- Home
- Reasoning
- Number Series
- Exercise 2
A257
B351
C349
D231
Answer: B
Explanation:
$\begin{array}{ccc}
Pattern & Series \\
{2^3} + 3 & 11 \\
{3^3} + 4 & 31 \\
{4^3} + 5 & 69 \\
{5^3} + 6 & 131 \\
{6^3} + 7 & 223 \\
{7^3} + 8 & \color{blue}{351} & \checkmark \\
\end{array}$
$\newcommand\pad[1]{\rlap{#1}\phantom{20}}
\begin{array}
\pad{11} &&\pad{31} &&\pad{69} &&\pad{131} &&\pad{223} &&\color{blue}{351}\checkmark \\
&\pad{+20} &&\pad{+38} &&\pad{+62} &&\pad{+92} &&\color{red}{+128} && \Leftarrow 1st\;Diff\\
&&{+18}&&{+24}&&{+30}&&\color{red}{+36} &&& \Leftarrow 2nd\;Diff
\end{array}$
General pattern of the series:\begin{array}
\pad{11} &&\pad{31} &&\pad{69} &&\pad{131} &&\pad{223} &&\color{blue}{351}\checkmark \\
&\pad{+20} &&\pad{+38} &&\pad{+62} &&\pad{+92} &&\color{red}{+128} && \Leftarrow 1st\;Diff\\
&&{+18}&&{+24}&&{+30}&&\color{red}{+36} &&& \Leftarrow 2nd\;Diff
\end{array}$
$\begin{array}{ccc}
Pattern & Series \\
{2^3} + 3 & 11 \\
{3^3} + 4 & 31 \\
{4^3} + 5 & 69 \\
{5^3} + 6 & 131 \\
{6^3} + 7 & 223 \\
{7^3} + 8 & \color{blue}{351} & \checkmark \\
\end{array}$
27, 5, 7, 17, 63, ?
A308
B302
C309
D409
Answer: C
Explanation:
This series is based on cube of consecutive numbers minus one.
$\begin{array}{cc}
Pattern & Series \\
7 \times 1 - 2 & 5 \\
5 \times 2 - 3 & 7 \\
7 \times 3 - 4 & 17 \\
17 \times 4 - 5 & 63 \\
63 \times 5 - 6 & \color{blue}{309} & \checkmark \\
\end{array}$
This series is based on cube of consecutive numbers minus one.
$\begin{array}{cc}
Pattern & Series \\
7 \times 1 - 2 & 5 \\
5 \times 2 - 3 & 7 \\
7 \times 3 - 4 & 17 \\
17 \times 4 - 5 & 63 \\
63 \times 5 - 6 & \color{blue}{309} & \checkmark \\
\end{array}$
350, ?, 61, 89, 154, 280
A52
B51
C60
D62
Answer: C
Explanation:
$\begin{array}{cc}
Pattern & Series \\
50 + \left( {{1^3} + 1} \right) &\color{blue}{52} & \checkmark \\
52 + \left( {{2^3} + 1} \right) & 61 \\
61 + \left( {{3^3} + 1} \right) & 89 \\
89 + \left( {{4^3} + 1} \right) & 154 \\
154 + \left( {{5^3} + 1} \right) & 280 \\
\end{array}$
$\begin{array}{cc}
Pattern & Series \\
50 + \left( {{1^3} + 1} \right) &\color{blue}{52} & \checkmark \\
52 + \left( {{2^3} + 1} \right) & 61 \\
61 + \left( {{3^3} + 1} \right) & 89 \\
89 + \left( {{4^3} + 1} \right) & 154 \\
154 + \left( {{5^3} + 1} \right) & 280 \\
\end{array}$
417, 19, 25, 37, ?, 87
A22
B29
C30
D32
Answer: C
Explanation:
$\begin{array}{cc}
Pattern & Series \\
17 + \left( {1 \times 2} \right) &19 & \\
19 + \left( {2 \times 3} \right) & 25 \\
25 + \left( {3 \times 4} \right) & 37 \\
37 + \left( {4 \times 5} \right) & \color{blue}57 & \checkmark \\
57 + \left( {5 \times 6} \right) & 87 \\
\end{array}$
$\begin{array}{cc}
Pattern & Series \\
17 + \left( {1 \times 2} \right) &19 & \\
19 + \left( {2 \times 3} \right) & 25 \\
25 + \left( {3 \times 4} \right) & 37 \\
37 + \left( {4 \times 5} \right) & \color{blue}57 & \checkmark \\
57 + \left( {5 \times 6} \right) & 87 \\
\end{array}$
59, 29, 89, 269, 809, ?
A2429
B2448
C2246
D2552
Answer: A
Explanation:
$\begin{array}{cc}
Pattern & Series \\
9 & 9 \\
9 × 3 + 2 & 29 \\
29 × 3 + 2 & 89 \\
89 × 3 + 2 & 269 \\
269 × 3 + 2 & 809 \\
809 × 3 + 2 & 2429 &\checkmark\\
\end{array}$
$\begin{array}{cc}
Pattern & Series \\
9 & 9 \\
9 × 3 + 2 & 29 \\
29 × 3 + 2 & 89 \\
89 × 3 + 2 & 269 \\
269 × 3 + 2 & 809 \\
809 × 3 + 2 & 2429 &\checkmark\\
\end{array}$
636, 19.5, 21, 33, 67.5, ?
A172.5
B170.5
C170.25
D170
Answer: C
Explanation:
$\begin{array}{cc}
Pattern & Series \\
36 & 36 \\
36 × 0.5 + 1.5 & 19.5 \\
19.5 × 1 + 1.5 & 21 \\
21 × 1.5 + 1.5 & 33 \\
33 × 2 + 1.5 & 67.5 \\
67.5 × 2.5 + 1.5 & 170.25 &\checkmark\\
\end{array}$
$\begin{array}{cc}
Pattern & Series \\
36 & 36 \\
36 × 0.5 + 1.5 & 19.5 \\
19.5 × 1 + 1.5 & 21 \\
21 × 1.5 + 1.5 & 33 \\
33 × 2 + 1.5 & 67.5 \\
67.5 × 2.5 + 1.5 & 170.25 &\checkmark\\
\end{array}$
722, 20, 37, 107, 423, ?
A2111
B2109
C2117
D2119
Answer: B
Explanation:
$\begin{array}{cc}
Pattern & Series \\
22 & 22 \\
22 × 1 - 2 & 20 \\
20 × 2 - 3 & 37 \\
37 × 3 - 4 & 107 \\
107 × 4 - 5 & 423 \\
423 × 5 - 6 & 2109 &\checkmark\\
\end{array}$
$\begin{array}{cc}
Pattern & Series \\
22 & 22 \\
22 × 1 - 2 & 20 \\
20 × 2 - 3 & 37 \\
37 × 3 - 4 & 107 \\
107 × 4 - 5 & 423 \\
423 × 5 - 6 & 2109 &\checkmark\\
\end{array}$
84, 8, 17, 42, ?, 212
A92
B95
C91
D98
Answer: C
Explanation:
$\newcommand\pad[1]{\rlap{#1}\phantom{120}}
\begin{array}
\pad{4} &&\pad{8} &&\pad{17} &&\pad{42} &&\color{blue}{91} &&\pad{212} \\
&\pad{2^2} &&\pad{3^2} &&\pad{5^2} &&\color{red}{7^2} &&\pad{11^2}&& \Leftarrow\text{1st Diff.} \\
\end{array}$
\begin{array}
\pad{4} &&\pad{8} &&\pad{17} &&\pad{42} &&\color{blue}{91} &&\pad{212} \\
&\pad{2^2} &&\pad{3^2} &&\pad{5^2} &&\color{red}{7^2} &&\pad{11^2}&& \Leftarrow\text{1st Diff.} \\
\end{array}$
