Math Olympiad Question | You should know this trick!!

[ektaverma]

let the constant be x
a.t.q
x+(x+1)+(x+2)=60
3x+3=60
x=60-3/3
x=19

Number x=19
x+1=19+1=20
x+2=19+2=21

thus the largest number is 21

[somebody_]

This is actually easy for a Math Olympiad question.
Suppose x is one number. The next one would be x+1, and the next one x+2. Now, we can write the sum: x+(x+1)+(x+2)=60.
We can simplify the equation to 3x+3=60. Subtracting 3 on both sides, we get 3x=57. We can divide 3 on both sides to get *x=19.*
The largest number will be x+2, and if we substitute 19 for x, we get 19+2, which equals *21.* Therefore, *D is the final answer.*

[RGGBMGO]

We can also write this as
3
Σ (x+n) = 60
n=0

[iqbalimrit]

Very nice. I'm not good in math. I love finding answers!

[CurryShivank]

Let the numbers be x-1, x, x+1. That adds up to 3x=60, x=20. The largest is x+1=21. This should be a pre-k to kindergarten Olympiad question (which doesn’t exist) max since people can guess the numbers easily.

[debalinabanerjee]

Actually There are 2 ways to do this question such as the one the teacher did and if x=19 because x+[x+1]+[x=2]=60
Then 19 plus 1 and 19 plus 2 is equal to 20 and 21
Therefore the largest number is D 21

[practicalbachelor.]

Haha...i calculated that in my mind just in 3 seconds 🤣

[DominickAngelo]

Great trick to solve this problem. But shouldn’t students know how to solve this problem algebraically?
Let x=smallest number, x+1=, middle number and x+2= largest number then x+x+1+x+2=60.
3x+3=60, x=19 largest number is x+2=21 choice d. I look forward to hearing, speaking, and conversing with you. Take care, bye, bye, and have fun!!!😅

[avinakrishna]

You are giving very nice knowledge to everyone…awesome

[himsikhakalita_]

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[PotatoDaPotato-]

X=60÷3+1 since there is 3 consecutive numbers are so the middle is 1 number away from the end and the start thats why we put +1
And 20+1=21 done

[JaadooGamer]

See look at the options DO NOT use traditional methods using x to calculate the value rather if you see the options you can infer that if 21 is the largest other two are 19 and 20 if you add these together you will get 60 so 21 is the correct answer

[Khidash_And_Kayaan]

First of all this is something a 1st grader must know to continue living in Asia…… No drama

[devmaurya]

Surprise test in grade 8 in my school used to have harder question than this.

[GreatnessStrikes]

let the middle number be x

x-1+x+x+1=60
=> 3x = 60
=> x = 20

Largest number = x + 1 = 20 + 1 = 21

[Erariz]

cool short especially for the time constraint but this question has the same difficulty as #4 on amc10 so i doubt it's olympiad level status

[-SweetWhimsy_Kim-]

This actually help's bc im preparing for one and it's tmr

[anteconfig]

Why not 30? Because 60/2 = 30…
30 + 30 = 60 _but_ we need 3 numbers so if we subtract 1 from the first 30 we get:
1+29+30 = 60
Right!?

Edit:
Why not 1+2+57 = 60

And are we limited to integers?

Am I stupid? Idk, I think the question needs to be re-stated because you can literally pick any number of the four options that were given.

Edit2: okay, nvm, she meant the mathematical definition of consecutive.

[samuelosei-somuah]

X + (x-1) +(x+1)=60. 3x=60 and x =20 therefore x+1=21 and d arrived at algebraically

[flavrt]

That's not a solution. If X is the number you seek, then
X+(X-1)+(X-2) = 60 = 3X -3. Then 3X = 63. So X = 21.