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52% (02:43) correct 48% (03:05) wrong based on 715 sessions

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Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earned a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III­


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B
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gmatophobia
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Carl invested a certain amount of money for one year, some of which ea 06 Nov 2023, 10:15
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yrozenblum
Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earnead a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III
Show more

The minimum principle value is when all the amount is invested at a 2.5% rate.

\(\frac{p_{\text{min}} * 2.5 * 1}{100} = 680\)

\(p_{\text{min}} = 680*\frac{100}{2.5} = 27200\)

The maximum principle value is when all the amount is invested at a 2.2% rate.

\(\frac{p_{\text{max}} * 2.2 * 1}{100} = 680\)

\(p_{\text{max}} = 680*\frac{100}{2.2} \approx 30900\)

Only one value lies in this range i.e. $27,896

Option B
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Carl invested a certain amount of money for one year, some of which ea 06 Nov 2023, 10:09
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1) 24708*2.5%=617.7 : thus not possible to reach 680

2) 27896 *2.5 =697.4 and 27896*2.2 = 613.7 . Since required value is in between, possible.

3) 31284 * 2.2 = 688.2. Thus both value would be above 680, hence value of 680 not possible.

Hence answer is B.
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Let’s have A total amount invested
X amount of A at a 2.2 rate and A-X at 2.5 rate

Interest 1 = X*2.2/100 and interest 2 = (A-X)*2.5/100

Total interest earned = X*2.2/100 + (A-X)*2.5/100 =680

—->> 22X + 25(A-X) =680.000
25 A -3X = 680.000

—->> A = [680.000+3X]/25
——>> A= 27.200 + 3X/25

We noticed that A should be greater than 27.200
We have to consider B and C
But knowing that, X <<<A let’s verify the worst case for X=27200
3*27200/25 = 3264

27200+3264= 30464 == max value

C can’t be our answer

Hence B

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gmatophobia

yrozenblum
Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earnead a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III
The minimum principle value is when all the amount is invested at a 2.5% rate.

\(\frac{p_{\text{min}} * 2.5 * 1}{100} = 680\)

\(p_{\text{min}} = 680*\frac{100}{2.5} = 27200\)

The maximum principle value is when all the amount is invested at a 2.2% rate.

\(\frac{p_{\text{max}} * 2.2 * 1}{100} = 680\)

\(p_{\text{max}} = 680*\frac{100}{2.2} \approx 30900\)

Only one value lies in this range i.e. $27,896

Option B
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­Hello,

I have seen this pattern in Gmat that some questions can be solved by getting the range.
But how can we figure out if this should be done by the range (min and max) or by using equations.

I solved this by using linear equation method. but realised it was time consuming so had to leave the Q after spending 2.5 min. 

Thank you for your help
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Carl invested a certain amount of money for one year, some of which ea 21 Jun 2024, 23:08
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yrozenblum
Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earnead a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III­


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­


The question tests your understanding of weighted averages. Since one sum was invested at 2.2% and the other at 2.5%, overall interest rate would lie between them.

Looking at the given options, say if the amount was 24800 (rounding up for easier calculations),
2.5% of this would be 248*2 + 124 = 496 + 124 = $620 (which is less than $680).
Hence, the amount must be more than $24800 to get $680 as interest.

Say if the amount was 31200, 
2.2% of this would be 312*2 + 62 = $686
So the amount should be less than $31200 to get $680 as interest.

Since option II is easily in the middle of the two, it will work. 

Answer (B)




 
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Why is X=27200 the worst case... can you please explain a bit more in detail
Edoua
Let’s have A total amount invested
X amount of A at a 2.2 rate and A-X at 2.5 rate

Interest 1 = X*2.2/100 and interest 2 = (A-X)*2.5/100

Total interest earned = X*2.2/100 + (A-X)*2.5/100 =680

—->> 22X + 25(A-X) =680.000
25 A -3X = 680.000

—->> A = [680.000+3X]/25
——>> A= 27.200 + 3X/25

We noticed that A should be greater than 27.200
We have to consider B and C
But knowing that, X <<<A let’s verify the worst case for X=27200
3*27200/25 = 3264

27200+3264= 30464 == max value

C can’t be our answer

Hence B

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Ok lets dumb this down for us. "A problem well defined is halfway through to the solution - Kidlins law"

Visualization
The first step is to visualize the problem. Let’s personalize it:
Imagine I invested in two accounts and earned a total of $680 in interest.
The accounts had interest rates of 2.2% and 2.5%.
The question now is to determine how much I could have invested in each account.


Translation
If I rethink the problem, they want us to find out the minimum and maximum amounts I might have invested in these two accounts.
The lowest total investment would occur if I had invested all my money in the account with a 2.5% interest rate, while the highest total investment would be if I had invested everything in the account with a 2.2% interest rate.
You see, if the interest yield is fixed, the lower the interest percentage, the higher the amount invested, right?


Approach
Now, all I have to do is some calculations to find out what the maximum and minimum amounts could be.

The minimum invested at 2.5% interest should yield $680. So we can calculate the maximum invested amount - $27,200
(You can make the calculations easier - realizing 2.5% is $680 that mean 10% is $680 x 4 and 100% is $680x40 = $27200)

The maximum invested at 2.2% interest should yield $680. So we can calculate it to be around ~ $30,000
(check image for estimation)

Conclusion
Thus we can now deduce that only one answer choice fits within our range so we eliminate (I) and (III) and the answer would be (II) only


Shu "TheGMATTutor"
The GMAT concepts are relatively basic, but they require a deep understanding to tackle nuanced questions effectively. So lets dumb it down for us. This is not just a math and English test—it is a deductive test designed to assess your problem-solving skills
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Carl invested a certain amount of money for one year, some of which ea 19 May 2025, 02:08
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Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earnead a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III­
Show more
Let x be the amount invested at 2.2% p.a. and (option given in Q - x) be amount the amount invested at 2.5% p.a.

Option (I):
x*\(\frac{2.2}{100}\) + (24708 - x)*\(\frac{2.5}{100}\) = 680

\(\frac{22*x}{1000}\) + (24708 - x)*\(\frac{25}{1000}\) = 680

22x + 24708*25 - 25x = 680000

3x = 24708*25 - 680000

Let this be the standard form we will use for options (II) and (III) too.

3x = 25000*25 - 680000
3x = 625000 - 680000

Since x is coming negative, option (I) is not possible as amount cannot be negative.

Option (II):
3x = 27896*25 - 680000 = 28000*\(\frac{100}{4}\) - 680000 = 700000 - 680000
3x = 20000
x = 6667

Also, to double check x is less than 27896, so x is a valid amount. Option (II) is possible.

Option (III):
3x = 31284*25 - 680000 = 31200*\(\frac{100}{4}\) - 680000 = 780000 - 680000
3x = 100000
x = 33333

But x is greater than 31284, so x is not a valid amount. Option (III) is not possible.

Only option (II) is allowed.

Answer: B.
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Carl invested a certain amount of money for one year, some of which ea 25 Sep 2025, 17:55
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Bunuel

Suggested question edit: there is a typo "earnead".

Thanks!
yrozenblum
Carl invested a certain amount of money for one year, some of which earned interest at a simple annual interest rate of 2.2 percent and the rest of which earned interest at a simple annual rate of 2.5 percent. If the amount of money that Carl invested for the year earnead a total of $680 in interest, which of the following could have been the total amount of money that he invested for the year?

I. $24,708
II. $27,896
III. $31,284

A. None
B. II only
C. III only
D. I and II
E. II and III­


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Bunuel

Suggested question edit: there is a typo "earnead".

Thanks!

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Fixed the typo. Thank you!
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Quite a pain to figure out which linear equation works. But if you do come up with equations fast, and the range approach discussed above by the rest doesn't click fast for you. I thought this might be an alternative.

22a + 25b = 680,000
a + b = one of the answers given

e.g 24,708

b=24,708 -a
substitute in eqn 1
22a + 25 (24,708-a)=680,000
22a-25a=680,000-25(24,708)
-3a=25(4*6800 - 24,708)
-3a=25(27,200-24,708) - you don't have to finish the calculations, as you see the - on the left won't cancel out; 24,708 can't be an answer

b=27,896
-3a=25(4*6800-27,896)
-3a=25(27,200-27,896)
-3a=25*-696 - the negative will cancel out and 6+9+6=27, divisible by 3; 27,896 can be an answer

b=31,284
-3a=25(4*6800-31,284)
-3a=25(27,200-31,284)
-3a=25*-4,084 - the negative will cancel out but 4+8+4=16, is not divisible by 3; 31,284 can't be an answer
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