# The Number Game

1,445.7K Views

The product of three consecutive numbers when divided by each of them in turn, the sum of the three quotients will be 74.
What are the numbers?

JamesBond Pundit Asked on 26th July 2015 in

4, 5 and 6.

John123 Expert Answered on 26th July 2015.

Let the three consecutive numbers be x, x+1, and x+2.

When we divide the product of these three numbers by the first number x, we get: (x)(x+1)(x+2)/x = (x+1)(x+2)
When we divide the product by the second number x+1, we get: (x)(x+1)(x+2)/(x+1) = (x)(x+2)/(x+1)
When we divide the product by the third number x+2, we get: (x)(x+1)(x+2)/(x+2) = (x)(x+1)
According to the problem, the sum of these three quotients is 74, so we can write the equation:
(x+1)(x+2) + (x)(x+2)/(x+1) + (x)(x+1) = 74
Expanding the terms and simplifying, we get:
3x^2 + 6x – 72 = 0

Dividing by 3 and factoring, we get:  x^2 + 2x – 24 = 0
(x+6)(x-4) = 0

So x = -6 or x = 4. Since the numbers are consecutive, x must be positive, so x = 4.

Therefore, the three consecutive numbers are 4, 5, and 6.

Moshe Expert Answered on 2nd March 2023.

• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
• ### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
• ### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
• ### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
• ### Five greedy pirates and gold coin distribution Puzzle

Five  puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
• ### Magical flowers!!

A  devotee goes to three temples,  temple1, temple2  and temple3  one after the other. In front of each temple, there ...Read More »
• ### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
• ### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
• ### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over ...Read More »
• ### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »
• ### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
• ### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
• ### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for \$10. It turned out ...Read More »
• ### Which letter replaces the question mark

Which letter replaces the question markRead More »
• ### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
• ### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
• ### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
• ### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
• ### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »