Are all the numbers in a certain list of 20 numbers equal?
(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.
Isn't statement 1 sufficient?
OA B
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Are all the numbers
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
-
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
Statement 1:lheiannie07 wrote:Are all the numbers in a certain list of 20 numbers equal?
(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are equal, so the answer to the question stem is YES.
Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are NOT equal, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2:
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be 5+5 = 10.
In this case, all of the numbers are equal, so the answer to the question stem is YES.
Now let's test whether it is possible to change any of the numbers in Case 1.
Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, 5+1 = 6 , violating the constraint that the sum of any two numbers is 10.
Thus, Case 2 is not viable.
Do you see the situation?
If we change any of the numbers in Case 1, we can't satisfy statement 2.
Implication:
Statement 2 will be satisfied only if every number is 5, with the result that all of the numbers are equal.
Thus, the answer to the 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
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's a similar question to practice with: https://www.beatthegmat.com/are-all-numb ... 74636.html
Cheers,
Brent
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Thanks a lot!GMATGuruNY wrote:Statement 1:lheiannie07 wrote:Are all the numbers in a certain list of 20 numbers equal?
(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are equal, so the answer to the question stem is YES.
Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, no matter which 2 numbers we choose, the sum will be an integer.
In this case, all of the numbers are NOT equal, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2:
Case 1: All 20 numbers are 5 --> {5, 5, 5...5, 5, 5}
Here, no matter which 2 numbers we choose, the sum will be 5+5 = 10.
In this case, all of the numbers are equal, so the answer to the question stem is YES.
Now let's test whether it is possible to change any of the numbers in Case 1.
Case 2: The first 19 numbers are 5, the last number is 1 --> {5, 5, 5...5, 5, 1}
Here, 5+1 = 6 , violating the constraint that the sum of any two numbers is 10.
Thus, Case 2 is not viable.
Do you see the situation?
If we change any of the numbers in Case 1, we can't satisfy statement 2.
Implication:
Statement 2 will be satisfied only if every number is 5, with the result that all of the numbers are equal.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is B.
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Thanks a lot!Brent@GMATPrepNow wrote:Here's a similar question to practice with: https://www.beatthegmat.com/are-all-numb ... 74636.html
Cheers,
Brent
