GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Feb 2019, 02:18

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

N is a 3-digit number, and the sum o

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3446
Location: Canada
N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 11 Jun 2018, 06:01
Top Contributor
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

52% (02:19) correct 48% (02:17) wrong based on 62 sessions

HideShow timer Statistics

N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions

_________________

Test confidently with gmatprepnow.com
Image

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2595
Re: N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 11 Jun 2018, 06:34
1

Solution



Given:
    • N is a 3-digit number
    • Sum of the digits of N is 10
    • When N is reversed, the new number is 99 less than N

To find:
    • The value of N

Approach and Working:
If we assume N = abc, then reverse of N = cba

As N – reverse of N = 99, we can write,
    • abc – cba = 99
    Or, 100a + 10b + c – 100c – 10b – a = 99
    Or, 99 (a – c) = 99
    Or, a – c = 1

As both a and c are single-digit integers, the possible values of (a, c) = (2, 1), (3, 2), (4, 3), (5, 4)
[(6, 5) onwards values are not possible as sum of the digits is equal to 10]

Using the relation, a + b + c = 10, the possible value sets of (a, b, c) = (2, 7, 1), (3, 5, 2), (4, 3, 3), (5, 1, 4)

Analysing Statement 1
    • As per the information given in statement 1, a = 1 + c
      o This is an information that we have already derived, and not giving us any new information

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, b = 2 + a
    • From the possible values of (a, b, c) we can have only one case where it is getting satisfied = (3, 5, 2)
Therefore, the number N = 352

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

Answer: B
_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories
Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Current Student
User avatar
B
Affiliations: All Day Test Prep
Joined: 08 May 2018
Posts: 72
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Re: N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 11 Jun 2018, 06:35
1
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions
Let's represent N as abc where:

a = hundreds digit
b = tens digit
c = ones digit

Therefore algebraically:

N = 100a + 10b + c

Reverse N = 100c + 10b + a

Given: N = Reverse N + 99
----> 100a + 10b + c = 100c + 10b + a + 99

Simplify: 99a = 99c + 99 -----> a = c + 1

From given info we know:
a = c + 1
a + b + c = 10

Our goal is to solve for N by finding a,b and c

Statement 1
Tells us a = c + 1. We already know this info so its not helpful
-------> INSUFFICIENT

Statement 2 says b = a + 2

Therefore everything can be written in terms of a:
a = a
b = a + 2
c = a - 1

Since a + b + c = 10
----> a + (a+2) + (a - 1) = 10

----> a = 3
----> c = 2
----> b = 5

Therefore N is 352.
-------------------------> sufficient

Answer: B





Sent from my SM-G920T using GMAT Club Forum mobile app
_________________

Adam Rosman, MD
University of Chicago Booth School of Business, Class of 2020
adam@alldaytestprep.com

Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.
https://www.alldaytestprep.com


Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Premium Member
N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 11 Jun 2018, 08:25
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions


Since we get a 3-digit number(reversed) after subtracting 99 from N(3-digit integer), therefore N must be greater than 200.

Property:- When the digits of a 3-digit number are reversed after subtracting the original number by 99, the hundred's place digit is one more than the unit's place digit.

Question stem:- N=?

Statement1:- As mentioned above in the property, this statement doesn't provide additional info. So, st1 is insufficient.

Statement-2

The affixed table may be referred.

From the table, N=352.

Hence, statement2 is sufficient.

Ans. B

Hope my logic is correct.
Attachments

File comment: I stopped checking at 100th digit=3 because any positive integer thereafter yields sum of digits>10.
N-3 digit.JPG
N-3 digit.JPG [ 27.35 KiB | Viewed 467 times ]


_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Premium Member
N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 11 Jun 2018, 13:24
1
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions


We are given the following information in the question stem:
1. Let N(3 digit number) be xyz where x - hundred's digit, y - ten's digit, z - one's digit.
2. x+y+z = 10.
3. xyz - zyx = 99(Here zyx is the reverse of the number N)

We have been asked the value of N.

1. When the hundred's digit of N is 1 more than it's units digit, there are 4 possibilities: 271,352,433,514.
Reversing these 4 numbers we will get 172,253,334,415 & each of these 4 numbers when subtracted from
the number it reverses, gives us 99. We can't find a unique value for N. (Insufficient)

2. If the tens digit of N is 2 more than its hundreds digit, there are 3 possibilities: 136,244,352. Reversing
these 3 numbers, we will get 631,442,253. Only 352 - 253 gives 99, making 352 our number (Sufficient - Option B)
_________________

You've got what it takes, but it will take everything you've got

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3446
Location: Canada
Re: N is a 3-digit number, and the sum o  [#permalink]

Show Tags

New post 13 Jun 2018, 07:29
Top Contributor
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions


Target question: What is the value of N?

Given: N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N.
Let N = wxy, where w, x and y represent the 3 digits in N
So, the first equation we can write is: w + x + y = 10

Now let's examine the situation where we REVERSE the digits.
First of all, the VALUE of N (wxy) is equal to 100w + 10x + y
Next, the VALUE of the REVERSED number (yxw) is equal to 100y + 10x + w
Since the REVERSED number is 99 less than N, we can write: 100y + 10x + w = 100w + 10x + y - 99
Subtract w from both sides: 100y + 10x = 99w + 10x + y - 99
Subtract 10x from both sides: 100y = 99w + y - 99
Subtract y from both sides: 99y = 99w - 99
Divide both sides by 99 to get: y = w - 1

Now onto the statements....

Statement 1: The hundreds digit of N is 1 more than its units digit.
In other words, w = y + 1, which is the SAME as y = w - 1
Notice that this provides NO NEW INFORMATION, since we already concluded that y = w - 1
Since statement 1 provides no new information, it is NOT SUFFICIENT

Statement 2: The tens digit of N is 2 more than its hundreds digit.
In other words, x = w + 2
Now that we've written x and w in terms of w (i.e., x = w + 2 and y = w - 1), we can take the given information (w + x + y = 10), and replace w and x
When we do so, we get: w + (w + 2) + (w - 1) = 10
Simplify: 3w + 1 = 10
Solve: w = 3
If w = 3, then x = 5, and y = 2
So, N =352
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

GMAT Club Bot
Re: N is a 3-digit number, and the sum o   [#permalink] 13 Jun 2018, 07:29
Display posts from previous: Sort by

N is a 3-digit number, and the sum o

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.