Question: Find the next number of series: 3, 4, 8, 17, 33, 58.

1. 68
2. 88
3. 94
4. 99
5. 113

Solution and Explanation:

Approach Solution (1):

In the series of 3, 4, 8, 17, 33, 58.
The next numbers in sequence shall be 94
Explanation given below for next numbers in sequence.

4-3=1 i.e., Difference of two consecutive numbers is 1 or square of 1=1
8-4=4. i.e., Difference of two consecutive numbers is 4 or square of 2 =4
17-8=9. i.e., Difference of two consecutive numbers is 9 or square of 3 = 9
33-17=16 i.e., Difference of two consecutive numbers is 16 or square of 4=16
58-33=25 i.e., Difference of two consecutive numbers is 25 or square of 5=25
94-58=36 i.e., Difference of two consecutive numbers is 36 or square of 6=36

Therefore series will be 3, 4, 8, 17, 33, 58, 94.

Correct Option: C

Approach Solution (2):

Series is:

a, a+1=b, b+(1+3)=c, c+(1+3+5)=d, d+(1+3+5+7)=e, e+(1+3+5+7+9)=f,…….

Comparing it with given problem:

a = 3
b = 3 + 1 = 4
c = 4 + (1 + 3) = 8
d = 8 + (1 + 3 + 5) = 17
e = 17 + (1 + 3 + 5 + 7) = 33
f = 33 + (1 + 3 + 5 + 7 + 9) = 58
g = 58 + (1 + 3 + 5 + 7 + 9 + 11) = 94

So 94 is the answer

Correct Option: C

Approach Solution (3):

We will use the logic:

\(T_n=T_{n-1}+n^2,T_1=4\)

So the solution of this question will be: 94

\(4+2^2=4+4=8\)
\(8+3^2=8+9=17\)
\(17+4^2=17+16=33\)
\(33+5^2=33+25=58\)
\(58+6^2=58+36=94\)

So the next term of the series 3, 4, 8, 17, 33, 58 is 94.

Correct Option: C

“Find the next number of series: 3, 4, 8, 17, 33, 58”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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