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

 It is currently 21 Jun 2018, 12:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the two-digit integers M and N are positive and have the

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

### Hide Tags

Intern
Joined: 07 Dec 2009
Posts: 14
If the two-digit integers M and N are positive and have the [#permalink]

### Show Tags

Updated on: 19 Sep 2013, 01:18
3
9
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:07) correct 23% (01:08) wrong based on 379 sessions

### HideShow timer Statistics

If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?

A. 181
B. 165
C. 121
D. 99
E. 44

Question 182 from The Official Guide for GMAT Review 12th Edition:

Originally posted by melissawlim on 12 Dec 2009, 09:04.
Last edited by Bunuel on 19 Sep 2013, 01:18, edited 1 time in total.
Edited the question and added the OA
VP
Joined: 05 Mar 2008
Posts: 1427
Re: Algebra - Applied Problems [#permalink]

### Show Tags

12 Dec 2009, 09:33
melissawlim wrote:
Hi,

I'm new here and I don't know if anyone has tried to explain this question or a something similar to it yet, but if so please direct me to the right thread. Anyway here goes:

Question 182 from The Official Guide for GMAT Review 12th Edition:

If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?

(A) 181
(B) 165
(C) 121
(D) 99
(E) 44

The correct answer is A. In the explanation given, it says to let M = 10t + u and N = 10u +t, where t and u are two digits.

I understand the t and u part, but I don't understand why we have to add a 10 in front of the u or t.

because t is the tens digit

assume a two digit number 36 where t = 3 and u = 6

10(3) + 6 = 36 you can't just put t and u together to make 36
t + u would mean 3 + 6 = 9

another example 867

100(8) + 10(6) + 7 = 867
Intern
Joined: 07 Dec 2009
Posts: 14
Re: Algebra - Applied Problems [#permalink]

### Show Tags

12 Dec 2009, 10:06
lagomez wrote:
melissawlim wrote:
Hi,

I'm new here and I don't know if anyone has tried to explain this question or a something similar to it yet, but if so please direct me to the right thread. Anyway here goes:

Question 182 from The Official Guide for GMAT Review 12th Edition:

If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?

(A) 181
(B) 165
(C) 121
(D) 99
(E) 44

The correct answer is A. In the explanation given, it says to let M = 10t + u and N = 10u +t, where t and u are two digits.

I understand the t and u part, but I don't understand why we have to add a 10 in front of the u or t.

because t is the tens digit

assume a two digit number 36 where t = 3 and u = 6

10(3) + 6 = 36 you can't just put t and u together to make 36
t + u would mean 3 + 6 = 9

another example 867

100(8) + 10(6) + 7 = 867

Thanks lagomez. Ah, it all makes sense now. I got confused by the part where they said "where t and u" are two digits. By that, i assumed, they are referring to two "two-digit integers" (i.e u = 36 and t = 49 and that 10(36) + 49 = 409) instead of two SEPARATE single digit integers.
Manager
Joined: 07 May 2013
Posts: 101
Re: Algebra - Applied Problems [#permalink]

### Show Tags

18 Sep 2013, 19:16
4
2
simple solution:
M=10x+y
N=10y+x
M+N=11x+11y=11(x+y)
In other words the answer is a multiple of 11.
Now the question becomes " which of the following is NOT a multiple of 11?"
answer----->181----->choice A
Intern
Joined: 13 Nov 2013
Posts: 23
Location: Brazil
Concentration: Strategy, Marketing
GMAT 1: 640 Q44 V35
GMAT 2: 690 Q48 V36
Re: Algebra - Applied Problems [#permalink]

### Show Tags

16 Mar 2014, 19:17
madn800 wrote:
simple solution:
M=10x+y
N=10y+x
M+N=11x+11y=11(x+y)
In other words the answer is a multiple of 11.
Now the question becomes " which of the following is NOT a multiple of 11?"
answer----->181----->choice A

madn800 is the best solution in my opinion.. :D

But, just to give another solution I've just saw: think of M = AB and N = BA.
(1) If A+B < 10, then:

AB
BA +
-----
B B ---> sum will result in a two digit number
+ +
A A

The sum of A + B will be less than 10, so the summed number digit's will be the same, so D and E satisfy. Now... if
2) A+B > 10, then:

AB
BA
----
1 B ---> sum will result in a three digit number
+ +
B A
+
A

Since B+A in this case is greater than 10, you should add a plus 1 in the sum of the next digit, then, this next digit will be the first digit + 1. In a 3 digit number __ ___ ___, the first two digits will be __ A+B+1 A+B , so B and C satisfy, leaving A as the only choice left.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11814
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If the two-digit integers M and N are positive and have the [#permalink]

### Show Tags

19 Apr 2015, 18:48
Hi All,

Since the question asks for the answer that CANNOT be the sum of M and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.

We're told that M and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of M and N.

Let's start with the 'easiest' answer first:

44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E

Now let's work through the rest of the list....

Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D

Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C

Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B

There's only one answer left....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Non-Human User
Joined: 09 Sep 2013
Posts: 7020
Re: If the two-digit integers M and N are positive and have the [#permalink]

### Show Tags

13 Jan 2018, 10:16
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.
_________________
Re: If the two-digit integers M and N are positive and have the   [#permalink] 13 Jan 2018, 10:16
Display posts from previous: Sort by

# If the two-digit integers M and N are positive and have the

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

 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®.