The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving

Question:The smallest 3 digit positive integer obtained by adding two positive two-digit numbers, one of which has the units and tens places interchanged as the other is ___

1. 100
2. 101
3. 105
4. 110
5. 121

‘The smallest 3-digit positive integer obtained by adding two positive two-digit numbers' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

This question can be solved by only one approach.
It is asked in the question to find out the smallest three-digit positive integer which can be obtained by adding two positive two-digit numbers, one which has the units and tens place interchanged with one another.
To understand this clearly
Let us take an example,
If a number is 34 then the other number had to be 43
Note that in both the numbers the digits in ones and tens place are replaced.
To solve this question let us assume that the number is ab
Where b is the one’s digit and a is the tens digit.
The number can be written as 10a + b
If this is the first number then the second number can be written as ba
This number can be written as 10b + a
This sum is required to be the minimum 3-digit number.
Taking sum of these numbers = 10a + b + 10b + a
= 11a + 11b
= 11 (a + b)
It can be clearly seen that the three digits number is divisible by 11.
The smallest three-digit number divisible by 11 is 110 and 121, but 110 is the smallest number therefore this is the correct answer.
The correct option will be option D.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
• An Equilateral Triangle ABC is Inscribed in Square ADEF GMAT Problem Solving
• A Popular Website Requires Users to Create a Password Consisting of Digits Only GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B GMAT Problem Solving
• In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• A palindrome is a number that reads the same forward and backward GMAT Problem Solving
• Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
• Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards GMAT Problem Solving
• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
• Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
• Of the 150 Houses in a Certain Development GMAT Problem Solving
• A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving