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.
percents
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Given : $5000 invested for one year at p percent simple annual interest yields $500kamalakarthi wrote: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.
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
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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:kamalakarthi wrote: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
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
Last edited by Brent@GMATPrepNow on Sun Aug 17, 2014 10:25 am, edited 1 time in total.
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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..
I guess a typo error occurred while you were typing the answer option. You meant Option 'D' but typed it 'C' by mistake..
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Thanks, Bhoopendra!
I've edited my response.
Cheers,
Brent
I've edited my response.
Cheers,
Brent
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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:kamalakarthi wrote: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
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
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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
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
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Since interest amount = principal x interest rate x time, we have:kamalakarthi wrote: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
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
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