GMAT Club Olympics 2024 (Day 3): Charlie invested $x for one year at

Question

Charlie invested $x in Fund A for one year at an annual simple interest rate of p percent. What would be the total value of this investment at the end of that period?

(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

Charlie invested $x in Fund A for one year at an annual simple interest rate of p percent. What would be the total value of this investment at the end of that period?

This is a fairly straightforward question, but some might fall into the C-trap or mistakenly choose D as the answer.

Essentially, we need to find the value of x(1 + p/100).

(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

This implies that (2x)(1 + p/100) = 220, which, by dividing by 2, yields x(1 + p/100) = 110. This is exactly what we want to find. Sufficient.

Or, by simple reasoning, if doubling the initial investment amounts to $220 in one year, the initial investment will amount to half of that, so $110.

(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

This implies that x(1 + 2p/100) = 120, which cannot be simplified to get the value of x(1 + p/100) nor can it be solved to get the individual values of x and p to calculate x(1 + p/100). Not sufficient.

Answer: A.

jack5397 · Answer

IMO -A

We need to find the total value of the investment after 1 year at p% interest rate.

As we know when we are doubling the amount invested so total value will be doubled.

Second statement would be insufficient as we can try with the values x=100 ; p% = 10 and 2p% = 20%. Values cannot be concluded for total values.

KshtriyaNaveen · Answer

Question statement analysis :

Let principle = x$
      ROI (Interset ) = p
      Time ( Year ) = 1
S.I = simple interset = P*T*R /100
given that annual simple interset , asked to find total investment value = Principle + S.I  
  
A = X  ? --> Equation 1

Statment analysis: 
1.  If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

Given that p = 2X & A= 220

220 = 2*X  
    X  = 110
 
    Therefor option 1 is sufficent. possible solution is A & D

2. If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

Given that ROI = 2*P, A = 120 
    
    120 = X 
    we can't find exact valye of A, so Statement 2 is not sufficient.

Therefor Option A is correct

RishS94 · Answer

A.
If 220 is output at X% return for 2P investment 
For P investment it will be 110.

So A is sufficient.

B.
120 can be the final return if 100 is invested at 20%.

Or 60 is invested at 100% rate

Or 30 is invested at 200% rate.

So here both Principal & Intrest rate can be varied. Hence not sufficient.

Ans.A

Posted from my mobile device

SKDEV · Answer

we need to find 
x + x(p/100) or x(1+(p/100))

using I) 220 = 2x + 2x(p/100)
or 220 = 2x(1+(p/100))
hence sufficient

using II) 120 = x + x(2p/100)
not sufficient

rg270903 · Answer

Charlie invested $x in Fund A for one year at an annual simple interest rate of p percent. What would be the total value of this investment at the end of that period?

(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

Answer: A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Let Total value of the investment = I

I = x (1 +p/100)

I = x + px/100

Statement (1) -

2x ( 1 +p/100) = 220

2I = 220

I = 110

Statement (I) alone is sufficient

Statement (2) -

x (1 + 2p/100) = 120

X +2 px/100 = 120

Solving the two equations simultaneously will give us the value for x and p, which can then give us the total value of the investment. This means that  statement (2) is not sufficient alone.

pranjalshah · Answer

Answer: A

To determine the total value of Charlie's investment in Fund A after one year at an annual simple interest rate of $ p $ percent, we need to calculate the amount of the investment using the simple interest formula:

\

Statement (1):

If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

This means:
\

Solving for $ x \left(1 + \frac{p}{100}\right) $:

\

So, the total value of Charlie's original investment at the end of the year is $110.

Statement (1) alone is sufficient to answer the question.

Statement (2):

If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

This means:
\

Solving for $ x \left(1 + \frac{2p}{100}\right) $:

\

This equation involves both $ x $ and $ p $, and alone it does not provide enough information to determine $ x \left(1 + \frac{p}{100}\right) $.

Statement (2) alone is not sufficient to answer the question.

Therefore, the answer is:

A. Statements (1) alone is sufficient.

DG1989 · Answer

Charlie invested $x in Fund A for one year at an annual simple interest rate of p percent. What would be the total value of this investment at the end of that period?

(1) If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.
(2) If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

Solution:  Given that
x: initial investment amount in Fund A.
p: annual simple interest rate in percent.
We need to find the total value of the investment i.e. x +  \frac{xp}{100} 
= x(1 +  \frac{p}{100} )

Statement 1:    If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year. 
This means, 2x +  \frac{2xp}{100}   = 220
2x(1 +  \frac{p}{100} ) = 220
or x(1 +  \frac{p}{100} ) = 110
  SUFFICIENT

Statement 2:    If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year. 
This means x +  \frac{2xp}{100}   = 120
x(1 +  \frac{2p}{100}  ) = 120
  NOT SUFFICIENT  
 
  The correct answer is Option A

d_patel · Answer

Question stem gives us following details,

Charlie invested x money for 1 year at simple interest rate of p.

Original money = x
Interest after 1 year =  x * \frac{p }{100}

We need to find,
So total value after 1 year =  x   +  x * \frac{p }{100}                      
 
 Statement-1 
If Charlie had invested twice as much money in Fund A, the total value of the investment would have been $220 at the end of the year.

So new money = 2x
Interest after 1 year =  2x * \frac{p }{100}

So new total value after 1 year =  2x   +  2x * \frac{p }{100}  = 220

Which we can rewrite as
 2(x + x * \frac{p }{100}) = 220 
 (x + x * \frac{p }{100}) = 110 
 
That's what we were looking for.
We got only 1 possible answer available.

Sufficient statement.

Statement-2 
 If Charlie had invested at twice the percentage in Fund A, the total value of the investment would have been $120 at the end of the year.

So new money = x
Interest after 1 year =  x * \frac{2p }{100}

So new total value after 1 year =  x   +  2x * \frac{p }{100}  = 110

Two variables and 2 equations if we count question stem. But we cannot solve it as we don't know the investment value for question stem equation. 
For this one, we can find multiple values for (x, p) and each will change the original investment value.
We can find many possible answers.

Not Sufficient statement.

Final answer -  A 
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

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