Aptitude - Problems on Numbers - Discussion

2. 

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

[A]. 9
[B]. 11
[C]. 13
[D]. 15

Answer: Option D

Explanation:

Let the three integers be x, x + 2 and x + 4.

Then, 3x = 2(x + 4) + 3      x = 11.

Third integer = x + 4 = 15.

Video Explanation: https://youtu.be/_77C9YE321Y


Saji said: (Sep 14, 2010)  
Hai can any one clear my doubt. They have mentioned it as three consecutive odd integers. If 0 is substituted in the place of x it becomes three even integers.

Nilesh said: (Oct 9, 2010)  
0 is considerd as even number.

Sandeep Pote said: (Oct 19, 2010)  
Third integer would be 9.

Explanation:

Suppose 3 numbers are . . x, x+2, x+4.

3x = 2(x + 4) - 3

3x = 2x + 8 -3

x = 5

Then third number is 5 + 4 = 9.

Bharghavi said: (Nov 14, 2010)  
The answer would be 9.

Explanation:
Suppose 3 nos. are x,x+2,x+4
The equations would be

3x+3=2(x+4),therefore x=5

So, the third no. is x+4=5+4=9.

Nishanthi said: (Jan 12, 2011)  
Here 3 more than that of the value of x so we use.

3x=2 (x+4) +3, 0 is odd or even number so in this problem 0 is used.

FRANCO said: (Mar 27, 2011)  
The first part is 3 more than the second part.

So to equate it we have to add 3 to the second part

I part = II part + 3

The ans 15 is correct

Md. Saifur Rahman said: (Apr 3, 2011)  
2x+1, 2x+3, 2x+5
3(2x+1)=2(2x+5)+3
... x=5
(2x+5)=15

Santhosh said: (Aug 7, 2011)  
Rahman is right.

Because the given numbers should be odd numbers.

So we have to take...the three consecutive odd numbers as 2x+1, 2x+3, 2x+5

Swetha said: (Sep 2, 2011)  
In this problem, they had given three consecutive odd integers.

If we take that 3 odd integers as x , x+2 and x+4,

if we put x = 2 => the numbers will become 2 , 4, 6

these nos are even numbers..then how we assume X,X+2,X+4 as three consecutive odd integers?

Can anyone Clear my doubt??

Vamshidhar Reddy said: (Sep 7, 2011)  
Three consecutive integers x, x+1, x+2

3x=2(x+2)+3
x=7
x+2=9

Srinu said: (Sep 11, 2011)  
I don't understand this problem. Can any one explain this problm please.

Shivaraj said: (Oct 9, 2011)  
Explain this problm please.

Virendra said: (Nov 22, 2011)  
Forget everything just go option wise then answer should be 9 or 15.

Utkarsh said: (Dec 3, 2011)  
If we put x=1,then three consecutive no's x,x+2,x+4 gets an odd no.

Namrata said: (May 16, 2012)  
Zero is neither odd nor even number.

Prerak said: (Jun 7, 2012)  
Hey can anyone explain this problem? I don't understand these "odd integers is 3 more than twice the third".

Satish said: (Jul 11, 2012)  
Hi all,
1> See it is said that first of 3 consecutive odd no is 3.
2> It is said 3 times the first no means i.e. 3*3 = 9.
3> It is also said that 3rd no is 3 more or twice the first i.e. 6.
4> That's how we get the answer 9+6=15.

Keerthi said: (Aug 13, 2012)  
How we take x, x+2, x+4 are odd integers if we take x=2 then it become even can any one clear this doubt ?

Sukruthi said: (Aug 30, 2012)  
As they hav given 3 consecutive odd integers then that 3 can be assumed as 2x+1,2x+3,2x+5 ...
because x,x+2,x+4 wont give us odd values if v substitute any positive integers. then the values which i have assumed can satisfy all consecutive odd integers so now
1st of 3 consecutive integers is 2x+1
so now 3*(2x+1)=3+(2*(2x+5)
=> 6x+3=4x+13
=> x=5
now 3rd integer is
2x+5
=> 2(5)+5=15.

Rashmi said: (Oct 29, 2012)  
Hi,

Consecutive nos are x, x+2, x+4. If we add 1 to these nos we get odd consecutive nos.
So read the question neatly.
3 times the first of three consecutive nos it means first consecutive no is x. 3 times means 3x.
So answer is 15.

Santhosh said: (Apr 15, 2013)  
Three consecutive odd integers are x+1, x+3, x+5

So,

3(x+1) = 3+2(x+5).

3x+3 = 3 + 2x + 10.

x = 10. So the third number is x+5.

10+5 = 15.

Answer 15.

Nusohel said: (Apr 29, 2013)  
Three conservatives odd integers are X, X+2, X+4

Three times the first of three consecutive odd integers is 3X.
3 more than is 3+
Twice the third is 2(X+4)

3x = 3+2(X+4).

x = 11.

Third integer = x + 4 = 15.

Kamal said: (Jul 17, 2013)  
How can we take x, x+2, x+4 as odd positive integers. Kindly clear my doubt?

Nani said: (Aug 2, 2013)  
If we take three consecutive numbers are x, x+2, x+4....

If we substitute x as 1 (because 1 is the 1st odd num).

We get odd numbers.....1, 3, 5..

Three times the first of three consecutive odd integers is 3X.
3 more than is 3+

Twice the third is 2(X+4).

3x = 3+2(X+4).

x = 11.

Third integer = x + 4 = 15.

Prashants.s.wagge said: (Nov 14, 2013)  
Just solve in simp way.

1st 3 odd int are 1, 3, 5.

Add those 1+3+5 = 9.

Now take 3 odd num after 9 i.e. = 15.

Govind said: (Jan 26, 2014)  
Num are 2x+1, 2X+3, 2X+5 then.

3(2X+1) = 2(2x+3)+3.

6x+3 = 4x+6+3.

x = 2.

Third integer: 2x+5 = 9.

Learner said: (Jan 29, 2014)  
I believe when integers have been mentioned in the question and not positive or negative so better to have them as
2x-1, x, 2x+1.... and then solve the problem.

So the third integer comes out to be 9.

Muthu said: (Apr 16, 2014)  
Hi guys. Any one clear my doubt.

3x = 2(x+4)+3.

How can you get above steps ?

Cutie said: (Jun 11, 2014)  
2x+1, 2x+3, 2x+5 is the correct form.

Cutie said: (Jun 11, 2014)  
@Muthu the answer is 15 you solved it as 11 this is wrong.

3x = 2(x+4)+3.
3x = 2x+8+3.
3x = 2x+11.
3x-2x = 11.
x = 11.

Like this :).

Sathish said: (Jul 4, 2014)  
How this 3x = 2(x + 4) + 3 came up, please explain?

Geetha said: (Aug 1, 2014)  
What they said in question in three consecutive odd numbers, first number 3 times and 2 times of 3 rd number different is 3.

So we can consider that number should be like this.

x, x+2, x+4.
3x-2 (x+4) = 3.
x-8 = 3.
x = 11.

They asked about the third number so it is x+4 = 11+4 = 15.

Amrith said: (Aug 18, 2014)  
Three times the first of three consecutive odd integers.

Why is 3x taken didn't get it.

Raj said: (Sep 4, 2014)  
Any one can explain these problems why we assume the number as X+1, X+2X, X+3?

Prabhu said: (Oct 10, 2014)  
How will come? please explain. I couldn't understand.

3x = 2(x+4)+3.

V.Ranjitha said: (Oct 11, 2014)  
Hi friends,

I think Govind is correct. Because the x value may be odd number or even number.(2x+1,2x+3,2x+5)

If x=0,
We get 1, 3, 5.

If x=1(odd),
We get 3, 5, 7.

If x=2(even),
We get 5, 7, 9.

Ssgm said: (Oct 17, 2014)  
An integer n any odd will be (2n+1).
After (2n+1) is (2n+3) then (2n+5).

From the Q:
3(2n+1) > 2(2n+5).

=> n > 3.5 => n start from 4 to infinity.

So the numbers (2(4)+1=9), 11, 13 and I say the answer is 13.

Neeraj Upadhyay said: (Oct 31, 2014)  
Three consecutive integer are 2x+1, 2x+3, 2x+5.

Now according to question.

3(2x+1) = 2(2x+5)+3.

6x+3 = 4x+10+3.

2x = 10.

x = 5.

And now third number is 2x+5 = 2*5+5 = 15.

15 is a answer.

HEMANTH REDDY G said: (Dec 2, 2014)  
3 times of 1st consecutive means 3x.
Twice of 3rd consecutive 2(x+4).

3 more than twice of 3rd consecutive 2(x+4)+3, then.

3x = 2(x+4)+3.
3x-2x = 8+3.
x = 11.

3rd integer is x+4 = 11+4 = 15.

Gayathri said: (Feb 14, 2015)  
Three consecutive odd numbers x+1, x+3, x+5.

(x+1)+(x+3)+(x+5) = 3+2(x+5).

x = 4. So the third integer x+5 = 4+5 = 9.

I think the answer will be 9 because in this problem three consecutive odd numbers is asked then, how can we start with 0 is my doubt.

Reshma said: (Jun 23, 2015)  
If you take x+1 as first odd no. Then put 1 in the place of x, it becomes 1+1=2 its not odd integer you got it.

Aandrew said: (Jul 7, 2015)  
Can any one say how to solve this in 32 seconds?

HYNDAVI said: (Jul 11, 2015)  
But whats the reason to multiply 3 on both sides?

Sony said: (Oct 7, 2015)  
At first three number is x, x+2, x+4 these are three consecutive number.

Then according to question (three times the first of three consecutive odd number) here is our first number is x then,

Our first condition will be 3x----- (1).

And then 3 more than twice the third (there third is x+4).

3 more means 3+, twice means 2.

Then twice of third is 2(x+4).

Then again 3+2(2x+4) -------- (2).

Then from equation first and second we get:

3x = 3+2(x+4).
3x = 3+(2x+8).

3x = 3+2x+8.
3x-2x = 11.
x = 11.

Then our third integer is x+4 ==> 11+4 = 15.

Our third integer is (x+4) = 15.

Gayathri Ganesan said: (Dec 7, 2015)  
I got idea about this solution. But if we assume the solution by question as,

3 times the x of three consecutive integers whether is my assumption also possible na.

3(x+X+2+x+4) = 3+2(x+4) // I consider it for first 3 con int respectively.

Anyone can explain my logic please.

Sanjay said: (Jan 19, 2016)  
Simple way to solve problem z that, 3 times the x of 3 consecutive integers.

So, he said about odd numbers, now we take 3 consecutive are x, x+2, x+4, then we know odd numbers are 1, 3, 5, 7, 9,... so, take first 3 odd numbers and place like this, x+x+2+x+4, 1+3+2+5+4 = 15.

Saksham said: (Feb 12, 2016)  
Answer: 13.

Because 11 + 13 = 24.

9*3 = 27.
27-24 = 3.

RKO said: (Apr 5, 2016)  
0 is an even number, about what basis the given question doesn't take o is let me assume if we take consecutive no i.e. X+0=0, so we took directly "X".

Kishan said: (Jun 8, 2016)  
Why we go through option answers.

Three times the first = 3 (first number).
Twice the third one = 2 (third number).
3 more than that = 3 + 2 (third number).

To find the third number;

So, we apply the option a (or) b (or) c (or) d.

The first option is 9 if the third integer is 9 then the three odd numbers are 5, 7, 9.

=>So 3 (5) is not equal to 3 + 2 (9).

Option b = 11.

So, the numbers are 7, 9, 11.

=>3 (7) is not equal to 3 + 2 (11).

So let's try option d = 15.

The three odd numbers 11, 13, 15.

=> 3 (11) is equal to 3 + 2 (15).

So, the answer is 15.

Akhilkondaparva said: (Aug 23, 2016)  
Let the three odd integers be x, x + 2 and x + 4.

(Integer = 1, 2 , 3).

If x = 1 then the three integers are 1, 3, 5 => which are odd.

Three times the first of three consecutive odd integers (Which is 3x) is.

3 more than (+3) twice the third [2 (x + 4) ] => 3x = 2 (x + 4) + 3x = 11.

Since we got "x", we have to find the third integer value i.e. x + 4 value.

=> Third integer = x + 4 = 15.

Hope you get this.

Akhilkondaparva said: (Aug 24, 2016)  
Let the three odd integers be x, x + 2 and x + 4.

(we know Integers I = 1, 2, 3, ....).

If x = 1 then,

The three integers are {sub x=1 in x, x + 2 and x + 4. } --> 1, 3, 5 => which are odd.

Three times the first of three consecutive odd integers (Which is 3x) is 3 more than (add +3) twice the third [2 (x + 4) ].

=> 3x = 2 (x + 4) + 3,

=> x = 11.

Since we got "x" value, we have to find the third integer value i.e. x + 4 value.

=> Third integer = x + 4 = 11+ 4 = 15.

Hope you get this.

Swati said: (Aug 30, 2016)  
Instead of that directly can't we take 1, 3, 5.

Vicky said: (Sep 27, 2016)  
Here is the perfect answer.

Let 3 numbers be x + 1, x + 3, x + 5.
3 (x + 1) = 3 + 2 (x + 5).

Simplify it then you will get x = 5,
Then substitute x in x + 5.
10 + 5 = 15.

Therefore, 15 is the answer.

Mahaprasad said: (Nov 28, 2016)  
Answer can be 11 also !
Suppose 7,9,11 are the hree consecutive odd numbers!

If the first number will be 7. Three times of 7 would be 21!
2 times of second number(9) would be 18.
21 is greater than 18 by 3 number.
So it justifies the equation.

Kavitha said: (Dec 15, 2016)  
Zero included in a set of whole numbers. So if we start putting 1, 3, 5 .....in x, we get the consecutive odd numbers only!!

Baal said: (Apr 15, 2017)  
In question written is three consecutive odd integer.

Can, I do like this if I take odd no time two?

3x + 5x + 7x= 15.

Megersa said: (Jun 23, 2017)  
Three consecutive integers are: x, x+2 &x+4 but if it says three times the first of three consecutive, it means that 3 (x+x+2+x+4) not 3x, so doing by this method the result becomes negative integer, so by itself, the question has its own problem.

A.M.M said: (Sep 13, 2017)  
Let the three consecutive old numbers be; x+3, x+5, x+7,
3 times the first odd num = 3(x+3).
2 times the third odd num = 2(x+7) +3(which is in the question
3(x+3)=2(x+7)+3,
=3x+9=2x+14+3,
3x-2x=14+3-9,
x = 8.

Now to know what the the third integer is (x+7),
So x =8+7,
=15.

M.Muthumari said: (Sep 15, 2017)  
Consecutive means numbers follow in a series or sequence (i.e) each number follow in order.

Ex: consecutive num-1 2 3 4 5 6 7 Etc.
consecutive even num - assume x is even
Then x x+2 x+4 is even
(i.e) x=2 x+2=4 x+4=6
2 4 6 is even
Consecutive odd num - assume x is odd
Then x x+2 x+4 is odd
(i.e) x=1 x+2=3 x+4=5
1 3 5 is odd
Soln.
First three consecutive odd x x+2 x+4
3x=3+(2*(x+4))
x=11
Third num=x+4=11+4=15.

Sukanya said: (Nov 29, 2017)  
But 2x+1,2x+3,2x+5. are better examples to understand this problem because if we substitute even numbers in x, x+2,x+3 we didn't get odd numbers.

Abinash said: (Dec 12, 2017)  
I could not get how 3X came in the question it is given that 3 times the first three consecutive number what my point is that it should be 3{X (X+2) (X+4) } but why is it 3X?

Kelhen said: (Mar 15, 2018)  
Three consecutive odd integers that's;

X+1, x+3, x+5,
From the question.
3(x+1) = 2(x+5)+3,
3x+3 = 2x+10+3,
X = 10.

Therefore the third integer is;
X+5;
10+5 = 15.

Chandan Kumar said: (May 20, 2018)  
Let first consecutive odd integer=x+1,
second consecutive odd integer= x+3,
Third consecutive odd integer=x+5,
3(x+1)=2(x+5)+3,
3x+3= 2x+10+3,
3x-2x=13-3,
x=10.

Third consecutive odd integer=x+5,
= 10+5,
= 15.

Sanjay said: (Jun 26, 2018)  
Consecutive mean 1 after one. i.e 1, 3, 5, 7etc.

Ramya said: (Dec 29, 2018)  
Anyone can explain this problem? Please anyone help me to solve this problem.

Pratap said: (Mar 20, 2019)  
X+1, X+3, X+5.
Atq:
3(X+1) = 3+2(X+5),
X = 10.

Shanu Kumar said: (May 9, 2019)  
Odd numbers are never be in form of x, x+2 etc.
Odd no Is in the form of 2x+1.

Mahin said: (Jul 8, 2019)  
The Consecutive odd integers are (2x+1, 2x+3, 2x+5). Sub any no.for 'x', you'll get an odd integer.

Now, try solving the question with these three, you'll get X = 5;
That means the 3rd integer, 2X + 5 = 15.

Vamsikrishnareddy said: (Dec 24, 2019)  
Anybody can explain short cut of this problem.

Lavanya said: (Jul 9, 2020)  
Let three consecutive odd integers are: x, x+2,x+4.

Three times the first of three integers, so--> 3x; is 3 more than twice the third so--> 3+ 2(x+4).

Then, we get an equation like 3x=3+2(x+4).
=3+2x+8.
3x-2x=11
X=11.

So, the third integer is x+4=15.

Pinky said: (Jan 30, 2021)  
My answer is 15.

Let 2n+1 be an odd number for any value of n from 0 up to infinity.

Take a look: If n=0, 2n+1 is 1. If n=1, 2n+1 is 3. See, the resulting number is always odd whether n is odd or even.

Let (2n+1), (2n+3), (2n+5) be the three consecutive numbers.
Just to see if these three are really consecutive odd, let us try to substitute n=0. If n=0, the resulting three consecutive odd are 1,2,3. If n=1, the resulting three consecutive odd are 3,5,7. This is just to show you that these three will really result to three consecutive odd for any value of n from 0 up to infinity.

Since we do not know exactly what are these three consecutive odd, so let us take these (2n+1), (2n+3), (2n+5) as the three consecutive odd numbers.

Solution:
3(2n+1) = 2(2n+5)+3
6n+3 = 4n+10+3
6n-4n = 10+3-3
2n = 10
n = 5.
Since the third odd number is represented by 2n+5, just substitute 5 to n. So the third odd number is 15.

We can also say that the three consecutive odds are 11, 13, 15. The third is 15.

Aryan said: (May 23, 2021)  
Here

Three odd consecutive number.
3, 5, 7 = 3 + 5 + 7 then ans 15.

Tashi Tshering said: (Aug 10, 2021)  
Here,
1,3,5 three odd consecutive no;
Three times the first of three consecutive odd integers is 3 more than twice the third,
3x when the third inter is x=5.
3*5=15.

Megersa Tadale said: (Nov 29, 2022)  
Suppose we take x,x+2,x+4 for odd consecutive numbers;

Then, according to the question, the first among the consecutive number is 3 more than twice the third number.

It means 3x+3=2(x+4) then;
we will get 3x+3=2x+8(now collecting like terms);
then 3x-2x=8-3.

x=5
So the third number is x+4----->>>> 9.

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