The Greatest Number of Four Digits Which is Divisible by 15, 25, 40 And 75 GMAT Problem Solving

Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

1. 9000
2. 9400
3. 9600
4. 9800
5. 9999

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
Since the 4-digit number is divisible by 15, 25, 40 and 75.
Hence, the number must be divisible by LCM of 15, 25, 40, 75
Therefore, the LCM of 15, 25, 40 and 75 = 600.
We know that the greatest 4-digit number in the number system is 9999.
To get the required number, we need to subtract the number 9999 from the remainder of 9999 divided by the LCM 15, 25, 40 and 75 i.e 600.
Therefore, the required number = 9999 – Remainder of (9999/600)
= 9999 – 399
= 9600
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

Approach Solution 2:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
We can solve the problem by analysing each of the options.
The number has to be a multiple of 5 and 2.
Therefore, the number has to have 0 as a unit digit. Hence, option E gets eliminated.
The number is also a multiple of 3.
Therefore, the sum of the digits of the number must be divisible by 3.
Option D: 9800 = 9 + 8 + 0 + 0 = 17 - NOT divisible by 3 so eliminate D
Option C: 9600 = 9 + 6 + 0 + 0 = 15 - divisible by 3. Hence, this option satisfies all the conditions. Therefore, option C is the answer.
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

Approach Solution 3:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
Therefore, the question is basically asking for multiple of the LCM of 15, 25, 40 and 75.
Let’s resolve the LCM of 15, 25, 40, and 75 to get the answer:
We know that the factors of 15 = 3 x 5
We know that the factors of 25 = 5^2
We know that the factors of 40 = 2^3 x 5
We know that the factors of 75 = 5^2 x 3
Therefore, the LCM 15, 25, 40, and 75 is 2^3 x 3 x 5^2 = 8 x 3 x 25 = 600.
The largest 4-digit number that is a multiple of 600 is 9600.
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

“The greatest number of four digits which is divisible by 15, 25, 40 and 75” - is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide Quantitative Review 2018”. The candidates must have a solid knowledge of mathematics in order to solve GMAT Problem Solving questions. The candidates can go through GMAT Quant practice papers to analyse varieties of questions that will enable them to achieve better ranking in the exam.

Suggested GMAT Problem Solving Questions

• If (1/3 + 1/4+ 1/5+ 1/6) = r(1/9 +1/12 + 1/15+ 1/18) then r = ? GMAT Problem Solving
• In a conference 10 speakers are present GMAT Problem Solving
• There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles GMAT Problem Solving
• Last Year Department Store X had a Sales total for December GMAT Problem Solving
• A Water Tank has Three Taps A, B, and C. A Fills four Buckets in 24 minutes GMAT Problem Solving
• What is the Units Digit of the Solution to 177^28 −133^ 23 GMAT Problem Solving
• What is the Probability for a Family with Three Children to have a Boy GMAT Problem Solving
• Two Friends A and B Simultaneously Start Running Around a Circular Track GMAT Problem Solving
• What are the Coordinates of the Foot of the Perpendicular from the Point GMAT Problem Solving
• Salaries of Moon and Shanto are in the Ratio of 4:5 GMAT Problem Solving
• Out of a Group of Swans, Seven Times Half of the Square Root GMAT Problem Solving
• The Number of Prime Numbers Divisible by 2 Plus the Number of Prime GMAT Problem Solving
• Total Expenses of a Boarding House are Partly Fixed and Partly Varying GMAT Problem Solving
• A Bouquet Contains 16 Flowers, Each of Them Either a Rose, Tulip GMAT Problem Solving
• A Club has 256 Members of Whom 144 Can Play Football, 123 Can Play Ten GMAT Problem Solving
• Box A Contains 2 Black Chips. Box B Contains 2 White Chips GMAT Problem Solving
• What is the Smallest Positive Integer k such that 126 * \sqrt k GMAT Problem Solving
• In a Class of 60 Students, 20 Like Math, 25 Like English GMAT Problem Solving
• For All Positive Integers m, [m] = 3m When m is Odd and [m] = (1/2)*m When GMAT Problem Solving
• In an Examination, 35% Candidates Failed in One Subject and 42% Failed GMAT Problem Solving
• Bouquets are to be Made Using White Tulips and Red Tulips GMAT Problem Solving
• An Equilateral Triangle that has an Area of 9√3 is Inscribed in a Circle GMAT Problem Solving
• A Cube is Painted Red on All Faces. It is Then Cut into 27 Equal Smaller GMAT Problem Solving
• A password on Mr. Wallace's briefcase consists of 5 digits GMAT Problem Solving
• There are 8 Magazines Lying on a Table; 4 are Fashion Magazines GMAT Problem Solving
• The Area Bounded by the Curves |x + y| = 1 and |x - y| = 1 is GMAT Problem Solving
• After 2/9 of the numbers in a data set A were observed GMAT Problem Solving
• Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow GMAT Problem Solving
• A Motorist Covers a Distance of 39 Km in 45 Min by Moving at a Speed GMAT Problem Solving
• Which of the Following is the Largest? GMAT Problem Solving
• Julie is Putting M Marbles in a Row in a Repeating Pattern GMAT Problem Solving
• A Pump Can Fill a Tank with Water in 2 Hours. Because of a Leak GMAT Problem Solving
• In a Country 55.55 % of the Population are Males and Rest Females GMAT Problem Solving
• Two Candles of the Same Height are Lighted at the Same Time GMAT Problem Solving
• A Telephone Number Contains 10 Digit, Including a 3-Digit Area Code GMAT Problem Solving
• A Regular Octagon (a Polygon with 8 Sides of Identical Length GMAT Problem Solving
• If x is a positive number and equals to GMAT Problem Solving
• The Present Ages of Three Persons are in the Proportion of 5:8:7 GMAT Problem Solving
• If x is a Product of 4 Consecutive Integers, and x is Divisible by 11 GMAT Problem Solving
• If y = |3x - 5|/(-x^2 - 3) for What Value of x will the Value of y be Greatest GMAT Problem Solving
• An Emergency Vehicle Travels 10 Miles at a Speed of 50 Miles Per Hour GMAT Problem Solving
• How Many Ordered Triplets (a, b, c), Where a, b, and c are Positive Integers GMAT Problem Solving
• At a Dinner Party, 5 People are to be Seated Around a Circular Table GMAT Problem Solving
• If The Product of 3 Consecutive Integers is 210, Then The Sum of The GMAT Problem Solving
• If the Points (a, 0) , (0, b) and (1, 1) are Collinear, What is the Value of 1/a + 1/b? GMAT Problem Solving
• In a Market, the Price of Medium Quality Mangoes is Half that of Good Mangoes GMAT Problem Solving
• The Sun is Approximately 1,400 Million Kilometers from the Planet GMAT Problem Solving
• If ^5\sqrt{-37} then Which of the Following Must be True? GMAT Problem Solving
• A Draining Pipe can Drain a Tank in 12 hours, and a filling Pipe can fill GMAT Problem Solving
• If the Number x3458623y is Divisible by 88, What is the Value of x? GMAT Problem Solving