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)
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GMATPrep - If $1000 is deposited in a certain bank
Source: Beat The GMAT — Data Sufficiency |
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)
How could Cramya possibly know what the square root of 1.15 is?
Can anyone show another way to eliminate S2?
Thanks,
Can anyone show another way to eliminate S2?
Thanks,
-
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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It takes time and effort to explain, so if my comment helped you please press Thanks button
It takes time and effort to explain, so if my comment helped you please press Thanks button
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.
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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...
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