Number Series 1-1

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• Exercise 1

120, 17, 34, 31, 62, 59, ?
A95
B118
C110
D128

Answer: B

Explanation:

$\newcommand\pad[1]{\rlap{#1}\phantom{20}}
\begin{array}
\pad{20} &&\pad{17} &&\pad{34} &&\pad{31} &&\pad{62} &&\pad{59} &&\color{blue}{118}\checkmark \\
&\pad{-3} &&\pad{×2} &&\pad{-3} &&\pad{×2} &&\pad{-3} &&\color{red}{×2}&&
\end{array}$

20, 7, 26, 63, 124, ?
A210
B215
C211
D224

Answer: B

Explanation:
This series is based on cube of consecutive numbers minus one.
$\begin{array}{cc}
Pattern & Series \\
0 & {1^3} - 1 \\
7 & {2^3} - 1 \\
26 & {3^3} - 1 \\
63 & {4^3} - 1 \\
124 & {5^3} - 1 \\
\color{blue}{215}\, \checkmark & \color{red}{6^3} - 1 \\
\end{array}$

3 4, 8, 6, 5, 15, 10, 10, 20, 15, 17, 15, 16, 18, 14, ?
A88
B96
C93
D95

Answer: C

Explanation:
$(4, 8, 6)$, $(5, 15, 10)$, $(10, 20, 15)$, $(17, 15, 16)$, $(18, 14, ?)$
In every triplet, the third number is the $average$ of the first two numbers. So next number is average of 18, 14 which is (14 + 18)/ 2 = 16

42, 3, 4, 7, 13, 12, 12, 23, 20, 17, 33, 28, ?
A22
B29
C30
D32

Answer: A

Explanation:
$\color{red}2$, 3, 4, $\color{red}7$, 13, 12, $\color{red}12$, 23, 20, $\color{red}17$, 33, 28, ?

$\newcommand\pad[1]{\rlap{#1}\phantom{20}}
\begin{array}
\pad{2} &&\pad{7} &&\pad{12} &&\pad{17} &&\color{blue}{22} \checkmark \\
&\pad{+5} &&\pad{+5} &&\pad{+5} &&\color{red}{+5}
\end{array}$

572, 9, 82, 10, 88, 16, 86, 14, 99, ?
A102
B22
C18
D16

Answer: B

Explanation:
$\begin{array}{cc}
Number & Digit\;sum \\
7+2 & 9 \\[2px]
8+2 & 10 \\[2px]
8+8 & 16 \\[2px]
8+6 & 14 \\[2px]
9+9 & \color{blue}{18} & \checkmark \\[2px]
\end{array}$

61, 2, 6, 15, 31, 56, 92, ?
A150
B128
C141
D149

Answer: C

Explanation:

$\newcommand\pad[1]{\rlap{#1}\phantom{20}}
\begin{array}
\pad{1} &&\pad{2} &&\pad{6} &&\pad{15} &&\pad{31} &&\pad{56} &&\pad{92 }&&\color{blue}{131} \checkmark \\
&\pad{+1^2} &&\pad{+2^2} &&\pad{+3^2} &&\pad{+4^2} &&\pad{+5^2} &&\pad{+6^2} &&\color{red}{+7^2}
\end{array}$

74, 4, 12, 16, 36, 36, 108, ?
A64
B66
C82
D86

Answer: B

Explanation:
It is a mixture of two series.
$4,$ $\boxed4$, 12, $\boxed{16}$, 36, $\boxed{36}$, 108, $\boxed{?}$
4, 12, 36, 108 and 4, 16, 36 and 64.
The logic of 4, 12, 36, 108 is previous term × 3.
The logic of 4, 16, 36, is previous term +12, +20 +28, and so on. Therefore, the next term would be 64 at a difference of +28 from the last term. Alternatively, 4, 16, 36,. . . squares of even numbers. So next number would be 64.

88, 9, 11, 15, 23, 39, ?
A65
B70
C71
D74

Answer: C

Explanation:

$\newcommand\pad[1]{\rlap{#1}\phantom{222}}
\begin{array}
\pad{8} &&\pad{9} &&\pad{11} &&\pad{15} &&\pad{23} &&\pad{39} &&\color{blue}{71}\checkmark\\
&\pad{+2^0} &&\pad{+2^1} &&\pad{+2^2} &&\pad{+2^3} &&\pad{+2^4} &&\color{red}{+2^5} \\
\end{array}$

123

Number Series: ShortcutsNumber Series: Exercise - 1Number Series: Exercise - 2