# Aptitude - Problems on Numbers - Discussion

Discussion Forum : 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:

Answer: Option

Explanation:

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

Then, 3*x* = 2(*x* + 4) + 3 *x* = 11.

Third integer = *x* + 4 = 15.

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

Discussion:

74 comments Page 1 of 8.
Pinky said:
3 years ago

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.

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.

(1)

M.Muthumari said:
6 years ago

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.

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.

Sony said:
8 years ago

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.

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.

Kishan said:
8 years ago

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.

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:
7 years ago

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.

(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.

Sukruthi said:
1 decade ago

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.

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.

Akhilkondaparva said:
7 years ago

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.

(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.

Megersa Tadale said:
1 year ago

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.

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.

(1)

Nani said:
1 decade ago

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.

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.

Swetha said:
1 decade ago

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??

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??

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