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

 It is currently 19 Sep 2018, 19:52

### 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

### Show Tags

30 Sep 2015, 12:15
4
1
13
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:35) correct 35% (02:55) wrong based on 128 sessions

### Show Tags

02 Oct 2015, 00:20
5
2
reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60%$100 was invested in each fund.

### Show Tags

01 Oct 2015, 00:08
2
reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60% reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

----------------------------------
we know Value of A after 1 year
V1a = V1b+10
and after second year
V2a = V2b+25

and initial amount is 100 for A and B

Substitute from answers and check if it matches the above equations

B : 30
After 1 year
Va1 = 130 = Vb1+10 => Vb1 = 120 => interest for B = 20

After 2nd year
Va2 = 169
Vb2 = 144
it fits our equation Va2 = Vb2+25

Substituting A:20 gives Va2-Vb2=23 but should be 25
C:40 => Va2-Vb2=27
Intern
Joined: 29 Mar 2015
Posts: 22
John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 01 Oct 2015, 19:36 4 The first part of the question tells us that there is a 10% difference between both rates: If, let's say, the fixed rate of fund A was 40%, then the value would have increased to$140 in the first year.
Fund B must have increased to $130 ($140 - $130 =$10) - thus fund B is appreciating at a fixed rate of 30%.

Note how these rates translate into 1.4 (=1+40/100) and 1.3. I like to translate those into 14 and 13.

The second piece of the question stems tell us that the difference between the squares of the two number is $25. Squares because the formula for two years of annual compounding is (1+ r/100)^2. What we are essentially looking for is a number X which square is 25 more than the square of the number X - 1. $$x^2 - (x-1)^2 = 25$$ $$x^2 - x^2 + 2x - 1 = 25$$ $$x = 13$$ Thus, the answer is 30%. Math Expert Joined: 02 Aug 2009 Posts: 6787 Re: John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

### Show Tags

02 Oct 2015, 00:37
4
1
reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60% Hi, since the increase is on 100$, the diff in values will be 10 so say A and B be the annual interest respectively...
A-B=10.. or A=B+10..
now for second year..
$$\frac{100(100+A)(100+A)}{100^2}-\frac{100(100+B)(100+B)}{100^2}=25$$
(100+A)(100+A)-(100+B)(100+B)=2500...
substitute A=B+10....
$$(110+B)^2-(100+B)^2=2500$$
or (110+B+100+B)(110+B-100-B)=2500
210+B=250
B=20..
so A=30
Ans B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 01 Aug 2015
Posts: 17
Location: India
Concentration: Technology, Statistics
GPA: 4
WE: Engineering (Computer Software)
John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 03 Oct 2015, 10:14 4 I think the quickest way to solve is through back solving, we know rA = rB +10 And after 2 years Amount(A) is higher than Amount(B) by 25$
C) 40%
so rB =30%
Amount(A) = 100x(1.4)^2
Amount(B) = 100x(1.3)^2
----------------
27$> 25$

So rA must be less than 40%, so its A or B.

A) 20%
so rB =10%
Amount(A) = 100x(1.2)^2
Amount(B) = 100x(1.1)^2
----------------
23$B) 30% so rB =10% Amount(A) = 100x(1.3)^2 Amount(B) = 100x(1.2)^2 ---------------- 25$
_________________

With the new day comes new strength and new thoughts.
~Eleanor Roosevelt
_____________________________________________

Feel free to +1 Kudos if you like this post

Retired Moderator
Joined: 29 Apr 2015
Posts: 853
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 04 Oct 2015, 01:17 3 reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

Plugging in seems most efficient:

Fund A, Fund B
100, 100
140, 130 (A is 10 more, from the statement, hence 30% growth rate)
196, 169 (A is not $25 more as ist should be, --> let's go on with B, one lower because we need a lower difference). Fund A, Fund B 100, 100 130, 120 (A is 10 more, as defined in the text, hence 20% p.a. growth rate). 169, 144 (Here we go, A is$25 higher, this is the solution).
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Intern
Joined: 31 Aug 2014
Posts: 22
Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 07 Oct 2015, 12:43 4 reto wrote: reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

Plugging in seems most efficient:

Fund A, Fund B
100, 100
140, 130 (A is 10 more, from the statement, hence 30% growth rate)
196, 169 (A is not $25 more as ist should be, --> let's go on with B, one lower because we need a lower difference). Fund A, Fund B 100, 100 130, 120 (A is 10 more, as defined in the text, hence 20% p.a. growth rate). 169, 144 (Here we go, A is$25 higher, this is the solution).

if rate of interest in fund A is 20%, rate of interest in fund B is 10% and difference in interest earned on interest = 20% of 20 - 10% of 10 = 4 -1 = 3
If rate of interest in fund A is 30%, rate of interest in fund B is 20% and difference in interest earned on interest = 30% of 30 - 20% of 20 = 9 - 4 = 5 (Correct)

_________________

Please press+ 1kudos if you appreciate this post and for motivation !!

Intern
Joined: 28 Oct 2014
Posts: 2
Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 08 Oct 2015, 21:45 1 Greetings Everyone! Had no interest in solving by the use of formulae which have already been stated brilliantly in the above posts. So I used the tragic method of trial and error. As stated in the question, the interest is compounded. It's also easy to spot the words "fixed interest rates and$10, $25" differences. A quick glance at the options and you might get a gist of the answer that awaits. A$10 difference will point to the rates being 10% apart. But what's also given is that the rates will differ by $25 the next year. So compounding the rates, you'll notice that at 30 you get$169 in the second, whilst a 10% gap to 20% at which fund B will be computed, and you will realize that the amount comes to $144. After 1st year (130 * 30%) and ($120* 20%). 130 and 120 are amounts with interests from the first year.
So an exact $25 difference arises and problem == solved. Non-Human User Joined: 09 Sep 2013 Posts: 8095 Re: John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

### Show Tags

30 May 2018, 08:57
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.
_________________

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.