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

 It is currently 20 Feb 2019, 13:51

### 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 GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

### Show Tags

03 Feb 2016, 09:41
BrainLab wrote:
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

I also avoided the route of quadratic equations here. The first thing I asked myself, how much compound interest (approx). would be earned with an 8% interest rate.
If I invest $1,000, I will get$80 interest the first year, and $80 interest the second year, makes$160 in total. Compound interest on the interest earned during the first year is another 8% on $80, so$6.4.

In total I received interest of $166.4 (1) Deposit earns$210, that is clearly more than what I would get with 8% interest => Sufficient
(2) If it's not immediately obvious that this statement actually tells you that you earn more than 15% compound interest on the investment in 2 years, look closely at the given formula in the stem. This equals to $150 for the$1,000 investment. So the compound interest could be lower or higher compared to what I get with 8% => Insufficient
Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 30 Jan 2017, 16:16 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 solution is perfect but I am still confused that why this statement is insufficient because if at r =8 this condition is true 1.16>1.15(1+r100)2=(1+8100)2=1.082≈1.16>1.15, then at r>8 this condition will also be true hence confused with this. Thanks in advance. _________________ Thanks & Regards, Anaira Mitch Intern Joined: 29 Jul 2017 Posts: 12 GMAT 1: 650 Q50 V27 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

### Show Tags

25 Sep 2017, 06:33
Dear Experts Bunuel, VeritasPrepKarishma,

In case of inequalities, can we take square roots on both sides?
Math Expert
Joined: 02 Sep 2009
Posts: 53020

### Show Tags

12 Oct 2018, 06:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________