GMAT Prep
Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?
1) Ann deposited $200 more in account B than in account A.
2) The total amount of interest that the two accounts earned in the first year was $120.
OA C
Ann deposited money into two new accounts, A and B. Account
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
SayAAPL wrote:GMAT Prep
Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?
1) Ann deposited $200 more in account B than in account A.
2) The total amount of interest that the two accounts earned in the first year was $120.
OA C
Ann deposited $A in Account A and $B in Account B.
Thus, she earned 5A/100 = $A/20 in the first year from Account A and earned 8B/100 = $2B/25 in the first year from Account B.
We have to get the value of 2B/25 - A/20.
Let's take each statement one by one.
1) Ann deposited $200 more in account B than in account A.
Thus, 2B/25 - A/20 = 2(A + 200)/25 - A/20 = 2A/25 - A/20 + 16 = 3A/100 + 16. We don't have the value of A. Insufficient
2) The total amount of interest that the two accounts earned in the first year was $120.
=> 2B/25 + A/20 = 120
Can't get the unique value of 2B/25 - A/20. Insufficient.
(1) and (2) together
From (2), we have 2B/25 + A/20 = 120; plugging-in the value of B = A + 200, we get
2(A + 200)/25 + A/20 = 120
2A/25 + 16 + A/20 = 120
13A/100 = 104
A = $800 and B = 800 + 200 = $1,000
Thus, 2B/25 - A/20 = (2*1,000)/25 - 800/20 = $40. Sufficient.
The correct answer: C
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: GRE Manhattan | TOEFL Prep Courses Boston | IELTS Prep Courses San Francisco | Philadelphia ACT Tutoring | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$SI=\frac{PRT}{100}$$
$$For\ account\ A,\ SI=\frac{ART}{100}=\frac{\left(A\cdot5\cdot1\right)}{100}=0.05A$$
$$For\ account\ B;\ SI=\frac{BRT}{100}=\frac{\left(B\cdot8\cdot1\right)}{100}=0.08B$$
Statement 1
Ann deposited 250 dollars more in account B than account A
$$B-200=A$$
$$B=A+200$$
$$SI\ for\ A\ =\ 0.05A=0.05\cdot\left(B-200\right)$$
$$=0.05B-10\ $$
$$Value\ of\ A<B\ still\ remains\ unknown$$
Statement 1 is INSUFFICIENT.
Statement 2
The Total amount of interest in the two accounts in the first year was 120 dollars.
(S.I for A) + (S.I for B) = 120 dollars
0.05A + 0.08B = 120 dollar
Value of A and B are not given, hence statement 2 is INSUFFICIENT.
Combining both statement together
0.05A + 0.08B = 120 dollars ----- statement 2
where A = B - 200 -----statement 1
$$0.05\left(B-200\right)+0.08B=120\ $$
$$0.05B-10+0.08B=120$$
$$0.05B+0.08B=120+10$$
$$0.05B+0.08B=130$$
$$\frac{0.13B}{0.13}=\frac{130}{0.13}$$
$$B=1000\ dollar$$
$$0.05A+0.08\left(1000\right)=120$$
$$0.05A=120-80$$
$$\frac{0.05A}{0.05}=\frac{40}{0.05}$$
$$A=800\ dollars$$
$$SI\ for\ A\ =0.05\cdot800$$
$$SI\ for\ B=0.08\cdot1000$$
$$Difference=\ 80-40=\ 40\ dollar$$
Interest in account B for first year is 40 dollar greater than interest in Account A
Both statement together are SUFFICIENT.
$$Answer\ is\ Option\ C$$
$$For\ account\ A,\ SI=\frac{ART}{100}=\frac{\left(A\cdot5\cdot1\right)}{100}=0.05A$$
$$For\ account\ B;\ SI=\frac{BRT}{100}=\frac{\left(B\cdot8\cdot1\right)}{100}=0.08B$$
Statement 1
Ann deposited 250 dollars more in account B than account A
$$B-200=A$$
$$B=A+200$$
$$SI\ for\ A\ =\ 0.05A=0.05\cdot\left(B-200\right)$$
$$=0.05B-10\ $$
$$Value\ of\ A<B\ still\ remains\ unknown$$
Statement 1 is INSUFFICIENT.
Statement 2
The Total amount of interest in the two accounts in the first year was 120 dollars.
(S.I for A) + (S.I for B) = 120 dollars
0.05A + 0.08B = 120 dollar
Value of A and B are not given, hence statement 2 is INSUFFICIENT.
Combining both statement together
0.05A + 0.08B = 120 dollars ----- statement 2
where A = B - 200 -----statement 1
$$0.05\left(B-200\right)+0.08B=120\ $$
$$0.05B-10+0.08B=120$$
$$0.05B+0.08B=120+10$$
$$0.05B+0.08B=130$$
$$\frac{0.13B}{0.13}=\frac{130}{0.13}$$
$$B=1000\ dollar$$
$$0.05A+0.08\left(1000\right)=120$$
$$0.05A=120-80$$
$$\frac{0.05A}{0.05}=\frac{40}{0.05}$$
$$A=800\ dollars$$
$$SI\ for\ A\ =0.05\cdot800$$
$$SI\ for\ B=0.08\cdot1000$$
$$Difference=\ 80-40=\ 40\ dollar$$
Interest in account B for first year is 40 dollar greater than interest in Account A
Both statement together are SUFFICIENT.
$$Answer\ is\ Option\ C$$
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
What is the value of 0.08B - 0.05A?AAPL wrote:GMAT Prep
Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?
1) Ann deposited $200 more in account B than in account A.
2) The total amount of interest that the two accounts earned in the first year was $120.
Statement 1:
B-A = 200
B = A+200
Case 1: A = $100 and B=$300, with the result that 0.08B - 0.05A = 0.08(300) - 0.05(100) = 24-5 = 19
Case 2: A = $200 and B=$400, with the result that 0.08B - 0.05A = 0.08(400) - 0.05(200) = 32-10 = 22
Since 0.08B-0.05A can be different values, INSUFFICIENT.
Statement 2:
0.05A + 0.08B = 120
No way to determine the value of 0.08B-0.05A.
INSUFFICIENT.
Statements combined:
Since we have two variables (A and B) and two distinct linear equations (B-A=200 and 0.05A + 0.08B = 120), we can solve for the two variables.
Thus, the value of 0.08B-0.05A can be determined.
SUFFICIENT.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3