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GMATPrep - If $1000 is deposited in a certain bank
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cramya
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Stmt I)
1000 ( (1+r/100) ^ 2 ) - 1) = 210
One eqn one variable we can easily find r (1 SPECIFIC INTEREST RATE) and tell if interest iS greater than 8 or not. No need to solve just knowing that this is sufficient to get to a definite answer will do
SUFF
Stmt II)
(1+r/100) ^ 2 > 1.15
Taking square root on both sides
1+r/100 > sqrt(1.15) (between 1.07 and 1.08 definitely not 1.08 sicne it will be bigger and here otself we know it will be r > 7.something)
r/100 >1.075(approx) - 1
r>7.5...
INSUFF
COULD BE 9 , 19, 7.6 ANYTHING
INSUFF
A)
1000 ( (1+r/100) ^ 2 ) - 1) = 210
One eqn one variable we can easily find r (1 SPECIFIC INTEREST RATE) and tell if interest iS greater than 8 or not. No need to solve just knowing that this is sufficient to get to a definite answer will do
SUFF
Stmt II)
(1+r/100) ^ 2 > 1.15
Taking square root on both sides
1+r/100 > sqrt(1.15) (between 1.07 and 1.08 definitely not 1.08 sicne it will be bigger and here otself we know it will be r > 7.something)
r/100 >1.075(approx) - 1
r>7.5...
INSUFF
COULD BE 9 , 19, 7.6 ANYTHING
INSUFF
A)
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jsl
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Thanks for your help. Can you elaborate a bit more on how you were able to quickly evaluate sqrt(1.15) - can you take me through the steps?cramya wrote:sqrt(1.15) (between 1.07 and 1.08 definitely not 1.08 sicne it will be bigger and here otself we know it will be r > 7.something)
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smackmartine
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(1+r/100)^n = (1+[n*r]/100) (approx.) REMEMBER THIS!navalpike wrote:How could Cramya possibly know what the square root of 1.15 is?
Can anyone show another way to eliminate S2?
Thanks,
So (1+r/100)^2 >1.15
(1+2r/100)> 1.15
2r/100 > 15/100
r>15/2
r>7.5
So, r can be , say, 7.6 or 9 (Insufficient)
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dabral
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Here is a video solution that shows another way to do it without the square root approach:
https://www.gmatquantum.com/shared-posts ... est14.html
Dabral
https://www.gmatquantum.com/shared-posts ... est14.html
Dabral
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GMATGuruNY
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Question: Is r > 8?jsl wrote:If 1,000 is deposited in a certain bank account and remains in the account and any accumulated interest, I, earned by the deposit in the first n years is given by the formula I = 1,000((1 + r/100)^n - 1), where r percent is the annual interest rate paid by the band, is the annual interest rate paid by the bank greater than 8 percent?
1) The deposit earns a total of $210 in interest in the first 2 years
2) (1 + r/100)^2 > 1.15
OA A
Statement 1: The deposit earns a total of $210 in interest in the first 2 years.
Plug I=210 and n=2 into the given equation:
210 = 1,000 ((1+r/100)^2 -1)
We can solve for r.
Sufficient.
Statement 2: (1+r/100)^2 > 1.15
Plug in r=8.
(1 + 8/100)² > 115/100
(108/100)² > 115/100
(108*108)/(100*100) > 115/100
(108*108)/100 > 115
Ballpark the left side:
(11,600)/100 > 115
116 > 115.
Since r=8 works, we know that r>8 also works.
Insufficient.
The correct answer is A.
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Anaira Mitch
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Hello Mitch,GMATGuruNY wrote:Question: Is r > 8?jsl wrote:If 1,000 is deposited in a certain bank account and remains in the account and any accumulated interest, I, earned by the deposit in the first n years is given by the formula I = 1,000((1 + r/100)^n - 1), where r percent is the annual interest rate paid by the band, is the annual interest rate paid by the bank greater than 8 percent?
1) The deposit earns a total of $210 in interest in the first 2 years
2) (1 + r/100)^2 > 1.15
OA A
Statement 1: The deposit earns a total of $210 in interest in the first 2 years.
Plug I=210 and n=2 into the given equation:
210 = 1,000 ((1+r/100)^2 -1)
We can solve for r.
Sufficient.
Statement 2: (1+r/100)^2 > 1.15
Plug in r=8.
(1 + 8/100)² > 115/100
(108/100)² > 115/100
(108*108)/(100*100) > 115/100
(108*108)/100 > 115
Ballpark the left side:
(11,600)/100 > 115
116 > 115.
Since r=8 works, we know that r>8 also works.
Insufficient.
The correct answer is A.
Your solution is perfect but I am confused why this statement is insufficient as you have mentioned
"Since r=8 works, we know that r>8 also works."
Please help me understand.
Thanks in advance.
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GMATGuruNY
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My solution in blue implies the following:Anaira Mitch wrote:Hello Mitch,GMATGuruNY wrote:Statement 2: (1+r/100)^2 > 1.15
Plug in r=8.
(1 + 8/100)² > 115/100
(108/100)² > 115/100
(108*108)/(100*100) > 115/100
(108*108)/100 > 115
Ballpark the left side:
(11,600)/100 > 115
116 > 115.
Since r=8 works, we know that r>8 also works.
Insufficient.
The correct answer is A.
Your solution is perfect but I am confused why this statement is insufficient as you have mentioned
"Since r=8 works, we know that r>8 also works."
Please help me understand.
Thanks in advance.
If r=8, then (1+r/100)² ≈ 1.16.
Question stem:
Is r > 8?
Statement 2: (1+r/100)² > 1.15
Case 1: r=8, with the result that (1+r/100)² ≈ 1.16.
In this case, the answer to the question stem is NO.
Case 2: r=9, with the result that (1+r/100)² > 1.16.
In this case, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Jay@ManhattanReview
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A couple of experts have presented their solutions. They are great. As far as Statement 1 is concerned, there seem to be no issues with regard to the understanding with any.
Statement 2 involves cumbersome calculation to reach the conclusion. So, I focus only on Statement 2.
S2: (1+r/100)^2 > 1.15
We are given that (1+r/100)^2 > 1.15, it means that $1000 would be more than $1150 in 2 years. If we considered (1+r/100)^2 = 1.15, and that the money were on simple interest instead of compound interest, the simple interest rate per annum = 1.5/2 = 7.5.
Since the money is on compounding, the rate in the above scenario must be less than 7.50%. For your interest, it is 7.23%.
So, the rate, r can be anything more than somewhat less than 7.50%.
If ~7.50% < r ≤ 8%, the answer is No.
If r > 8%, the answer is Yes. No unique answer. Insufficient.
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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Statement 2 involves cumbersome calculation to reach the conclusion. So, I focus only on Statement 2.
S2: (1+r/100)^2 > 1.15
We are given that (1+r/100)^2 > 1.15, it means that $1000 would be more than $1150 in 2 years. If we considered (1+r/100)^2 = 1.15, and that the money were on simple interest instead of compound interest, the simple interest rate per annum = 1.5/2 = 7.5.
Since the money is on compounding, the rate in the above scenario must be less than 7.50%. For your interest, it is 7.23%.
So, the rate, r can be anything more than somewhat less than 7.50%.
If ~7.50% < r ≤ 8%, the answer is No.
If r > 8%, the answer is Yes. No unique answer. Insufficient.
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Frankfurt | Hong Kong | Zurich | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
