GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Feb 2019, 07:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

### Show Tags

01 Nov 2010, 16:32
7
54
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:22) correct 51% (02:21) wrong based on 1028 sessions

### HideShow timer Statistics

If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, I, earned by the deposit in the first n years is given by the formula $$I=1,000((1+\frac{r}{100})^n-1)$$, where r percent is the annual interest rate paid by the bank. 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 two years

(2) $$(1 + \frac{r}{100})^2 > 1.15$$

Attachment:

GMAT Prep Q29_NA.JPG [ 57.45 KiB | Viewed 29355 times ]
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India

### Show Tags

15 Mar 2013, 15:47
9
I think the gmat is always about insight and not about arithemetic
.
Question: Is r>8%? If r can be 8 percent or greater, the statement will be insufficient.

Stmt 2) Overall interest earned over two years, is greater than 15% (If you read this far down, you know what I am talking about)
Lets say the interest was 8%, then overall compound interest earned over two years will be greater than 16% and so greater than 15%
It goes without saying that if the interest rate was greater than 8%, then the amount of interest earned over two years, will still be greater than 15%.

It took me 1:30 seconds to see this, and another 40 seconds to type this entire post because I was not satisfied with the explanations given
.No messy calculations or nail biting necessary.
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 01 Nov 2010, 19:07 15 18 If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. (2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$. Answer: A. _________________ Intern Joined: 18 Aug 2010 Posts: 10 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

01 Nov 2010, 19:16
ah... for S2, I approached it from the other angle and had to take the square root of 1.15. I got stuck there and time was running out, so I took a guess. It's much easier to multiply 1.08 by 1.08 than to take the square root of 1.15.

Thanks!
Senior Manager
Joined: 27 Jun 2012
Posts: 368
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 25 Dec 2012, 19:42 Bunuel wrote: If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. (2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$. Answer: A. Hello Bunuel, your explanation for second DS choice suggests that, if we have only 1 variable in the equation, then we need not solve it. However, I have observed few of the GMAT problems that have similar quadratic equations (with second degree) solve to two different positive roots, hence the DS choice could not be true. I believe it would be safe to solve the equation until you know if its only going to give you "one" root. e.g. $$ax^2+bx-c=0$$, this equation will have one positive and one negative root. As rate in this case is supposed to be positive, hence only 1 root. However, if the equation resolves to $$ax^2-bx+c=0$$ then it can have two positive roots (one of which may be less than 8 and other more than 8), hence the choice may not be true. Only if both positive roots are more than 8, then the choice can be taken as true. Please advice. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1101
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 02 Jan 2013, 20:32 2 1 kiyo0610 wrote: If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. 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 two years. (2) (1+r/100)^2 >1.15 statement 1) I=$210, n=2
Putting this in the equation given in the question, we will be able to find the value of r and thereby be able to answer the question. Suffiicient.

Statement 2) Using Binomial theorem, we can infer $$(1+r/100)^2 > 1.15$$ as $$(1+2r/100) > 1.15$$.
On solving this relation we will get, r>7.5.
But since its not given that r is an integer then r can be 7.51, 7.6,9, 11 etc. Hence insufficient.

+1A
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India

### Show Tags

14 Mar 2013, 23:40
Marcab wrote:
kiyo0610 wrote:
If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. 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 two years.

(2) (1+r/100)^2 >1.15

The total interest is given as I=1,000[(1+r/100)^n - 1].

From F.S 1 we have that I = 210. Thus, we have a quadratic equation and we know that it can be solved leading to a fixed value for r. Sufficient.Also, one can notice that an interest of 210$is obtained when r=10% and this is greater than 8%. Sufficient. From F.S 2, we know that n=2. And the Interest earned would be greater than 150.Thus, I=1,000[(1+r/100)^2 - 1] = $$1000[r/100*(2+\frac{r}{100})]$$. We know for r=8% we have this equal to 2.08*80 = 166.4 which is anyways greater than 150. Now, for r=7%, the expression equals 2.07*70 = 144.9. Thus, for a value between 7 and 8 , this value will change and become more than 150. Thus we wouldn't know for sure if r>8 or not. Insufficient. A. _________________ Manager Joined: 14 Aug 2005 Posts: 66 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

16 Mar 2013, 13:26
Brilliant!

I was convinced the answer is D, when i realized that 7.99^2 is also a matter of concern!
_________________

One Last Shot

Intern
Joined: 18 Jan 2013
Posts: 1

### Show Tags

19 Mar 2013, 19:39
chandrak wrote:
hi all , why not D?
From first statement, one can answer that interest rate is greater than 8%
From second second statement, one can answer that interest rate is less than 8%

So, either statement can be used to answer the question. Am I missing any thing? Please reply.

How can you say that the interest rate is less than 8% from the second statement?

If r were 8%, we would have (1 + r/100 )^2 = 1.08^2 = 1.1664

Now all that statement 2 tells us is that (1 + r/100 )^2 > 1.15
We don't know whether it is less than 1.1664 or greater. Hence statement 2 alone is not sufficient.

Besides, it is not possible that statement 1 tells you that r is greater than 8% and statement 2 tells you that it is less than 8%. This is a conflict. If both statements independently give you the answer, the answer you will get will be the same i.e. either both will tell that r is greater than 8% or both will tell that r is less than 8%.
_________________

Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 22 Nov 2010
Posts: 221
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 29 Mar 2013, 07:54 Bunuel wrote: If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. (2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$. Answer: A. Bunuel, As this is a quadratic equation , how did you concluded that we will get one value after solving this equation? _________________ YOU CAN, IF YOU THINK YOU CAN Intern Joined: 23 Mar 2011 Posts: 27 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

17 Jul 2013, 10:15
greatps24 wrote:
Bunuel wrote:
If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent? Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$. (1) The deposit earns a total of$210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient.

Bunuel,

As this is a quadratic equation , how did you concluded that we will get one value after solving this equation?

Same question for Bunuel or any of the other experts here.

My calculations:

1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$

2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$

3) $$210=1000(\frac{200r+r^2}{10,000})$$

4) $$210=\frac{200r+r^2}{10}$$

5) $$2100=r(200+r)$$

How do you solve for the variable r at this point?

Any further explanation would help.

~ Im2bz2p345
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 17 Jul 2013, 20:05 3 3 Im2bz2p345 wrote: greatps24 wrote: Bunuel wrote: If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. Bunuel, As this is a quadratic equation , how did you concluded that we will get one value after solving this equation? Same question for Bunuel or any of the other experts here. My calculations: 1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$ 2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$ 3) $$210=1000(\frac{200r+r^2}{10,000})$$ 4) $$210=\frac{200r+r^2}{10}$$ 5) $$2100=r(200+r)$$ How do you solve for the variable r at this point? Any further explanation would help. ~ Im2bz2p345 Solving this quadratic is a little time consuming though we will see how to do in a minute. But you don't really need to solve it to figure out that you will have only one solution. $$2100=r(200+r)$$ $$r^2 + 200r - 2100 = 0$$ In a quadratic, $$ax^2 + bx + c = 0$$, sum of the roots = -b/a and product of the roots = c/a Notice that the product of the roots (-2100) is negative. This means one root is positive and the other is negative. So we will have only one acceptable solution (the positive one) Now, if you would like to solve it: $$r^2 + 200r - 2100 = 0$$ 2100 = 2*2*5*5*3*7 Now you need to split 2100 into two factors such that one is a little larger than 200 and the other is a small factor e.g. 5 or 7 or 10 etc. Once you think this way, you easily get 210 and 10 $$r^2 + 210r - 10r - 2100 = 0$$ (r + 210)(r - 10) = 0 r = -210 or 10 _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 23 Mar 2011 Posts: 27 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

17 Jul 2013, 20:17
VeritasPrepKarishma wrote:
Solving this quadratic is a little time consuming though we will see how to do in a minute. But you don't really need to solve it to figure out that you will have only one solution.

$$2100=r(200+r)$$
$$r^2 + 200r - 2100 = 0$$

In a quadratic, $$ax^2 + bx + c = 0$$, sum of the roots = -b/a and product of the roots = c/a
Notice that the product of the roots (-2100) is negative. This means one root is positive and the other is negative. So we will have only one acceptable solution (the positive one)

Now, if you would like to solve it:
$$r^2 + 200r - 2100 = 0$$

2100 = 2*2*5*5*3*7
Now you need to split 2100 into two factors such that one is a little larger than 200 and the other is a small factor e.g. 5 or 7 or 10 etc. Once you think this way, you easily get 210 and 10

$$r^2 + 210r - 10r - 2100 = 0$$
(r + 210)(r - 10) = 0
r = -210 or 10

Perfect! Thank you Karishma for filling in these last steps for me. You're always a big help!

As PraPon pointed out earlier in the thread, I believe it's important to bring the first statement down to the $$r^2 + 200r - 2100 = 0$$ level, otherwise there is no "guarantee" that r will only have one root.

Once you realize there is will be a positive & negative solution and that you can simply "ignore" the negative solution since we checking to see if r > 8 (leaving you with truly one solution), then you can make the judgement that the first statement is sufficient.

I just don't know how you can assume the solution of $$210=1,000((1+\frac{r}{100})^2-1)$$ will have only ONE positive solution (as you pointed out Karishma, if the simplified form gave you "+ 2100" instead of "- 2100," the statement would be insufficient due to having TWO positive solutions).

~ Im2bz2p345
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 17 Jul 2013, 22:49 5 Im2bz2p345 wrote: greatps24 wrote: Bunuel wrote: If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. Bunuel, As this is a quadratic equation , how did you concluded that we will get one value after solving this equation? Same question for Bunuel or any of the other experts here. My calculations: 1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$ 2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$ 3) $$210=1000(\frac{200r+r^2}{10,000})$$ 4) $$210=\frac{200r+r^2}{10}$$ 5) $$2100=r(200+r)$$ How do you solve for the variable r at this point? Any further explanation would help. ~ Im2bz2p345 Actually you don't need to solve this way: $$1,000((1+\frac{r}{100})^2-1)=210$$ $$(1+\frac{r}{100})^2-1=\frac{210}{1,000}$$ $$(1+\frac{r}{100})^2=\frac{21}{100}+1$$ $$(1+\frac{r}{100})^2=\frac{121}{100}$$ $$1+\frac{r}{100}=\frac{11}{10}$$ ($$1+\frac{r}{100}$$ cannot equal to $$-\frac{11}{10}$$ because it would men that r is negative.) $$1+\frac{r}{100}=\frac{11}{10}$$ $$\frac{r}{100}=\frac{1}{10}$$ $$r=10$$ _________________ Intern Joined: 23 Mar 2011 Posts: 27 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

18 Jul 2013, 07:47
Bunuel wrote:
Actually you don't need to solve this way:

$$1,000((1+\frac{r}{100})^2-1)=210$$

$$(1+\frac{r}{100})^2-1=\frac{210}{1,000}$$

$$(1+\frac{r}{100})^2=\frac{21}{100}+1$$

$$(1+\frac{r}{100})^2=\frac{121}{100}$$

$$1+\frac{r}{100}=\frac{11}{10}$$ ($$1+\frac{r}{100}=\frac{11}{10}$$ cannot equal to $$-\frac{11}{10}$$ because it would men that r is negative.)

$$1+\frac{r}{100}=\frac{11}{10}$$

$$\frac{r}{100}=\frac{1}{10}$$

$$r=10$$

Thank you Bunuel for this alternate calculation method!

It's much easier this way you showed. Greatly appreciate your follow-up.

~ Im2bz2p345
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 31 Oct 2015, 23:26 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. 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 two years (2) (1 + r/100 )^2 > 1.15 There are 3 variables (r,I,n) and 1 equation (I=1,000((1+r/100)^n-1) in the original condition, 2 equations from the 2 conditions; there is high chance (C) will be our answer. In condition 1, there are 2 equations, and if the interest is$210, the interest rate is either greater (yes) or smaller (no) than 8%, therefore sufficient.
In condition 2, (1.08)^2=1.1664, the interest rate is not greater than 8%, so this is insufficient.

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 10 Mar 2013 Posts: 498 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

20 Jan 2016, 12:36
butterfly wrote:
If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of 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 bank. 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 two years
(2) (1 + r/100 )^2 > 1.15

No need for complex calculations here.
(1) Interest=210 r=10% (if you have done several compound interest problems this number is very frequent, so I could see this within 10 seconds because of my previous experience). Sufficient
(2) This statment tells us that r was slightly more than 7,5% --> see 1,15 on the other side, so r can be <>8% . Not Sufficient

Amswer A
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660