### Discussion :: Problems on Numbers - General Questions (Q.No.2)

2. | Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: |
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Answer: Option D Explanation: Let the three integers be Then, 3 Third integer = 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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