GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The “hash” of a three-digit integer with three distinct digi
[#permalink]
23 Jan 2020, 10:54
23 Jan 2020, 10:54
Expert Reply
3
Bookmarks
00:00
Question Stats:
61% (02:26) correct
38% (01:18) wrong based on 34 sessions
Hide Show timer Statistics
The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Kudos for the right answer and explanation
A. 9
B. 7
C. 5
D. 4
E. 2
Kudos for the right answer and explanation
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Given Kudos: 0
GPA: 3.72
Re: The “hash” of a three-digit integer with three distinct digi
[#permalink]
23 Jan 2020, 12:01
23 Jan 2020, 12:01
2
Question:
The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Solution:
Let the 3-digit number be N = abc where a is the hundreds digit, b is the tens digit and c is the units digit
Thus, we can write the number as: N = 100a + 10b + c
Thus, "hash" N i.e. #N = 100c + 10b + a (since we have to interchange the units and hundreds digits keeping the tens digit unchanged)
Thus, absolute value of the difference: |N - #N| = |99a - 99c| = 99 * |a - c|
Thus, the difference is divisible by 9 and 11.
Answer A
The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Solution:
Let the 3-digit number be N = abc where a is the hundreds digit, b is the tens digit and c is the units digit
Thus, we can write the number as: N = 100a + 10b + c
Thus, "hash" N i.e. #N = 100c + 10b + a (since we have to interchange the units and hundreds digits keeping the tens digit unchanged)
Thus, absolute value of the difference: |N - #N| = |99a - 99c| = 99 * |a - c|
Thus, the difference is divisible by 9 and 11.
Answer A
Re: The “hash” of a three-digit integer with three distinct digi
[#permalink]
02 Mar 2022, 21:26
02 Mar 2022, 21:26
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
