percents

[kamalakarthi]

If $5000 invested for one year at p percent simple annual interest yields $500,what amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?


1. k=0.8p
2. k=8

This question is from OG. Can you please help me to solve and understand. Thanks in advance.

[GMATinsight]

If $5000 invested for one year at p percent simple annual interest yields $500,what amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?


1. k=0.8p
2. k=8

This question is from OG. Can you please help me to solve and understand. Thanks in advance.

Given : $5000 invested for one year at p percent simple annual interest yields $500

i.e. (p/100)$5000 = $500
i.e. p = 10%

Question : Amount to be invested to earn $500 as interest at k% rate
i.e. we need the value of k

Statement 1) k = 0.8p
i.e. k = 0.8 x 10 = 8%
i.e. (k/100)X = $500
i.e. (8/100)X = $500
i.e. X = 500 x 12.5 = $6250
Sufficient

Statement 2) k = 8
Same Process
Sufficient

Answer: Option D

[Brent@GMATPrepNow]

If $5000 invested for one year at p percent simple annual interest yields $500,what amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?

1) k = 0.8p
2) k = 8

The great thing about DS questions is that we aren't required to perform calculations if we know that we COULD perform those calculations. Here's what I mean:

Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?

Given: If $5000 invested for one year at p percent simple annual interest yields $500
IMPORTANT: There's ONLY ONE possible value of p that will yield $500 interest after 1 year (if $5000 is invested). So, we COULD perform some calculations to determine that ONE VALUE of p.

Statement 1: k = 0.8p
Since we COULD determine the value of p, we COULD also determine the value of k Using the fact that k = 0.8p).
Once we know the ONE value of k, we COULD determine how much money needs to be invested to get $500 in interest after 1 year.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k = 8
Perfect!
Once we know the value of k, we COULD determine how much money needs to be invested to get $500 in interest after 1 year.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

[GMATinsight]

Hi Brent,

I guess a typo error occurred while you were typing the answer option. You meant Option 'D' but typed it 'C' by mistake..

[Brent@GMATPrepNow]

Thanks, Bhoopendra!

I've edited my response.

Cheers,
Brent

[Brent@GMATPrepNow]

If $5000 invested for one year at p percent simple annual interest yields $500,what amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?


1. k=0.8p
2. k=8

The great thing about DS questions is that we aren't required to perform calculations if we know that we COULD perform those calculations. Here's what I mean:

Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?

Given: If $5000 invested for one year at p percent simple annual interest yields $500
IMPORTANT: There's ONLY ONE possible value of p that will yield $500 interest after 1 year (if $5000 is invested). So, we COULD perform some calculations to determine that ONE VALUE of p.

Statement 1: k = 0.8p
Since we COULD determine the value of p, we COULD also determine the value of k Using the fact that k = 0.8p).
Once we know the ONE value of k, we COULD determine how much money needs to be invested to get $500 in interest after 1 year.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k = 8
Perfect!
Once we know the value of k, we COULD determine how much money needs to be invested to get $500 in interest after 1 year.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

[[email protected]]

Hi All,

We're told that $5000 invested for one year at P percent simple annual interest yields $500. We're asked for the AMOUNT that must be invested at K percent simple annual interest for one year to yield the same amount of dollars.

To start, the Simple Interest Formula is:

Total = (Principal)[1 + (R)(T)] where R is the annual interest rate and T is the number of years. Since we're focused on the INTEREST generated, we'll be dealing with (Principal)(R)(T).

Since $5,000 is invested for 1 year at simple annual interest, the interest rate (P) is 10%

1) K = 0.8P

With the information in Fact 1 - and the fact that P = 10, we know that K = 8%. Knowing this, we COULD calculate the amount that would need to be invested at 8%...

(Principal)(.08) = $500

With one variable and one equation, we CAN solve this equation (the good news is that we don't technically have to do that math here - we KNOW that there will be just one answer).
Fact 1 is SUFFICIENT

2) K = 8

With the value of K, we can solve the necessary equation (from Fact 1).
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

If $5000 invested for one year at p percent simple annual interest yields $500,what amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?


1. k=0.8p
2. k=8

Since interest amount = principal x interest rate x time, we have:

500 = 5000 x p/100 x 1

500 = 50 x p

p = 10

Let A = principal that yields $500 interest at k percent simple annual interest rate in one year, so we have:

500 = A x k/100 x 1

50000/k = A

So if we know the value of k, we can determine the value of A.

Statement One Alone:

k=0.8p

Since p = 10, then k = 0.8(10) = 8. Since we know the value of k, we can determine the value of A (without actually determining it). Statement one alone is sufficient.

Statement Two Alone:

k=8

Since we know the value of k, we can determine the value of A (without actually determining it). Statement two alone is sufficient.

Answer: D