Which Among the Following is the Smallest 7-digit Number that is Exactly Divisible by 43? GMAT Problem Solving

Question: Which among the following is the smallest 7-digit number that is exactly divisible by 43?

1. 1,000,043
2. 1,000,008
3. 1,000,006
4. 1,000,002
5. 1,000,001

“Which among the following is the smallest 7-digit number that is exactly divisible by 43?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide”. 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:

It is asked in the question to find out the smallest 7-digit number which is exactly divisible by 43.
The smallest seven-digit number will be 1000000.
Firstly let's divide this number by 43
1000000/43
This gives quotient = 23,255 and remainder = 35.
Now the difference between 43 and 35 = 43 - 35 = 8
Adding 8 to the smallest seven-digit number we get = 1000000+8 = 1000008
Dividing this number by 43 we get
1000008/43 = 0 remainder
Hence the smallest seven-digit number which is divisible by 43 is 1000008

Correct Answer: B

Approach Solution 2:

It is asked in the question to find out the smallest 7-digit number which is exactly divisible by 43.
The smallest seven-digit number will be 1000000.
Option A is not divisible by 43 since 1000,000 is not divisible by 43 as
1000,000 /43+43/ 43
Out of other options only one needs to be checked as they all are near to each other.
Taking option C, we need to have a remainder of '37+6' from 1000,000/43+6/43
1000,000/43= (860,000+140,000)/43
1000,000/43= (860,000+140,000)/43
1000,000/43 = 860,000/43+(86,000+54000)/43 860,000/43+(86,000+54000)/43
1000,000/431000,00043 = 860,000/43 + (51,600+2400)/43 860,000/43+86,000/43+51,600+2400/43
1000,000/43 = 860,000/43+51,600 /43+(1,720+680)/43
860,000/ 43 = 86,000/43+51,600/43+(1,720+680)/43
1000,000/ 43 = 860,000/ 43+51,600 / 43+1,720 /43+(645+35)/43
                      = 860,000/43+51,600/43+1,720/43+(645+35)/43

From the last term, we have a remainder of 35 so a total of 41 as a remainder is not possible. Since we are short of '2' in the remainder we add that to the 1000,006 to get 1000,008 which must be divisible by 43.

Correct Answer: B

Approach Solution 3:

Let's take 1,000,000.1,000,000.
--> 1000000−860000=1400001000000−860000=140000
--> 140000−129000=11000140000−129000=11000
--> 11000−8600=240011000−8600=2400
--> 2400−2150=2502400−2150=250
--> 25043=5354325043=53543

In order 7 digit number to be divisible by 43, 8 should be added to 1000000
--> 1000000+8=1000008.

Correct Answer: B

Suggested GMAT Problem Solving Questions

• Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ? GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• The Figure Shown Above Consists of a Shaded 9-Sided Polygon GMAT Problem Solving
• A list of measurements in increasing order is 4, 5, 6, 8, 10 and x GMAT Problem Solving
• Rahul Can Finish a Job in 30 Days GMAT Problem Solving
• Which of the Following Equation is NOT Equivalent to 25x^2 = y^2 - 4? GMAT Problem Solving
• The Variable x is Inversely Proportional to the Square of the Variable y GMAT Problem Solving
• 16 Ounces of Fresh Orange Juice Contains 216 Calories GMAT Problem Solving
• An Urn Contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles GMAT Problem Solving
• The Price of Raw Materials Has Gone up by 15% GMAT Problem Solving
• In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics, GMAT Problem Solving
• If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
• Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
• Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
• 16 Ounces of Birdseed Mix Contains 10% Sesame Seed by Weight GMAT Problem Solving
• The Diameter of Circle S is Equal in Length to a Side of a Certain Square GMAT Problem Solving
• In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. GMAT Problem Solving
• If The Sum of 9 Consecutive Integers is 90 GMAT Problem Solving
• If a Carton Containing a Dozen Mirrors is Dropped GMAT Problem Solving