Flip the digits!

Expert replies

sodha.rakesh: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Nov 21, 2010 8:07 pm; Thanked: 2 times

by sodha.rakesh » Tue Jan 25, 2011 6:55 am

If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jan 25, 2011 6:55 am

Target2009: Legendary Member; Posts: 574; Joined: Sat Oct 31, 2009 1:47 pmFollowed by: 5 members; Location: USA; Thanked: 29 times

by Target2009 » Tue Jan 25, 2011 7:11 am

sodha.rakesh wrote:If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?

The number which is not divisible by 11 will be the ans.
say two digits are a & b.
So number M = 10a+b
Number N = 10b + a
M + N = (10a + b ) + (10b +a) = 11a + 11b = 11(a+B) .. so to be the sum of M and N is has to be divisible by 11.

Regards
Abhishek
------------------------------
MasterGmat Student

Like this post

stormier: Master | Next Rank: 500 Posts; Posts: 139; Joined: Fri Nov 26, 2010 4:45 pmFollowed by: 1 member; Location: Boston; Thanked: 20 times; GMAT Score:720

by stormier » Tue Jan 25, 2011 7:14 am

sodha.rakesh wrote:If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?

Let the numbers be 10x+y (x is the ten's digit, and y the unit's) and 10y + x (y the ten's digit, and x the unit's)

sum = 10x+y + 10y+x = 11(x+y)

Thus, 11 should be a factor of the number.

Answer choice A is the only one that is not divisible by 11, and thus the correct answer.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 25, 2011 7:53 am

sodha.rakesh wrote:If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?

Look at the units digits of the answer choices.
For the sum of M and N to have a units digit of 1, the sum of the units digits of M and the units digit of N must be 11.
Thus, to obtain answer choice A (181) or answer choice C (121), the units digits of M and N must be either 2 and 9, 3 and 8, 4 and 7, or 5 and 6.

29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 121.

No way to get a sum of 181.

The correct answer is A.

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

Like this post

AIM GMAT: Legendary Member; Posts: 857; Joined: Wed Aug 25, 2010 1:36 amFollowed by: 15 members; Thanked: 56 times

by AIM GMAT » Tue Jan 25, 2011 9:24 am

Thanks Mitch for such nice and fast approches , normally i do get involved into the making equations and solving the questions by equations whereas this method is pretty fast and simple . May be i cant get rid of my Engineering b/g effect

Thanks & Regards,
AIM GMAT

Like this post

sodha.rakesh: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Nov 21, 2010 8:07 pm; Thanked: 2 times

by sodha.rakesh » Wed Jan 26, 2011 8:01 am

GMATGuruNY wrote:
sodha.rakesh wrote:If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?
Look at the units digits of the answer choices.
For the sum of M and N to have a units digit of 1, the sum of the units digits of M and the units digit of N must be 11.
Thus, to obtain answer choice A (181) or answer choice C (121), the units digits of M and N must be either 2 and 9, 3 and 8, 4 and 7, or 5 and 6.

29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 121.

No way to get a sum of 181.

The correct answer is A.

Thank you for your reply and good strategy (that is the reason why I posted this que. here), Would you please provide some details why we are considering the answer choices 121 & 181 only and how to eliminate other options e.g. 99,44,165?

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jan 26, 2011 8:44 am

sodha.rakesh wrote:
GMATGuruNY wrote:
sodha.rakesh wrote:If 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

Source : OG 12th Edition, Q-182
Official Ans. A

Is there any shortcut/efficient method ?
Look at the units digits of the answer choices.
For the sum of M and N to have a units digit of 1, the sum of the units digits of M and the units digit of N must be 11.
Thus, to obtain answer choice A (181) or answer choice C (121), the units digits of M and N must be either 2 and 9, 3 and 8, 4 and 7, or 5 and 6.

29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 121.

No way to get a sum of 181.

The correct answer is A.
Thank you for your reply and good strategy (that is the reason why I posted this que. here), Would you please provide some details why we are considering the answer choices 121 & 181 only and how to eliminate other options e.g. 99,44,165?

Two reasons I focused on answer choices A and C:

-- they each have the same units digit (1), increasing the likelihood that one of them won't be possible.
-- there is only way to get a units digit of 1: the sum of the digits M and N must be 11.

Once I determined that MN + NM = 181 is impossible, there was no reason to check the other answer choices.

The other answers choices can be eliminated because they are all easily achieved:

E) 44 = 13+31 (any two digits whose sum is 4 will work)
D) 99 = 45+54 (any two digits whose sum is 9 will work)
B) 165 = 78+87 (any two digits whose sum is 15 will work)

Hope this helps!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review