For integers x and y, 1 < x < y. Is x^y a factor of 11!?
(1) x > 3
(2) x is prime
OA A
Source: Veritas Prep
For integers x and y, 1 < x < y. Is x^y a factor of 11
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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
Given: 1 < x < y; where x and y are positive integersBTGmoderatorDC wrote:For integers x and y, 1 < x < y. Is x^y a factor of 11!?
(1) x > 3
(2) x is prime
OA A
Source: Veritas Prep
We have to determine whether x^y is a factor of 11!.
Let's take each statement one by one.
(1) x > 3
Case 1: Say x = Very big number; thus, y is also a very big number. So, can conclude that x^y would not be a factor of 11!. The answer is No,
Let's see at smaller values of x and y, do we have x^y a factor of 11!?
Case 2: Say x = 4, smallest possible number; thus, y = 5, smallest possible value for y.
x^y = 4^5 = 2^10
Note that 11! = 1.2.3.4.5.6.7.8.9.10.11. There are eight 2's in 11!. Since the exponent of 2^10 is 10 and is greater than 8, x^y cannot be a factor of 11!. The answer is No,
There is no need to explore further such as x^y = 5^6 since greater numbers would obviously be insufficient in 11!.
Unique answer. Sufficient.
(2) x is prime
Case 1: Say = 2 and y = 3; thus, x^y = 2^3. We already saw that 11! has eight 2's, more than sufficient for 2^3 to be its factor. The answer is Yes.
Case 2: Say x = Very big prime number; thus, y is also a very big number. So, can conclude that x^y would not be a factor of 11!. The answer is No,
No unique answer. Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review
Locations: Manhattan Review Mumbai | GMAT Prep New Delhi | GRE Prep Malleswaram | Vijayawada GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.