What is the value of the two-digit positive integer n?

Question

(1) The sum of the digits in n is 12

(2) If the digits in n are reversed, the value of the number formed is 36 more than the value of n

I'm having a hard time setting up this problem, wondering if ya'll could help me out:

1) a + b = 12 = insuff
2) a + b + 36 = b + a == this just gives me an equation that is "0=36" which I don't understand?

OA is C.

Thanks!

viksingh15 · Answer

1) sum of the digits in n is 12, that means : 39,48,57,66,75,84,93- not sufficient

2) this means : 10a + b = 10b + a - 36 => 9a=9b-36

a+4 =b, so b is 4 more than a and difference is 36, such as : 15 & 51, 26 & 62, 37 & 73, 48 & 84, ... - not sufficient

1 + 2, we have only one common answer 48 & 84.

So answer is C

minwoswoh · Answer

Hi viksingh15,

I didn´t plug in any number and used a 100% algebraic process. Hope you find my approach “elegant”.

Question Stem Translation: n = 10t + u --> I am using t for tens digit and u for units digit.
Question Itself: 10t + u = ?

(1) t + u = 12
(2) 10u + t = 10t + u + 36 --> 9u = 9t + 36 --> u = t + 4

(1+ 2) Since we now have 2 variables and 2 distinct, linear equations, we can then solve this stuff!

OA = C

narendran1990 · Answer

Bunuel  : Not able to understand the procedures mentioned above. Would be great if I can get your approach.

Bunuel · Answer

What is the value of the two-digit positive integer n?

Any two-digit integer ab can be expressed as 10a+b, for example: 45 = 10*4 + 5.

So, given that n = 10a + b

(1) The sum of the digits in n is 12 --> a + b = 12. Not sufficient.

(2) If the digits in n are reversed, the value of the number formed is 36 more than the value of n --> (10a + b) + 36 = 10b + a --> b = a + 4. Not sufficient.

(1)+(2) Solve a + b = 12 and b = a + 4 to get a = 4 and b = 8 --> n = 10a + b = 48. Sufficient.

Answer: C.

Ilomelin · Answer

Doing this problem I noticed something odd:

When we flip the digits of a two digit positive integer, the difference between the new integer and the first one is the result of 9*(difference of the 2 digits):

A difference of 36 by flipping the digits of the integer means that the difference of the 2 digits will be  36/9=4 .

I have tried it with several combinations and it seems to work, I really can't tell why. Examples:

Difference of the digits = A
Difference between the two integers = B

Say B = 27, then:

B = A*9 
 A = 27/9 = 3

So every combination of digits with a difference of 3 will create two integers with a difference of 27: 30-03, 41-14, 52-25, etc.

Say B = 63, then A would be 7: 70-07, 81-18, 92-29.

In that sence if they tell me that the difference of two integers when their digits are flipped is 54, I can immediately know that the difference of the 2 digits will be 6. IF it is 36, then 4. 81, then 9. ETC.

I think once I grasped this, this type of problems will be much easier.

kawal27 · Answer

statement 1 gives us : 66,93,84,75
not sufficient
statement 2 says: difference is 36 by revering digit with original digit
not sufficient
1+2 : gives us 84-48=36
 84 is only value of n 
 ...ANSWER :C

woohoo921 · Answer

Can an expert confirm that statement 2 is not sufficient because there are three variables? Thank you!

KarishmaB

KarishmaB · Answer

We have 2 unknowns. The value of a and the value of b, the two digits of n. If we get a and b, we know what n is.

Stmnt 2 gives us 10b + a = 36 + 10a + b
We get b = a + 4
But here, a = 1, b = 5,
a = 2, b = 6
a = 3, b = 8 
etc. values are possible

Guest96 · Answer

Bunuel

This question is also available in GMATPrep Practice Exam 4. I think we can add that as a source (tag).

Bunuel · Answer

_______________________
Added the tag. Thank you!

What is the value of the two-digit positive integer n?

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