For how many integers n is 1^n = n^1?
A. none
B. 1
C. 2
D. 3
E. More than 3
The OA is the option B.
How can I show that there is no more than 1 integer? Experts, can you show me this? Thanks.[/spoiler]
For how many integers n is 1^n = n^1?
This topic has expert replies
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi M7MBA,For how many integers n is 1^n = n^1?
A. none
B. 1
C. 2
D. 3
E. More than 3
The OA is the option B.
How can I show that there is no more than 1 integer? Experts, can you show me this? Thanks.[/spoiler]
Let's take a look at your question.
We are asked to find, for how many integers,
$$1^n=n^1$$
Let's try out some random values.
For n = -1
$$1^{(-1)}=(-1)^1$$
$$\frac{1}{1}=-1$$
$$1\ne-1$$
For n = 0
$$1^0=(0)^1$$
$$1\ne0$$
For n = 1
$$1^1=(1)^1$$
$$1=1$$
Therefore, 1^n=n^1 is true for n = 1
Let's check for n = 2,
$$1^2=(2)^1$$
$$1\ne2$$
The given equation will only be true for n = 1
Hence, Option B is correct.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since 1^n always equals 1, we need to determine the number of values of n such that n^1 will equal 1. The only way for n^1 = 1, is when n = 1.M7MBA wrote:For how many integers n is 1^n = n^1?
A. none
B. 1
C. 2
D. 3
E. More than 3
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews