[GMAT math practice question]
If n is a positive integer, is 3^4+3^{n+4} divisible by 5?
1) n is an even integer.
2) 3^8 +3^{n+8} is divisible by 5.
If n is a positive integer, is 3^4+3^{n+4} divisible by 5?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- 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
3� + 3^(n+4) = 3� + (3^n)(3�) = 3�(1 + 3^n) = 3�(3^n + 1).Max@Math Revolution wrote:[GMAT math practice question]
If n is a positive integer, is 3^4+3^{n+4} divisible by 5?
1) n is an even integer.
2) 3^8 +3^{n+8} is divisible by 5.
The expression in blue will be divisible by 5 only if (3^n + 1) is a multiple of 5.
Question stem, rephrased:
Is (3^n + 1) a multiple of 5?
Statement 1:
Case 1: n=2, with the result that 3^n + 1 = 3² + 1 = 10.
In this case, the answer to the rephrased question stem is YES.
Case 2: n=4, with the result that 3^n + 1 = 3� + 1 = 82
In this case, the answer to the rephrased question stem is NO.
INSUFFICIENT.
Statement 2:
3� + 3^(n+8) = 3� + (3^n)(3�) = 3�(1 + 3^n) = 3�(3^n + 1).
For the expression in red to be divisible by 5, (3^n + 1) must be a multiple of 5.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.
The correct answer is B.
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
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
If n = 2, then 3^4 + 3^{n+4} = 3^4 + 3^6 = 3^4(1+3^2) = 81*10 = 810, and the answer is "yes".
If n = 0, then 3^4 + 3^{n+4} = 3^4 + 3^4 = 3^4(1+1) = 81*2 = 162, and the answer is "no".
Condition 1) is not sufficient.
Condition 2)
Now, 3^8 + 3^{n+8} = 3^8(1+3^n) is divisible by, but 3^8 is not divisible by 5. Since 5 is a prime number, 1+3^n must be divisible by 5.
Thus, 3^4 + 3^{n+4} = 3^4(1+3^n) is also divisible by 5.
Condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
If n = 2, then 3^4 + 3^{n+4} = 3^4 + 3^6 = 3^4(1+3^2) = 81*10 = 810, and the answer is "yes".
If n = 0, then 3^4 + 3^{n+4} = 3^4 + 3^4 = 3^4(1+1) = 81*2 = 162, and the answer is "no".
Condition 1) is not sufficient.
Condition 2)
Now, 3^8 + 3^{n+8} = 3^8(1+3^n) is divisible by, but 3^8 is not divisible by 5. Since 5 is a prime number, 1+3^n must be divisible by 5.
Thus, 3^4 + 3^{n+4} = 3^4(1+3^n) is also divisible by 5.
Condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Statement One Alone:Max@Math Revolution wrote:[GMAT math practice question]
If n is a positive integer, is 3^4+3^{n+4} divisible by 5?
1) n is an even integer.
2) 3^8 +3^{n+8} is divisible by 5.
n is an even integer.
If n = 2, 3^4 + 3^6 = 3^4(1 + 3^2) = 3^4(10), which is divisible by 5.
If n = 4, 3^4 + 3^8 = 3^4(1 + 3^4) = 3^4(82), which is not divisible by 5.
Statement one alone is not sufficient.
Statement Two Alone:
3^8 + 3^{n+8} is divisible by 5.
3^8 + 3^{n+8} = 3^4(3^4 + 3^{n+4})
We are given that 3^8 + 3^{n+8} is divisible by 5. So 3^4(3^4 + 3^{n+4}) is divisible by 5. However, since 3^4 is not divisible by 5, 3^4 + 3^{n+4} must be divisible by 5. Statement two alone is sufficient.
Answer: B
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews