Question: A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John, were appointed by the colony in charge. Tim was to protect each house whose number is a multiple of 2 and 5, Jack was to protect each house whose number is a multiple of 2 and 3 whereas John was asked to protect rest of the houses. How many houses were to be protected by both Tim & Jack?

1. 2
2. 3
3. 4
4. 5
5. More than 5

Correct Answer: D

Solution and Explanation:

Approach Solution 1:

Given that houses in a colony range from 1 to 150. The colony in charge appointed Tim, Jack, and John as three guards. Tim was tasked with guarding each house whose number was a multiple of 2 and 5, Jack with guarding each house whose number was a multiple of 2 and 3, and John with guarding the other houses.

Tim guards houses that are multiples of 2 and 5, meaning house no.s 10, 20, so on.
Multiples of 10.
Similarly, Jack guards houses that are multiples of 2 and 3, meaning house no.s 6, 12, 18, so on.
Multiples of 6.
Question is- How many houses did they guard together.
That would be given by the houses that are both the multiples of 10 and 6.
That can be given by LCM (10,6) = 30.

So there will be 150 / 30 = 5 houses that will be guarded by both Tim and Jack together.

Approach Solution 2:

Given that houses in a colony range from 1 to 150. The colony in charge appointed Tim, Jack, and John as three guards. Tim was tasked with guarding each house whose number was a multiple of 2 and 5, Jack with guarding each house whose number was a multiple of 2 and 3, and John with guarding the other houses.

Now we know that Tim guards the houses that are multiple of 2 and 5.

The house numbers will be multiple of both 5 and 2

LCM(5,2) = 10
The houses numbers will be 10, 20, 30, 40, 50
Jacl guards the houses that are multiple of 2 and 3.
The house numbers will be multiple of both 3 and 2
LCM(3,2) = 6
The houses numbers will be 6, 12, 18, ..
The houses which will be common in them has to be counted twice. Those houses will be multiple of 6 as well as 10
LCM(6,10) = 30
Total common houses = 150 / 30 = 5

“A colony has houses numbered 1 to 150. Three guards, Tim, Jack & John, were appointed by the colony in charge" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”. To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. The problem-solving section of the GMAT Quant topic is made up of very complicated maths problems that must be solved by using the right maths facts.

Suggested GMAT Quant Questions:

• A Takes 5 More Days Than B To Do A Certain Job And 9 Days More Than C GMAT Problem Solving
• A Watch Which Gains 5 Seconds In 3 Minutes Was Set Right At 7 A.M. GMAT Problem Solving
• Of The 800 Employees Of Company X, 70 Percent Have Been With The Company GMAT Problem Solving
• To 100 Litres Of Milk, 10 Litres Of Water Is Added And Then 20 Litres GMAT Problem Solving
• Walking at 3/4 of his normal speed, Mike is 16 minutes late GMAT Problem Solving
• There are 12 yes or no questions. How many ways can these be answered? GMAT Problem Solving
• There are 7 Red and 5 Blue Marbles in a Jar GMAT Problem Solving
• A Basket Contains 3 White and 5 Blue Balls GMAT Problem Solving
• Working together, John and Jack can type 20 pages in one hour GMAT Problem Solving
• Is x^2 *x^5*z>0? GMAT Problem Solving
• The average (arithmetic mean) of four distinct positive integers is 10 GMAT Problem Solving
• How many roots does the equation √x2+1+√x2+2=2 have? GMAT Problem Solving
• A Box Contains 10 Tablets of Medicine A and 15 Tablets of Medicine B GMAT Problem Solving
• If x=√10+3√9+4√8+5√7+6√6+7√5+8√4+9√3+10√2 then which of the following must be true? GMAT Problem Solving
• What is the last digit of (3)^(3)^3? GMAT Problem Solving
• It takes Jack 2 more hours than Tom to type 20 pages GMAT Problem Solving
• The angles in a triangle are x, 3x, 5x degrees GMAT Problem Solving
• If among 5 children, there are 2 siblings; in how many ways can the children be seated GMAT Problem Solving
• Among 200 People, 56% like Strawberry Jam, 44% like Apple Jam, and 40% like Raspberry Jam GMAT Problem Solving
• If 4 Women and 6 Men Work in the Accounting Department GMAT Problem Solving
• If 2^98=256L+N, where L and N are integers and 0≤N≤4, what is the value of N? GMAT Problem Solving
• A draining pipe can empty a pool in 4 hours GMAT Problem Solving
• If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region? GMAT Problem Solving
• Kate and David each have $10 GMAT Problem Solving
• How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4, and 5 which are divisible by 3, without repeating the digits? GMAT Problem Solving
• Which of the following lines are parallel to line x = 4 – 2y? GMAT Problem Solving
• John has 12 clients and he wants to use color coding to identify each client GMAT Problem Solving
• Which of the following expressions has the greatest values? GMAT Problem Solving
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
• What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving
• If 69% of k is 23, approximately how much is 23% of k? GMAT Problem Solving
• Metropolis Corporation has 4 Shareholders GMAT Problem Solving
• If x and y are positive integers and (1/7)^x * (1/8)^12 = (1/8)^1/18y, then what is the value of y-x? GMAT Problem Solving
• At Springfield High, three-fourths of the male students and half of the female students speak a foreign language GMAT Problem Solving
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• A conference room is equipped with a total of 45 metal or wooden chairs GMAT Problem Solving
• A welder received an order to make a 1 million litre cube-shaped tank GMAT Problem Solving
• After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving
• If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution? GMAT Problem Solving
• A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain GMAT Problem Solving
• A circle is inscribed in a square with the diagonal of 4 centimeters GMAT Problem Solving
• At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams GMAT Problem Solving
• Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours GMAT Problem Solving
• Simplify:\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75 GMAT Problem Solving
• There are 6 points on xy-plane GMAT Problem Solving
• Mike, Tom, and Walt are working as sales agents for an insurance company GMAT Problem Solving
• A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month GMAT Problem Solving