NUMBER SYSTEM QUESTIONS PART 1

FIND THE NUMBER THAT FITS SOMEWHERE INTO THE MIDDLE OF THE SERIES. SOME OF THE ITEMS INVOLVE BOTH NUMBERS AND LETTERS

LOOK AT THIS SERIES: F2, __, D8, C16, B32, ... WHAT NUMBER SHOULD FILL THE BLANK?

A. A16
B. G4
C. E4
D. E3

ANSWER & EXPLANATION:

ANSWER: OPTION C

EXPLANATION: THE LETTERS DECREASE BY 1; THE NUMBERS ARE MULTIPLIED BY 2.


QUESTION DIVIDER LINE

LOOK AT THIS SERIES: 664, 332, 340, 170, ____, 89, ... WHAT NUMBER SHOULD FILL THE BLANK?

A. 85
B. 97
C. 109
D. 178

ANSWER & EXPLANATION:

ANSWER: OPTION D

EXPLANATION: THIS IS AN ALTERNATING DIVISION AND ADDITION SERIES: FIRST, DIVIDE BY 2, AND THEN ADD 8.


QUESTION DIVIDER LINE

LOOK AT THIS SERIES: V, VIII, XI, XIV, __, XX, ... WHAT NUMBER SHOULD FILL THE BLANK?

A. IX
B. XXIII
C. XV
D. XVII

ANSWER & EXPLANATION:

ANSWER: OPTION D

EXPLANATION: THIS IS A SIMPLE ADDITION SERIES; EACH NUMBER IS 3 MORE THAN THE PREVIOUS NUMBER.


QUESTION DIVIDER LINE

LOOK AT THIS SERIES: 70, 71, 76, __, 81, 86, 70, 91, ... WHAT NUMBER SHOULD FILL THE BLANK?

A. 70
B. 71
C. 80
D. 96

ANSWER & EXPLANATION:

ANSWER: OPTION A

EXPLANATION: IN THIS SERIES, 5 IS ADDED TO THE PREVIOUS NUMBER; THE NUMBER 70 IS INSERTED AS EVERY THIRD NUMBER.


QUESTION DIVIDER LINE


LOOK AT THIS SERIES: 8, 43, 11, 41, __, 39, 17, ... WHAT NUMBER SHOULD FILL IN THE BLANK?


A. 8
B. 14
C. 43
D. 44



ANSWER & EXPLANATION:


ANSWER: OPTION B



EXPLANATION: THIS IS A SIMPLE ALTERNATING ADDITION AND SUBTRACTION SERIES. THE FIRST SERIES BEGINS WITH 8 AND ADDS 3; THE SECOND BEGINS WITH 43 AND SUBTRACTS 2.

1. Insert the missing number. $12,25,49,99,197,395,\_$
A. $789$	B. $812$
C. $1579$	D. $722$

answer with explanation

Answer: Option A

Explanation:

Each number is twice the previous one with $1$ added or subtracted alternatively.

2. Insert the missing number. $34,7,37,14,40,28,43,\_$
A. $42$	B. $56$
C. $31$	D. $46$

answer with explanation

Answer: Option B

Explanation:

We have two series here.

$34,37,40,43,\cdots \text{(increase by 3)}7,14,28,\cdots \text{(multiply by 2)}$

Hence, next term is $28\times 2=56$

3. Find the missing number. $1,4,9,16,25,36,49,\_$
A. $64$	B. $81$
C. $54$	D. $56$

answer with explanation

Answer: Option A

Explanation:

The series is $1^2,2^2,3^2,4^2,5^2,6^2,7^2,\cdots$

Hence, next term $=8^2=64$

4. Insert the missing number. $2,7,10,22,18,37,26,\_$
A. $52$	B. $42$
C. $62$	D. $46$

answer with explanation

Answer: Option A

Explanation:

There are two series here

$2,10,18,26,\cdots \text{(increase by 8)}7,22,37,\cdots \text{(increase by 15)}$

Hence, next term $=37+15=52$

5. Find the missing number. $4,12,48,240,1440,\_$
A. $10020$	B. $10080$
C. $7620$	D. $6200$

answer with explanation

Answer: Option B

Explanation:

$4\times 3=1212\times 4=4848\times 5=240240\times 6=14401440\times 7=10080$

6. Find the missing number. $2,3,6,0,10,-3,14,\_$
A. $2$	B. $-2$
C. $-6$	D. $6$

answer with explanation

Answer: Option C

Explanation:

There are two series

$2,6,10,14,\cdots \text{(adding 4)}3,0,-3,\cdots \text{(subtracting 3)}$

Hence, next term $=-3-3=-6$

7. Find the missing number. $5,10,13,26,29,58,61,\_$
A. $64$	B. $128$
C. $122$	D. $125$

answer with explanation

Answer: Option C

Explanation:

Numbers are alternatively multiplied by $2$ and increased by $3$

$5\times 2=10$
$10+3=13$
$13\times 2=26$
$26+3=29$
$29\times 2=58$
$58+3=61$
$61\times 2=122$

8. Find the missing number. $1,8,27,64,125,216,\_$
A. $392$	B. $245$
C. $343$	D. $354$

answer with explanation

Answer: Option C

Explanation:

The pattern is $1^3,2^3,3^3,4^3,5^3,6^3,\cdots$

Hence, next number $=7^3=343$

9. Find the missing number. $4,5,7,11,19,\_$
A. $22$	B. $32$
C. $35$	D. $27$

answer with explanation

Answer: Option C

Explanation:

$4\times 2-3=55\times 2-3=77\times 2-3=1111\times 2-3=1919\times 2-3=35$

10. Find the missing number. $23,29,31,37,41,43,\_$
A. $53$	B. $47$
C. $59$	D. $48$

answer with explanation

Answer: Option B

Explanation:

All are prime numbers in their order, starting from $23$

Hence, next number $=47.$

11. Find the missing number. $8,24,12,36,18,54,\_$
A. $108$	B. $27$
C. $72$	D. $68$

answer with explanation

Answer: Option B

Explanation:

$8\times 3=2424÷2=1212\times 3=3636÷2=1818\times 3=5454÷2=27$

12. Find the missing number. $7,26,63,124,215,342,\_$
A. $391$	B. $421$
C. $481$	D. $511$

answer with explanation

Answer: Option D

Explanation:

$2^3-1=73^3-1=264^3-1=635^3-1=1246^3-1=2157^3-1=3428^3-1=511$

13. Find the missing number. $2,-6,18,-54,162,\_$
A. $-428$	B. $486$
C. $422$	D. $-486$

answer with explanation

Answer: Option D

Explanation:

$2\times -3=-6-6\times -3=1818\times -3=-54-54\times -3=162162\times -3=-486$

14. Find the missing number. $2,6,12,20,30,42,56,\_$
A. $70$	B. $61$
C. $64$	D. $72$

answer with explanation

Answer: Option D

Explanation:

Solution 1

$1\times 2=22\times 3=63\times 4=124\times 5=205\times 6=306\times 7=427\times 8=568\times 9=72$

Solution 2

$2+4=66+6=1212+8=2020+10=3030+12=4242+14=5656+16=72$

15. Find the missing number. $8,12,18,27,40.5,\_$
A. $62$	B. $60.5$
C. $58$	D. $60.75$

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answer with explanation

Answer: Option D

Explanation:

$8\times 3÷2=1212\times 3÷2=1818\times 3÷2=2727\times 3÷2=40.540.5\times 3÷2=\mathrm{60.75.}$ 196,144,100,64,36,$$ 8$$ 16$$ 18$$ 12$$

$$ {14}^2,{12}^2,{10}^2,8^2,6^2,\cdots $$

$$ =4^2=16$$

$$ 2,3,5,16,231,?$$ 53105$$ 52120$$ 62005$$ 422$$

$$ 3^2-2^2=55^2-3^2=16{16}^2-5^2=231{231}^2-{16}^2=53105$$

$$ 279936,46656,7776,1296,216,?$$ 66$$ 36$$ 60$$ 46$$ 279936÷6=4665646656÷6=77767776÷6=12961296÷6=216216÷6=36$$ 220,218,214,208,200,190,$$ 166$$ 178$$ 182$$ 190$$ 220-2=218218-4=214214-6=208208-8=200200-10=190190-12=178$$ 12,38,116,350,1052,?$$ 2200$$ 1800$$ 2800$$ 3158$$ 12\times 3+2=3838\times 3+2=116116\times 3+2=350350\times 3+2=1052.1052\times 3+2=3158.$ 9,35,91,189,341,?$$ 559$$ 611$$ 521$$ 502$$$ $$ $$ $$ $ 1^3+2^3=92^3+3^3=353^3+4^3=914^3+5^3=1895^3+6^3=3416^3+7^3=559$$$ $ 78,64,48,30,10,?$$ 8$$ -14$$ 2$$ -12$$$ $$ $$ $$ $ 78-14=6464-16=4848-18=3030-20=1010-22=-12$$$ $ 16384,8192,2048,256,16,?$$ 1$$ 0.5$$ 2$$ 8$$ 16384÷2=81928192÷4=20482048÷8=256256÷16=1616÷32=0.5$$ 46080,3840,384,48,8,2,?$$ 1$$ \frac{1}{8}$$ \frac{1}{64}$$ 46080÷12=38403840÷10=384384÷8=4848÷6=88÷4=22÷2=1$$ 7,21,63,189,567,?$$ 1307$$ 1609$$ 1521$$ 1701$$ 3$$ 1,0.5,0.25,0.125,0.0625,?$$ 0.03125$$ 0.0078125$$ 0.015625$$ 2$$ 20,19,17,?,10,5$$ 13$$ 16$$ 14$$ 15$$ 20-1=1919-2=1717-3=1414-4=1010-5=5$$ \frac{1}{2},\frac{3}{4},\frac{5}{8},\frac{7}{16},?$$ \frac{9}{32}$$ \frac{9}{30}$$ \frac{9}{28}$$ \frac{11}{32}$$ 2.$$ 1,3,5,7,\cdots $$ =7+2=9$$ 2.$$ 2,4,8,16,\cdots $$ =16\times 2=32$$ =\frac{9}{32}$$ 4,10,?,82,244,730$$ 40$$ 26$$ 28$$ 48$$ 4\times 3-2=1010\times 3-2=2828\times 3-2=8282\times 3-2=244244\times 3-2=730$$ 95,115.5,138,?,189$$ 164.5$$ 166.5$$ 162.5$$ 160.5$$ 95+20.5=115.5115.5+22.5=138138+24.5=162.5162.5+26.5=189$$$