Three Times the First of Three Consecutive Odd Integers is 3 More Than GMAT Problem Solving

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

1. 7
2. 9
3. 11
4. 13
5. 15

Correct Answer: E

Solution and Explanation
Approach Solution 1:
It is given in the question that Three times the first of three consecutive odd integers is 3 more than twice the third.now let us find the 3rd integer
Let x, x+2, and x+4 be three consecutive odd integers.
Three times the first of three successive odd integers is three times the third.
∴ 3x=2(x+4)+3
∴ x=11
As a result, the third integer is 11+4=15
The answer is E which is 15.

Approach Solutiion 2:
There is another approach to solve this question which is pretty simple and could help in finding the answer more quickly, let us look at the reasoning below-
Let num-2, num, and num+2 be three consecutive odd integers, where num is an odd integer.
The problem statement states that three times the first of three consecutive odd integers is three times more than twice the third, i.e.
3*(num-2) = 2*(num+2) + 3
Let us solve the equation using above steps:
3*(num-2) = 2*(num+2) + 3
3*num – 6 = 2*num + 4 + 3
3*num – 6 = 2*num + 7
3*num -2*num = 7 + 6
num = 13

As a result, the value of num is 13, which is the second integer.
The first integer is num - 2, which equals 13 - 2 = 11.
The third integer is num + 2, which equals 13 + 2 = 15.
The answer is E which is 15.

Approach Solution 3:
Let the three integers be x, x + 2 and x+4 Then, 3x = 2 (x+4) + 3 ⇔x=11.

Therefore, third integer = x + 4 = 15

“Three times the first of three consecutive odd integers is 3 more than”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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