How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?
(a) 5
(b) 6
(c) 7
(d) 8
(e) 9
n reversed
This topic has expert replies
- krishnasty
- Master | Next Rank: 500 Posts
- Posts: 142
- Joined: Mon Jan 10, 2011 8:03 am
- Thanked: 19 times
- 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
Let T = tens digit and U = units digit.krishnasty wrote:How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?
(a) 5
(b) 6
(c) 7
(d) 8
(e) 9
N = 10T + U.
When the digits are reversed, New N = 10U + T.
Since the difference between new N and old N is 9, we get:
(10U + T) - (10T + U) = 9.
9U - 9T = 9
9(U-T) = 9
U-T = 1
U = T+1.
Thus, the units digit of N is 1 more than the tens digit, yielding the following options:
12, 23, 34, 45, 56, 67, 78, 89.
8 integers.
The correct answer is D.
Last edited by GMATGuruNY on Mon Aug 01, 2011 11:17 am, edited 2 times in total.
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
-
- Master | Next Rank: 500 Posts
- Posts: 401
- Joined: Tue May 24, 2011 1:14 am
- Thanked: 37 times
- Followed by:5 members
let t be tens digit and u unit digit
10t + u = 10u + t +9
9t = 9u +9
t = u+1,
21 = 12 +9
32 = 23 +9
43
54
65
76
87
98 = 89 +9
total 8
10t + u = 10u + t +9
9t = 9u +9
t = u+1,
21 = 12 +9
32 = 23 +9
43
54
65
76
87
98 = 89 +9
total 8
- cuteprince1989
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Mon Nov 07, 2016 1:30 am
he is asking for the integer not the 2 digit number so why did not u include '01'so that makes the answer 9,
01 also satisfies the condition given inthe question.
01 also satisfies the condition given inthe question.
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
The question limits the integers to those greater than 10 ("How many integers n greater than 10....")cuteprince1989 wrote:he is asking for the integer not the 2 digit number so why did not u include '01'so that makes the answer 9,
01 also satisfies the condition given inthe question.
So, n = 01 does not count.
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since n is greater than 10 and less than 100, n is a two-digit number. To start, we can represent n as 10A + B, in which A = the tens digit of n and B = the units digit of n.krishnasty wrote:How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?
(a) 5
(b) 6
(c) 7
(d) 8
(e) 9
Since we are given that when the digits of n are reversed the resulting integer is n + 9, we can say:
10A + B + 9 = 10B + A
9A - 9B + 9 = 0
A - B + 1 = 0
A = B - 1
Our possible values of n are such that the tens digit is one less than the units digit. Thus n can be the following values:
12, 23, 34, 45, 56, 67, 78, 89
Answer: D
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
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
I'm a little surprised that nobody has pointed out that anyone asking this question isn't likely to think of the algebraic approach at first.
With that in mind, under test conditions, TRY NUMBERS and look for a pattern.
Start with n = 24. Reversed, that gives 42, and 42 ≠ 24 + 9.
If we try n = 25, things get worse! Reversed we've got 52, and the distance is even further.
That means we should go the other way: n = 23. Aha! Success.
It seems that this works when the numbers are close together, so let's test to be sure. n = 34 works (reverse is 43), n = 45 works (reverse is 54), etc. etc.
So it should always work if the tens digit is one more than the units digit. That gives us 12, 23, ..., 89, and we're set.
This approach always helps when you can't think of the algebra, and since the GMAT is an adaptive test, you'll often get questions hard enough for you that you won't be able to think of the algebra! Have a backup plan, and you can work yourself out of the jam.
With that in mind, under test conditions, TRY NUMBERS and look for a pattern.
Start with n = 24. Reversed, that gives 42, and 42 ≠ 24 + 9.
If we try n = 25, things get worse! Reversed we've got 52, and the distance is even further.
That means we should go the other way: n = 23. Aha! Success.
It seems that this works when the numbers are close together, so let's test to be sure. n = 34 works (reverse is 43), n = 45 works (reverse is 54), etc. etc.
So it should always work if the tens digit is one more than the units digit. That gives us 12, 23, ..., 89, and we're set.
This approach always helps when you can't think of the algebra, and since the GMAT is an adaptive test, you'll often get questions hard enough for you that you won't be able to think of the algebra! Have a backup plan, and you can work yourself out of the jam.