1) and (2):

The interest for 1 year is $50 for investment A and $150 for investment B AND the amount that Linda put into investment B is twice the amount that she put into investment A


RM/100 = 50 ........... (a)

3RN/200 =150 ..............(b)

N = 2M .....................(c)

From (a) and (c):

RN = 10,000

From (b) and (c):

RN = 10,000

This does not provide us with any new information. INSUFFICIENT to calculate either M or N.

ANSWER: (E)