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GMATPrep - If $1000 is deposited in a certain bank

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Source: — Data Sufficiency |
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by cramya » Mon Nov 03, 2008 5:46 pm
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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by jsl » Tue Nov 04, 2008 2:02 am
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)
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?
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by navalpike » Sun Aug 02, 2009 6:43 pm
How could Cramya possibly know what the square root of 1.15 is?

Can anyone show another way to eliminate S2?

Thanks,
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by smackmartine » Mon Jun 27, 2011 7:41 pm
navalpike wrote:How could Cramya possibly know what the square root of 1.15 is?

Can anyone show another way to eliminate S2?

Thanks,
(1+r/100)^n = (1+[n*r]/100) (approx.) REMEMBER THIS!
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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by dabral » Tue Jun 28, 2011 11:02 am
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
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by GMATGuruNY » Tue Jun 28, 2011 1:07 pm
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
Question: Is r > 8?

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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by Anaira Mitch » Mon Jan 30, 2017 4:19 pm
GMATGuruNY wrote:
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
Question: Is r > 8?

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.
Hello Mitch,

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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by GMATGuruNY » Tue Jan 31, 2017 5:20 am
Anaira Mitch wrote:
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.
Hello Mitch,

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.
My solution in blue implies the following:
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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by Jay@ManhattanReview » Tue Jan 31, 2017 9:58 pm
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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