Last visit was: 04 Oct 2024, 04:19 It is currently 04 Oct 2024, 04:19
Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95937
Own Kudos [?]: 665018 [75]
Given Kudos: 87505
Send PM
Most Helpful Reply
Joined: 29 Jun 2017
Posts: 305
Own Kudos [?]: 833 [21]
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 95937
Own Kudos [?]: 665018 [2]
Given Kudos: 87505
Send PM
General Discussion
Joined: 04 Oct 2016
Posts: 7
Own Kudos [?]: 3 [2]
Given Kudos: 3
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
2
Bookmarks
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

A. 3
B. 6
C. 7
D. 60
E. 70
100x+10y+z-100z+10y+x=297
99(x-z)=297
x-z = 3
there are 6 possible numbers for x. for example: 9y6-6y9=297 and so on till x=4
as for y. there are 10 possibilities: from 0 to 9
so 6*10=60 pairs possible.
so answer is D
Joined: 12 Dec 2015
Posts: 462
Own Kudos [?]: 548 [2]
Given Kudos: 84
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
1
Kudos
1
Bookmarks
Ans: D

N=100x+10y+z
=> (100x+10y+z) - (100x+10y+z) =297
=> x-z =3
(1) x <=9, z <=6 <=> Total 6 pairs z=1,2,3,4,5 & 6
(2) y can be 0 to 9(Total 10)

Total possibilities = 6*10=60
Joined: 26 Sep 2017
Posts: 11
Own Kudos [?]: 4 [0]
Given Kudos: 16
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
sahilvijay
IMO D

abc -cba =297
100a+10b+c - (100c+10b+a) = 297
100(a-c) +c-a = 297
99(a-c) =297
a-c =3
b can take 0-9 => 10 values
but c can not be 0 since reverse number is also 3 digit humber
so c can take 1,2,3,4,5,6 => 6 values
Hence total numbers possible
6x10=60

D is the Answer

What about a?
b*c= 10 * 6= 60
so what about a? where have it gone?
Joined: 29 Jun 2017
Posts: 305
Own Kudos [?]: 833 [0]
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
lor12345
sahilvijay
IMO D

abc -cba =297
100a+10b+c - (100c+10b+a) = 297
100(a-c) +c-a = 297
99(a-c) =297
a-c =3
b can take 0-9 => 10 values
but c can not be 0 since reverse number is also 3 digit humber
so c can take 1,2,3,4,5,6 => 6 values
Hence total numbers possible
6x10=60

D is the Answer



What about a?
b*c= 10 * 6= 60
so what about a? where have it gone?



No need to consider a - above solution is self explanatory
Joined: 19 Sep 2011
Posts: 23
Own Kudos [?]: 6 [1]
Given Kudos: 9
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
1
Bookmarks
Answer is D
Possible combinations are 4b1, 5b2, 6b3,7b4,8b5, 9b6
B can be any dogit from 0-9 , hence 10 possiblities. and the above combination are only 6 , therefore answer is 6*10 = 60
Joined: 07 Dec 2014
Posts: 1056
Own Kudos [?]: 1672 [3]
Given Kudos: 27
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
3
Kudos
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

A. 3
B. 6
C. 7
D. 60
E. 70

xyz-zyx=297
297/99=3=x-z
6 possible x-z combinations: 9-6,8-5,7-4,6-3,5-2,4-1
10 possible y values: 0-9
6*10=60 possible pairs
D
Math Expert
Joined: 02 Sep 2009
Posts: 95937
Own Kudos [?]: 665018 [0]
Given Kudos: 87505
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Expert Reply
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

A. 3
B. 6
C. 7
D. 60
E. 70

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5380
Own Kudos [?]: 4415 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

A. 3
B. 6
C. 7
D. 60
E. 70

Asked: If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

Let the 3-digit positive integer be of the form xyz

(100x + 10y + z) - (100z + 10y + x) = 99(x-z) = 297
x -z = 3

Since x & z are not 0

(x,z) = {(4,1),(5,2),(6,3),(7,4),(8,5),(9,6)} = 6 cases
y can take 10 values

Total such numbers = 6*10 = 60

IMO D
Joined: 24 Nov 2016
Posts: 1710
Own Kudos [?]: 1381 [0]
Given Kudos: 607
Location: United States
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?

A. 3
B. 6
C. 7
D. 60
E. 70

\( ABC-CBA=297:100a+10b+c-100c-10b-a=297, 99(a-c)=297, (a-c)=3\)
\((A,C)=(9,6;8,5;7,4;6,3;5,2;4,1)…(A,C)≠(3,0):C>0\)
\((A,C)=6.pairs…B=(0,1,2,3,4,5,6,7,8,9)=10\)
\(Total.cases:6*10=60\)

Ans (D)
Joined: 02 Jan 2022
Posts: 257
Own Kudos [?]: 102 [0]
Given Kudos: 3
GMAT 1: 760 Q50 V42
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Considering the three-digit number to be ABC.
The value of the three-digit number is given by 100*A+10*B+C.
When the digits are reversed the number becomes CBA.
The value becomes : 100*C + 10*B+A.
Since the value decreased by 297 this can be represented as :
\(\left(100A+10B+C\right)-\left(100C+10B+A\right)\ =\ 297\)
99(A-C) = 297.
A-C = 3.
The different possibilities include : (A = 9, C = 6), (A = 8, C = 5), (A = 7, C = 4), (A = 6, C = 3), (A = 5, C = 2), (A = 4, C = 1)
A and C cannot take the value of 0 because then the numbers do not satisfy the three digit number condition.
For the 6 case B can take any value from 0 to 9.
A total of 10*6 = 60 cases.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 35109
Own Kudos [?]: 890 [0]
Given Kudos: 0
Send PM
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
GMAT Club Bot
Re: If a three-digit positive integer has its digits reversed, the [#permalink]
Moderator:
Math Expert
95937 posts