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

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

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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:
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Sep 2013, 00:18, edited 1 time in total.
Edited the question and added the OA
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Re: Algebra - Applied Problems [#permalink]

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New post 12 Dec 2009, 08:33
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
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Re: Algebra - Applied Problems [#permalink]

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New post 12 Dec 2009, 09:06
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.
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Re: Algebra - Applied Problems [#permalink]

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New post 18 Sep 2013, 18:16
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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
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Re: Algebra - Applied Problems [#permalink]

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New post 16 Mar 2014, 18:17
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.
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Re: If the two-digit integers M and N are positive and have the [#permalink]

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New post 19 Apr 2015, 17:48
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:
[Reveal] Spoiler:
A


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Re: If the two-digit integers M and N are positive and have the [#permalink]

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Re: If the two-digit integers M and N are positive and have the   [#permalink] 13 Jan 2018, 09:16
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