Mathematical Reasoning (unit-5) UGC NET Paper-1 Study Notes (E-books) Download Pdf For Free

DIWAKAR EDUCATION HUB
2020
Mathematical Reasoning
and Aptitude
UGC NET PAPER-1
Prepared By – Diwakar Rajput & Neha Sharma
No.1 Supportive institiute ugc net

Preface Of Book
Mathematical Reasoning Unit -5 is Very Important For
Exam Perspective Here we Mention Tricks & Tips
Summary For Each Mathematical Topic Like Profit &
Loss,Ratio Etc . Also Provide 200 Practice Question
Answer of Each Topic .Here You Avail Topic Wise
MCQ with Trick To solved Through This Book You Can
practice Many Topic Will Help you To Make Grip On
Topic’s Also Increase Accuracy .

Reasoning: Meaning, Definition and Types
Meaning of Reasoning:
It is one of the best forms of controlled thinking consciously towards the solution of a
problem. It is realistic in the sense that the solution is sought always in reference to the
reality of the situation. We can solve many problems in our day-dreams, dreams and
imaginations but they are unrealistic solutions.
As Sherman defined, “reasoning is a process of thinking during which the
individual is aware of a problem identifies, evaluates, and decides upon a
solution”.
Reasoning is used not only when we want to solve an immediate problem but also when we
anticipate future problems.
Reasoning plays a significant role in one’s adjustment to the environment. It not only
determines one’s cognitive activities but also influences the behaviour and personality.
Definitions of Reasoning:
1. “Reasoning is a stepwise thinking with a purpose or goal in mind” —Garrett.
2. “Reasoning is the term applied to highly purposeful, controlled and selective thinking”—
Gates.
3. “Reasoning is the word used to describe the mental recognition of cause and effect
relationships, it may be the prediction of an event from an observed cause or the inference
of a cause from an observed event”—Skinner.

Thus reasoning is a highly specialized thinking which helps an individual to explore
mentally the cause and effect relationship of an event or solution of a problem by adopting
some well-organized systematic steps based on previous experience combined with present
observation.
Types of Reasoning:
Reasoning may be classified into two types.
1. Inductive reasoning:
It is a specialized thinking aimed at the discovery or construction of a generalized principle
by making use of particular cases, special examples and identifying of elements or
relations.
For example, Mohan is mortal, Radha is mortal, Karim is mortal; therefore, all human
beings are mortal.
2. Deductive reasoning:
It is the ability to draw some logical conclusions from known statement or evidences. Here
one starts with already known or established generalized statement or principle and
applies it to specific cases. For example, all human beings are mortal you are a human
being, therefore, you are mortal.
Henry has categorized three types of deductive reasoning:
i. Conditioned reasoning:
It is the reasoning tied down by some specific condition such as the following.
For example, if there is a solar eclipse, the street will be dork. There is a solar eclipse
... The streets are dark.
ii. Categorical reasoning:
This type of reasoning is based on some categorical statements.

For example, all Robins are birds.
All birds lay eggs.
... All Robins lay eggs.
iii. Linear reasoning:
This type of reasoning involves straight forward relationships among elements.
For example, If Ram is taller than Mohan and Mohan is taller than Sohan, Ram is the
tallest.
DEDUCTIVE, INDUCTIVE, AND ABDUCTIVE REASONING
Reasoning is the process of using existing knowledge to draw conclusions, make predictions,
or construct explanations. Three methods of reasoning are the deductive, inductive, and
abductive approaches.
Deductive reasoning: conclusion guaranteed
Deductive reasoning starts with the assertion of a general rule and proceeds from there to a
guaranteed specific conclusion. Deductive reasoning moves from the general rule to the
specific application: In deductive reasoning, if the original assertions are true, then the
conclusion must also be true. For example, math is deductive:
If x = 4
And if y = 1
Then 2x + y = 9
In this example, it is a logical necessity that 2x + y equals 9; 2x + y must equal 9. As a
matter of fact, formal, symbolic logic uses a language that looks rather like the math equality
above, complete with its own operators and syntax. But a deductive syllogism (think of it as a
plain-English version of a math equality) can be expressed in ordinary language:

If entropy (disorder) in a system will increase unless energy is expended,
And if my living room is a system,
Then disorder will increase in my living room unless I clean it.
In the syllogism above, the first two statements, the propositions or premises, lead logically to
the third statement, the conclusion. Here is another example:
A medical technology ought to be funded if it has been used successfully to treat patients.
Adult stem cells are being used to treat patients successfully in more than sixty-five new
therapies.
Adult stem cell research and technology should be funded.
A conclusion is sound (true) or unsound (false), depending on the truth of the original
premises (for any premise may be true or false). At the same time, independent of the truth
or falsity of the premises, the deductive inference itself (the process of "connecting the dots"
from premise to conclusion) is either valid or invalid. The inferential process can be valid even
if the premise is false:
There is no such thing as drought in the West.
California is in the West.
California need never make plans to deal with a drought.
In the example above, though the inferential process itself is valid, the conclusion is false
because the premise, There is no such thing as drought in the West, is false. A syllogism
yields a false conclusion if either of its propositions is false. A syllogism like this is particularly
insidious because it looks so very logical–it is, in fact, logical. But whether in error or malice, if
either of the propositions above is wrong, then a policy decision based upon it (California need
never make plans to deal with a drought) probably would fail to serve the public interest.
Assuming the propositions are sound, the rather stern logic of deductive reasoning can give
you absolutely certain conclusions. However, deductive reasoning cannot really increase
human knowledge (it is nonampliative) because the conclusions yielded by deductive
reasoning are tautologies-statements that are contained within the premises and virtually self-
evident. Therefore, while with deductive reasoning we can make observations and expand

implications, we cannot make predictions about future or otherwise non-observed
phenomena.
Inductive reasoning: conclusion merely likely
Inductive reasoning begins with observations that are specific and limited in scope, and
proceeds to a generalized conclusion that is likely, but not certain, in light of accumulated
evidence. You could say that inductive reasoning moves from the specific to the general. Much
scientific research is carried out by the inductive method: gathering evidence, seeking
patterns, and forming a hypothesis or theory to explain what is seen.
Conclusions reached by the inductive method are not logical necessities; no amount of
inductive evidence guarantees the conclusion. This is because there is no way to know that all
the possible evidence has been gathered, and that there exists no further bit of unobserved
evidence that might invalidate my hypothesis. Thus, while the newspapers might report the
conclusions of scientific research as absolutes, scientific literature itself uses more cautious
language, the language of inductively reached, probable conclusions:
What we have seen is the ability of these cells to feed the blood vessels of tumors and to heal
the blood vessels surrounding wounds. The findings suggest that these adult stem cells may
be an ideal source of cells for clinical therapy. For example, we can envision the use of these
stem cells for therapies against cancer tumors [...].1
Because inductive conclusions are not logical necessities, inductive arguments are not simply
true. Rather, they are cogent: that is, the evidence seems complete, relevant, and generally
convincing, and the conclusion is therefore probably true. Nor are inductive arguments simply
false; rather, they are not cogent.
It is an important difference from deductive reasoning that, while inductive reasoning cannot
yield an absolutely certain conclusion, it can actually increase human knowledge (it
is ampliative). It can make predictions about future events or as-yet unobserved phenomena.
For example, Albert Einstein observed the movement of a pocket compass when he was five
years old and became fascinated with the idea that something invisible in the space around
the compass needle was causing it to move. This observation, combined with additional

observations (of moving trains, for example) and the results of logical and mathematical tools
(deduction), resulted in a rule that fit his observations and could predict events that were as
yet unobserved.
Abductive reasoning: taking your best shot
Abductive reasoning typically begins with an incomplete set of observations and proceeds to
the likeliest possible explanation for the set. Abductive reasoning yields the kind of daily
decision-making that does its best with the information at hand, which often is incomplete.
A medical diagnosis is an application of abductive reasoning: given this set of symptoms, what
is the diagnosis that would best explain most of them? Likewise, when jurors hear evidence in
a criminal case, they must consider whether the prosecution or the defense has the best
explanation to cover all the points of evidence. While there may be no certainty about their
verdict, since there may exist additional evidence that was not admitted in the case, they
make their best guess based on what they know.
While cogent inductive reasoning requires that the evidence that might shed light on the
subject be fairly complete, whether positive or negative, abductive reasoning is characterized
by lack of completeness, either in the evidence, or in the explanation, or both. A patient may
be unconscious or fail to report every symptom, for example, resulting in incomplete evidence,
or a doctor may arrive at a diagnosis that fails to explain several of the symptoms. Still, he
must reach the best diagnosis he can.
The abductive process can be creative, intuitive, even revolutionary.2 Einstein's work, for
example, was not just inductive and deductive, but involved a creative leap of imagination and
visualization that scarcely seemed warranted by the mere observation of moving trains and
falling elevators. In fact, so much of Einstein's work was done as a "thought experiment" (for
he never experimentally dropped elevators), that some of his peers discredited it as too
fanciful. Nevertheless, he appears to have been right-until now his remarkable conclusions
about space-time continue to be verified experientially.
Number series-

Number Series Tricks
Number Series is a very important part of quantitative aptitude and usually asked in UGC NET Paper-1 exam. , it
covers 2 to 3 questions which may play very important roll in selection.
So, students should aware with all type of pattern of number series asked in exams and should practice more and more
on the number series. Here, we are providing some important notes and tricks for number series which will be helpful in
your preparation.
Number Series
In UGC NET Exam, generally two types of number series are asked.
First one is Missing Number Series in which some numbers are given which are following certain
pattern. Student is expected to find out the missing number.
Second one is Wrong Number Series in which some numbers are given but one number is wrong and
does not follow the required pattern. Student is expected to find out the wrong number.
• Following patterns have been frequently asked in UGC NET exams which are further explained below
in detail.
Single stage difference
1. 3, 23, 63, ?, 303 , 623 (Ans: 143)
Pattern is:
+ 20, + 40, + 80, + 160, ………
2. 240, 205, 177, 156, 142, ? (Ans: 135)
Pattern is:
– 35, – 28, – 21, – 14, ………
Double stage difference
3. 12, 20, 30, 43, 60, ? (Ans: 82)
Square Series
4. 121, 117, 108, 92, 67, ? (Ans:- 31)
Pattern is:
5. 8, 12, 28, 64, 128, ? (Ans:- 228)

Cubic Series
6. 107, 108, 100, 127, 63, ? (Ans:- 188)
Square/Cubic with Arithmetic
These types of series can also be solved by two/three stage difference
7. 15, 15, 17, 23, 35, ? (Ans:- 55)
8. 26, 63, 124, 215, ?, 511 (Ans:- 342)
9. 3, 5, 15, 45, 113, ? (Ans:- 243)
Multiplication/Division series
10. 32, 8, 4, 4, 8, ? (Ans:- 32)
11. 108, 72, 36, 24, 12, ? (Ans:- 8)
Pattern is:
÷1.5,÷2,÷1.5,÷2…………
Mix type series
12. 12, 26, 54, ?, 222, 446 (Ans:- 110)
Pattern is: ×2+2,×2+2,×2+2, ……..
13. ?, 8, 29, 152, 1073, 9668 (Ans:- 5)
Pattern is:
×1+3,×3+5,×5+7,×7+9,……..
PRACTICE MCQ-

1) 2, 12, 36, 80, 150, ?
A. 250
B. 252
C. 200
D. 270
ans. B
Explanation:
A unique pattern has been made into use in this series.
All numbers are (n^3 + n^2) where n is 1, 2, 3 and so on.
2) 6, 14, 36, 98, ?
A. 276
B. 275
C. 220
D. 274
ans. A
Explanation:
6 = 1^1 + 2^1 + 3^1
14 = 1^2 + 2^2 + 3^2
36 = 1^3 + 2^3 + 3^3
98 = 1^4 + 2^4 + 3^4
Thus the next number will be
1^5 + 2^5 + 3^5 = 276
3) 5, 16, 49, 104, ?
A. 171
B. 191
C. 181
D. 161
Explanation:
+11 =16

+33 =49
+55 =104
+77 =181
4) 8, 7, 11, 12, 14, 17, 17, 22, ?
A. 27
B. 20
C. 24
D. 22
ans. B
Explanation:
There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.
5) 2, 6, 12, 20, 30, 42, 56, ?
A. 61
B. 64
C. 70
D. 72
ans. D
Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.
So, the next number is 8 x 9 = 72.
6) 4, -8, 16, -32, 64, ?
A. 128
B. -128
C. 192
D. -192
ans. B

Explanation:
Each number is the proceeding number multiplied by -2.
So, the required number is -128.
7) 7, 26, 63, 124, 215, 342, ?
A. 481
B. 511
C. 391
B. 421
ans. B
Explanation:
Numbers are (23 – 1), (33 – 1), (43 – 1), (53 – 1), (63 – 1), (73 – 1) etc.
So, the next number is (83 – 1) = (512 – 1) = 511.
8) 3, 12, 27, 48, 75, 108, ?
A. 147
B. 183
C. 162
D. 192
ans. A
Explanation:
The numbers are 3 x 12, 3 X 22, 3 X 32, 3 X 42, 3 X 52, 3 X 62, Missing number= 3 X 72 = 147
9) 20, 19, 17, ?, 10, 5
A. 14
B. 15
C. 13
D. 11
ans. A

Explanation:
The Pattern is – 1, – 2,…
Missing number = 17 – 3 = 14.
10) 1, 6, 13, 22, 33, ?
A. 44
B. 45
C. 46
D. 47
Ans . C
The pattern is + 5, + 7, + 9, + 11,...
.'. Missing number = 33 + 13 = 46.
11) 24, 60, 120, 210, ?
A. 300
B. 420
C. 336
D. 400
ans. C
Explanation:
The pattern is 36, 60, + 90, … i.e. + 16 x (6 + 0), + 16 x (6 + 4), + [6 * (6 + 9)], Missing number 210 + 16 x (6 +
15) = 210 + 126 = 336.
12) 3, 6, 18, 72, ?
A. 144
B. 360
C. 288
D. 216
ans. B

Explanation:
pattern is * 2, * 3,*4, number is = 72 x 5 = 360.
13) 3, 7, 6, 5, 9, 3, 12, 1, 15, ?
A. 18
B. 13
C. -1
D. 3
ans. C
Explanation:
There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted.
The next number is 1 – 2 = -1.
14) 192, 021, 222, 324, 252, 627, 2_, 9_?
A. 280, 930
B. 282, 930
C. 248, 920
D. 250, 940
ans. B
Explanation:
If you look closely, you will find a sequence in every alternating number.
192, 222 and 252 form one series where 30 is added each time.
021, 324 and 627 form one series where 303 is added each time.
Thus the next two numbers will be 282 and 930.
15) 2, 4, 12, 48, 240,?
A. 960
B. 1440
C. 1080
D. 1920

ans. B
Explanation:
Go on multiplying the given numbers by 2, 3, 4, 5, 6.
So, the correct next number is 1440.
16. 1, 4, 9, 16, 25?
(A) 35
(B) 36
(C) 48
(D) 49
Ans . B
17. 2, 3, 5, 6 ,? , 9, ?, 12
(A) 9, 11
(B) 11, 8
(C) 8, 11
(D) 8, 10
Ans . C
18. 563, 647, 479, 815, (…)
(A) 672
(B) 386
(C) 279

(D) 143
Ans . D
19. 4, 10 (..), 82, 244,730
(A) 24
(B) 28
(C) 77
(D) 218
Ans . B
20. 3, 4, 7, 7, 13, 13, 21, 22, 31, 34, (..)
(A) 42
(B) 43
(C) 51
(D) 52
Ans . B
Part -2 Number Series
Directions (1-50): What will come in place of (?) in
following series
following a certain pattern?

Question 1: 375, 75, 30, 18, ?, 14.4
A) 15
B) 15.2
C) 16
D) 14.4
E) 16.5
Question 2: 25, 89, 332, 588, 713, ?
A) 855
B) 856
C) 749
D) 860
E) 785
Question 3: 18, 36, 62, 96, 138, ?

A) 172
B) 206
C) 244
D) 220
E) 188
Question 4: 16, 24, 60, 210, 945, ?
A) 5197.5
B) 4234.5
C) 5848.5
D) 4113.5
E) 5434.5
Question 5: 8, 18, 86, 308, 828, ?
A) 1955

B) 1902
C) 1406
D) 1838
E) 1629
Question 6: 16, 20, 28, 27, 42, ?
A) 26
B) 45
C) 67
D) 42
E) 32
Question 7: 5, 7, 11, 37, ?, 721
A) 143
B) 294

C) 138
D) 147
E) 256
Question 8: 21, 33, 85, 301, 1359, ?
A) 6066
B) 7359
C) 7480
D) 6242
E) 5155
Question 9: 6, 9, 24, 90, 432, ?
A) 2380
B) 1340
C) 2460

D) 2520
E) 1420
Question 10: 4, 13, 41, 126, ?, 1151
A) 382
B) 688
C) 453
D) 562
E) 436
Question 11: 210 209 213 186 202 (?)
A) 138
B) 77
C) 177
D) 327

E) None of these
Question 12: 27 38 71 126 203 (?)
A) 212
B) 202
C) 301
D) 312
E) None of these
Question 13: 435 354 282 219 165 (?)
A) 103
B) 112
C) 120
D) 130
E) None of these

Question 14: 4 200 369 513 634 (?)
A) 788
B) 715
C) 734
D) 755
E) None of these
Question 15: 95 485 465 425 345 ?
A) 195
B) 165
C) 185
D) 175
E) None of these
Question 16: 16 22 33 49 70 ?

A) 95
B) 96
C) 85
D) 91
E) None of these
Question 17: 32 36 52 88 152 ?
A) 266
B) 232
C) 242
D) 256
E) None of theses
Question 18: 17 289 425 493 527 ?
A) 534

B) 542
C) 544
D) 594
E) None of these
Question 19: 13 27 55 97 153 ?
A) 243
B) 265
C) 215
D) 223
E) None of these
Question 20: 50 60 75 97.5 ? 184.275 267.19875
A) 120.50
B) 130.50

C) 131.625
D) 124.25
E) None of these
Question 21: 509, 68, 429, 140, 365, ?
A)194
B) 192
C)196
D) 195
E) 197
Question 22: 1, 12, 14, ?, 66, 142
A) 40
B) 50
C) 56

D) 42
E) 38
Question 23: 2√3, 2√5, √30, √42, 2√14, ?
A) 6√2
B) √60
C) 5√3
D) 3√5
E) √50
Question 24: 1, 2, 6, 3, 289, ?
A) 3172
B) 3414
C) 3192
D) 3429

E) 3439
Question 25: 8, 17, 34, 58, 88, ?
A) 130
B) 123
C) 102
D) 132
E) 120
Question 26: 2556, 636, 156, ?, 6
A) 36
B) 72
C) 100
D) 112
E) 20

Question 27: 21, 85, 253, 509, ?
A) 506
B) 505
C) 510
D) 521
E) 511
Question 28: 19, 33, 67, 97, 147, ?
A) 193
B) 200
C) 210
D) 205
E) 199
Question 29: 49, 60, 98, 102, 133, ?

A) 139
B) 145
C) 140
D) 130
E) 120
Question 30: 318, 206, 150, ?, 108, 101
A) 130
B) 115
C) 122
D) 120
E) 132
Question 31: 32, ?, 1024, 2048, 2048
A) 324

B) 256
C) 224
D) 326
E) 274
Question 32: 9, 5, 6, 10.5, 23 ?
A) 50
B) 65
C) 70
D) 55
E) 60
Question 33: 17, 98, 26, ?, 35, 80
A) 79
B) 69

C) 89
D) 59
E) 49
Question 34: 2, 17, 89, 359, 1079, ?
A) 2143
B) 2152
C) 2169
D) 2159
E) 214
Question 35: 7, 4.5 ,5.5, 12, 49,?
A)393
B)351
C)362

D)375
E)364
Question 36: 7, 7, 13, 37, 97, ?
A) 237
B) 247
C) 217
D) 227
E) 257
Question 37: 1, 20, 58, 134, 286, ?
A)600
B)590
C)580
D)570

E)560
Question 38: 3, 5, 15, 45, 113, ?
A)253
B)263
C)243
D)651
E)655
Question 39: 3.25, 6.5, 19.5, 78, 390, ?
A)2140
B)2350
C)2670
D)2340
E)2250

Question 40: 68, 117, 61, 124, 54, ?
A)141
B)121
C)151
D)131
E)111
Question 41: 17, 18, 26, 35, 99, ?
(a) 224
(b) 124
(c) 148
(d) 164
(e) 225
Question 42: 23, 40, 74, 142, 278, ?

(a) 392
(b) 478
(c) 544
(d) 496
(e) 550
Question 43: 69, 82, 71, 80, 73, ?
(a) 78
(b) 77
(c) 79
(d) 83
(e) 86
Question 44: 53, 58, 75, 112, 177, ?
(a) 261

(b) 275
(c) 278
(d) 285
(e) 317
Question 45: 23, 40, 64, 96, 137, ?
(a) 197
(b) 188
(c) 183
(d) 192
(e) 201
Question 46: 23 , 25, 79, 401, 2815, ?
(a) 25345
(b) 25340

(c) 25350
(d) 25445
(e) 25355
Question 47: 14/3, 8, 14, 24, 40, ?
(a) 45
(b) 85
(c) 70
(d) 65
(e) 60
Question 48: ?, 32, 51, 74, 103, 134
(a) 7
(b) 15
(c) 13

(d) 17
(e) 19
Question 49: ?, 164, 178, 157, 185, 150
(a) 158
(b) 169
(c) 171
(d) 173
(e) 167
Question 50: ?, 124, 215, 342, 511, 728
(a) 64
(b) 63
(c) 61
(d) 60

(e) 45
Question 51: 2, 3, 6, 15, 45, 156.5, 630
A) 3
B) 45
C) 15
D) 6
E) 156.5
Question 52: 36, 20, 12, 8, 6, 5.5, 4.5
A) 5.5
B) 6
C) 12
D) 20
E) 8

Question 53: 1, 3, 9, 31, 128, 651, 3913
A) 651
B) 128
C) 31
D) 9
E) 3
Question 54: 2, 3, 10, 40, 172, 885, 5346
A) 3
B) 855
C) 40
D) 172
E) 10
Question 55: 5, 8, 16, 26, 50, 98, 194

A) 8
B) 26
C) 50
D) 16
E) 98
Question 56: 8 59 358 1796 7186 21565
A) 59
B) 358
C) 1796
D) 7186
E) 21565
Question 57: 1250 1201 1166 1140 1124 1115 1111
A) 1111

B) 1201
C) 1140
D) 1166
E) 1124
Question 58: 12 7 8 13 27 69 206.5
A) 13
B) 69
C) 27
D) 8
E) 206.5
Question 59: 17 23 35 59 108 203 395
A) 395
B) 23

C) 108
D) 59
E) 35
Question 60: 221 230 256 320 445 661 1004
A) 320
B) 256
C) 445
D) 230
E) 661
Question 61: 461, 922, 5532, 66385, 1327680
(a) 922
(b) 66385
(c) 5532

(d) 1327680
(e) 461
Question 62: 592, 628, 854, 2078, 8007
(a) 592
(b) 628
(c) 854
(d) 2078
(e) 8007
Question 63: 324, 3276, 32984, 329924 , 3305169
(a) 32984
(b) 3276
(c) 324
(d) 329924

(e) 3305169
Question 64: 12, 10, 8, 6.94, 5.78
(a) 10
(b) 12
(c) 8
(d) 6.94
(e) 5.78
Question 65: 64, 96, 146, 216, 324
(a) 64
(b) 146
(c) 96
(d) 216
(e) 324

Question 66: 621, 417 , 281, 191, 129.88
(a) 417
(b) 621
(c) 281
(d) 129.88
(e) 191
Question 67: 100, 0 , 50, -37, 62.5
(a) -37
(b) 100
(c) 0
(d) 50
(e) 62.5
Question 68: 125, 50, 32, 30, 42, 92.4

(a) 125
(b) 50
(c) 24
(d) 32
(e) 28.8
Question 69: 5896, 5685, 4904, 2805, -1848
(a) 5896
(b) 2805
(c) 4904
(d) 1848
(e) 5685
Question 70: 0, 275, 1542, 5690, 16592
(a) 242

(b) 275
(c) 1542
(d) 5690
(e) 16592
Question 71: 2, 8, 12, 27, 58, 121
A) 8
B) 12
C) 27
D) 58
E) 121
Question 72: 895, 870, 821, 740, 619, 445
A) 895
B) 870

C) 821
D) 619
E) 445
Question 73: 664, 320, 150, 67, 28, 9.75
A) 664
B) 150
C) 67
D) 28
E) 150
Question 74: 8, 13, 9, 11, 10, 15
A) 8
B) 13
C) 11

D) 10
E) 15
Question 75: 16, 9, 8, 13, 25, 64
A) 64
B) 9
C) 13
D) 8
E) 16
Question 76: 12, 13, 24, 75, 296, 1480
A) 13
B) 296
C) 24
D) 1485

E) 12
Question 77: 11, 13, 16, 33, 100, 353
A) 13
B) 33
C) 16
D) 353
E) 100
Question 78: 4, 20, 120, 595, 2376
, 7125
A) 7125
B) 120
C) 20
D). 595

E) 2376
Question 79: 64, 60, 75, 103, 168, 294
A) 64
B) 60
C) 75
D) 294
E) 103
Question 80: 13, 25, 39, 50, 83, 125
A) 39
B) 25
C) 125
D) 13
E) 50

Question 81: 5 7 16 57 244 1245 7506
A) 5
B) 16
C) 7506
D) 7
E) None of these
Question 82: 5 3 4 7.5 17 47 138
A) 5
B) 4
C) 47
D) 17
E) None of these
Question 83: 3 5 13 43 178 891 5353

A. 43
B. 178
C. 891
D. 5353
E. None of these
Question 84: 972 484 240 118 56 26.5 11.25
A. 240
B. 11.25
C. 118
D. 56
E. None of these
Question 85: 25 313 457 529 565 585 592
A. 457

B. 592
C. 313
D. 529
E. None of these
Question 86: 25 35 50 75 110 155 210
A. 50
B. 210
C. 25
D. 110
E. None of these
Question 87: 900 890 879 858 830 795 753
A. 753
B. 795

C. 890
D. 858
E. None of these
Question 88: 16800, 7770, 1290, 3120, 1000, 240, 30
A. 1000
B. 7770
C. 3120
D. 78
E. None of these
Question 89: 15 22 32 111 428 1538 12900
A. 22
B. 428
C. 1538

D. 12900
E. None of these
Question 90: 2580 645 322.5 80.62 45 10.07 5
A. 322.5
B. 645
C. 45
D. 10.07
E. None of these
Question 91: 14 21 35 57 88 ?
A. 182
B. 129
C. 166
D. 127

E. 180
Question 92: 13, 21, 37, 61, ?, 133
A. 96
B. 93
C. 92
D. 97
E. None of these
Question 93: 9, 10, 18, 57, ?, 1125
A. 164
B. 230
C. 210
D. 224
E. 115

Question 94: 14, 8, 7, 11.5, 22, ?
A. 56
B. 59
C. 53
D. 58
E. 52
Question 95: 13, 14, 26, 108, ? , 13712
A. 836
B. 896
C. 842
D. 856
E. 824
Question 96: 12, 14, 19, 36, ?, 358

A. 105
B. 104
C. 106
D. 102
E. 101
Question 97: 4, ?, 4, 9, 32 155
A. 7
B. 2
C. 3
D. 5
E. 6
Question 98: 34, 34, 43, 69, 134, ?
A. 164

B. 160
C. 175
D. 258
E. 103
Question 99: 12, 23, 35, 49, ?, 93
A. 67
B. 75
C. 65
D. 23
E. 50
Question 100: 25, 13, 14, ?, 47, 120
A. 19.5
B. 17.5

C. 22.5
D. 23.5
E. 15.5
SOLUTION
(1-50):
1. Option D
Pattern:
Here last value is in decimals
So there is a possibility that the numbers are multiplied or divided
by some decimal quantity
× 0.2, × 0.4, × 0.6, × 0.8, × 1.0
2. Option C
Pattern:
When the number increase suddenly, we use multiplication to find
pattern. But here they are not increasing suddenly, so try
addition/subtraction
25 + 26, 89 + 35, 332 + 44, 588 + 53, 713 + 62
3. Option E
Pattern:
18 + 18 = 36
36 + (18+8) = 36 + 26 = 62
62 + (26+8) = 62 + 34 = 96
96 + (34+8) = 96 + 42 = 138
138 + (42+8) = 188
4. Option A
Pattern:
16×1.5, 24×2.5, 60×3.5, 210×4.5, 945×5.5
5. Option D

Pattern:
8 + (2^3 + 2) = 18,
18 + (4^3 + 4) = 86,
86 + (6^3 + 6) = 308,
308 + (8^3 + 8) = 828,
828 + (10^3 + 10) = 1838

6. Option E
Pattern:
16………. 20……….. 28…………. 27………. 42……….. 32
. +4 +8 -1 +15 -10
. +22 -32 +42 -52
7. Option A
Pattern:
5*1 + 2, 7*2 – 3, 11*3 + 4, 37*4 – 5, 143*5 + 6
8. Option C
Pattern:
×1.5 + 1.5, ×2.5 + 2.5, ×3.5 + 3.5, ×4.5 + 4.5, ×5.5 + 5.5,
9. Option D
Pattern:
6×2 – 6/2 = 9,
9×3 – 9/3 = 24,
24×4 – 24/4 = 90,
90×5 – 90/5 = 432,
432×6 – 432/6 = 2520
10. Option A
Pattern:
4×3 + 1 = 13,
13×3 + 2 = 41,
41×3 + 3 = 126,
126×3 + 4 = 382,
382×3 + 5 = 1151
11. B
The pattern of the number series is :
 210 - 1³= 209
 209 + 2² = 213
 213 - 3³ = 186
 186 + 4² = 202
 202 - 5³ = 202 - 125 = 77

12. E
 27 + 11 = 38
 38 + 33 = 71
 71 + 55 = 126
 126 + 77 = 203
 203 + 99 = 302
13. C
14. C
15. C
 495 - 1 × 10 = 485
 485 - 2 × 10 = 465
 465 - 4 × 10 = 425
 425 - 8 × 10 = 345
 345 - 16 × 10 = 185
 4 + 14² = 4 + 196 = 200
 200 + 13² = 200 + 169 = 369
 369 + 12² = 369 + 144 = 513
 513 + 11² = 513 + 121 = 634
 634 + 10² = 634 + 100 = 734
 435 - 9 × 9 = 354
 354 - 9 × 8 = 282
 282 - 9 × 7 = 219
 219 - 9 × 6 = 165
 165 - 9 × 5 = 120

16. B
 16 + 6 = 22
 22 + 11 = 33
 33 + 16 = 49
 49 + 21 = 70
 70 + 26 = 96
17. E
19. D
 13 + 1 × 14 = 27
 27 + 2 × 14 = 55
 55 + 3 × 14 = 97
 97 + 4 × 14 = 153
 153 + 5 × 14 = 223
 32 + 2² = 36
 36 + 4² = 52
 52 + 6² = 88
 88 + 8² = 152
 152 + 10² = 252
18. C
 17 + 272 = 289
 289 + 136 = 425
 425 + 68 = 493
 493 + 34 = 527
 527 + 17 = 544

20. C
 50 × 1.2 = 60
 60 × 1.25 = 75
 75 × 1.3 = 97.5
 97.5 × 1.35 = 131.625
 131.625 × 1.4 = 184.275
21. C
Solution:
22. E
Solution:
23. A
Solution:
24. B

Solution:
Solution:
25. B
Solution:
26. A
Solution:
27. B
Solution:

28. A
Solution:
29.
29.D
Solution:
30.C
Solution:

31.B
Explanation :
32 * 8 = 256
256 * 4 = 1024
1024 * 2 = 2048
32. E
Ex
pl
an
ati
on
:
9 * 0.5 + 0.5 = 5
5 * 1 + 1 = 6
6 * 1.5 + 1.5 = 10.5
10.5 * 2 + 2 = 23
23 * 2.5 + 2.5 = 60
33. C
Explanation :
26 -17 = 9; 35 – 26 = 9
98 – 9 = 89
34. D

7 × 0.5 + 1 = 4.5.
4.5 × 1 + 1 = 5.5.
5.5 × 2 + 1 = 12.
12 × 4 + 1 = 49.
49 × 8 + 1 = 393.
35. C
Explanation :
7 + 1³ – 1 = 7
7 + 2³ – 2 = 13
13 + 3³ – 3 = 37
36. B
Explanation :
1 * 2 + 18 = 20
20 * 2 + 18 = 58
58 * 2 + 18 = 134
134 * 2 + 18 = 286
37. C
Explanation :
3 * 1³ + 1 = 5
5 * 2³ + 2 = 15
15 * 3³ + 3 = 45
45 * 4³ + 4 = 113
38. D
Ex
pl
an
at
io
n :
3.
25

*
2
=
6.
5
6.
5
*
3
=
19
.5
19
.5
*
4
=
78
39. D
Explanation :
68 – 7 = 61; 61 – 7 = 54
124 + 7 = 131

40. B
1^2+ 2^3+ 3^2+ 4^3+ 5^2=124
44. C
45. B
46. A
47. D
48. B
49. C
50. B
(51-100):
Series Pattern Given Series
2 2 ✓
2 × 1.5 = 3 3 ✓
3 × 2 = 6 6 ✓
6 × 2.5 = 15 15 ✓
15 × 3 = 45 45 ✓
45 × 3.5 = 157.5 156.5 ✕
157.5 × 4 = 630 630 ✓
Hence, there should be 157.5 in place of 156.5.
Hence, option E is correct.
51. Correct Option: E
The series pattern is ×1.5, ×2, ×2.5, ×3, × 3.5, ×4.
42. E
17+34+68+ 136+ 272=550
43. A
+13, -11 , +9, -7, +5

Hence, there should be 5 in place of 5.5.
52. Correct Option: A
The series is –16, –8, –4, –2, –1, –0.5, and so on.
Hence, option A is correct.
1 1 ✓
1 × 1 + 2 = 3 3 ✓
3 × 2 + 3 = 9 9 ✓
9 × 3 + 4 = 31 31 ✓
31 × 4 + 5 = 129 128 ✕
129 × 5 + 6 = 651 651 ✓
651 × 6 + 7 = 3913 3913 ✓
Hence, there should be 129 in place of 128.
36 36 ✓
36 – 16 = 20 20 ✓
20 – 8 = 12 12 ✓
12 – 4 = 8 8 ✓
8 – 2 = 6 6 ✓
6 – 1 = 5 5.5 ✕
5 – 0.5 = 4.5 4.5 ✓
53. Correct Option: B
The series is ×1+2, ×2+3, ×3+4, and so on.

Hence, option B is correct.
54: Correct Option: C
The series is ×1+12, ×2+22, ×3+32, and so on.
Hence, option C is correct.
55. Correct Option: D
The series is ×2–2.
5 5 ✓
5 ×2–2 = 8 8 ✓
8 ×2–2= 14 16 ✕
14 ×2–2= 26 26 ✓
26 ×2–2= 50 50 ✓
50 ×2–2= 98 98 ✓
98 ×2–2= 194 194 ✓
2 2 ✓
2 ×1+12 = 3 3 ✓
3 ×2+22 = 10 10 ✓
10 ×3+32 = 39 40 ✕
39 ×4+42 = 172 172 ✓
172 ×5+52 = 885 885 ✓
885 ×6+62 = 5346 5346 ✓

Therefore, there must be 1165 in place of 1166.
Hence, option D is correct.
56. Correct Option: C
The series pattern is (×7+3), (×6+4), (×5+5).....so on.
57: Correct Option: D
The series is – 72, –62, –52 ........so on.
Series pattern Series
1250 1250✓
1250 – 72 = 1201 1201✓
1201 – 62 = 1165 1166 ×
1165 – 52 = 1140 1140✓
1140 – 42 = 1124 1124✓
1124 – 32 = 1115 1115✓
1115 – 22 = 1111 1111✓
Hence, option D is correct.
58. Correct Option: B
8 8 ✓
8 × 7 + 3 = 59 59 ✓
59 × 6 + 4 = 358 358 ✓
358 × 5 + 5 = 1795 1796 ×
1795 × 4 + 6 = 7186 7186 ✓
7186 × 3 + 7 = 21565 21565 ✓

The pattern of the series is (×0.5+1), (×1+1), (×1.5+5).....so on.
Hence, option B is correct.
59. Correct Option: C
The pattern of the series is +6, +12, +24, +48....so on.
17 17 ✓
17 + 6 = 23 23 ✓
23 + 12 = 35 35 ✓
35 + 24 = 59 59 ✓
59 + 48 = 107 108 ×
107 + 96 = 203 203 ✓
203 + 192 = 395 395 ✓
221 221 ✓
221 + (2)3= 229 230 ×
12 12 ✓
12 × 0.5 + 1 = 7 7 ✓
7 × 1 + 1 = 8 8 ✓
8 × 1.5 + 1 = 13 13 ✓
13 × 2 + 1 = 27 27 ✓
27 × 2.5 + 1 = 68.5 69 ×
68.5 × 3 + 1 = 206.5 206.5 ✓
60. Correct Option: D
The pattern of the series is +23, +33, +43, +53...........so on.

229 + (3)3 = 256 256 ✓
256 + (4)3 = 320 320 ✓
320 + (5)3 = 445 445 ✓
445 + (6)3 = 661 661 ✓
661 + (7)3 = 1004 1004 ✓
61. B
62. C
64. C
64× 3/2=96
96× 3/2=144≠146
144× 3/2=216
12× 5/6=10
10× 5/6=8.33≠8
8.33× 5/6=6.94
6.94× 5/6=5.78
65. B
592+(2^2×3^2 )=628
628+(3^2×5^2 )=853≠854
853+(5^2×7^2 )=2078
2078+(7^2×〖11〗^2 )=8007
63. C
324×10+(2^2×3^2 )=3276
3276×10+(3^2×5^2 )=32985≠32984
329854×10+(5^2×7^2 )=329924
329924×10+(7^2×〖11〗^2 )=3305169
461×(1×2)=922
922×(2×3)=5532
5532×(3×4)=66384≠66385
66384×(4×5)=1327680

216× 3/2=324
66. E
67. E
(100×1/4)-25=0
(0×1/2)+50=50
(50×3/4)-75= -37.5≠-37
(-37×4/4)+100=62.5
68. D
125× 2/5=50
50× 3/5=30≠32
30× 5/5=30
30× 7/5=42
42× 11/5=92.4
69. B
5896+(2^5-3^5 )=5896-211=5685
5685+(3^5-4^5 )=5865-781=4904
4904+(4^5-5^5 )=4904-2101=2803≠2805
2803+(5^5-6^5 )=2803-4651=-1848
70. D
0+(2^5+3^5 )=275
275+(3^5+4^5 )=1542
1542+(4^5+5^5 )=5691≠5690
5690+(5^5+6^5 )=16592
(621×2/3)+3=417
(417×2/3)+3=281
(281×2/3)+3=190.33≠191
(190.33×2/3)+3=129.88

71. C
Explanation :
5
72. E
Explanation :
Wrong Number: 445
Correct Number: 450
73. D
Explanation :
Wrong Number: 28
Correct Number: 27.50
74. C
Wrong Number: 8
Correct Number:

Correct Number: 1
Explanation :
Wrong Number: 11
4
75. A
Explanation :
Wrong Number: 64
16 * 0.5 + 1 = 9
9 * 1 – 1 = 8
8 * 1.5 + 1 = 13
76. D
Explanation :
Wrong Number: 470
Correct Number: 465
12 * 1 + 1 = 13
13 * 2 – 2 = 24
24 * 3 + 3 = 75
75 * 4 – 4 = 296
296 * 5 + 5 = 1485
77. E
Explanation :
Wrong Number: 100
Correct Number: 96
11 + 1² + 1= 13
13 + 2² – 1= 16
16 + 4² + 1= 33……..

78. C
Explanation :
(6 * 2) + 2² = 16….
Correct Number: 6
Wrong Number: 20
Correct Number: 21
4*7 -7 = 21
21*6 -6 = 120
120*5 -5 = 595.
79. B
Explanation :
Wrong Number: 60
Correct Number: 66
64 + (1³ + 1) = 66
66 + (2³ + 1) = 75
75 + (3³ + 1) = 103
Wrong Number: 50
Correct Number: 57
13*2 – 1 = 25
25*2 – 11 = 39
39*2 – 21 = 57
81. D
Explanation : (5
* 1) + 1² = 6
80. E
Explanation :

82. C
Explanation :
86. C
5 * 0.5 + 0.5 =
3 * 1 + 1 = 4
4 * 1.5 + 1.5 = 7.5…..
Correct Number: 45
83. C
Explanation :
3 * 1 + 2 = 5
5 * 2 + 3 = 13
13 * 3 + 4 = 43…..
Correct Number: 177
84. D
Explanation : 972
/ 2 – 2 = 484 484
/ 2 – 2 = 240
240 / 2 – 2 = 118…..
Correct Number: 57
85. E
Explanation :
25 + 9 * 32 = 313
313 + 9 * 16 = 457
3

Explanation :
88. A
Explanation
30 + 5 * 1 = 35
35 + 5 * 3 = 50
50 + 5 * 5 = 75…..
Wrong Number: 25
Correct Number: 30
87. C
Explanation :
900 – 7 = 893
893 – 14 = 879
879 – 21 = 858……
Wrong Number: 890
Correct Number: 893
:
7^5 – 7, 6^5 – 6, 5^5 – 5, 4^5 – 4…
Wrong Number: 1000
Correct Number: 1020
89. C
Explanation :
15 * 1 + (1 * 7) = 22
22 * 2 – (2 * 6) = 32
32 * 3 + (3 * 5) = 111
111 * 4 – (4 * 4) = 428
428 * 5 + (5 * 3) = 2155
2155 * 6 – (6 * 2) = 12918
Correct Number: 12918
90. C

Explanation :
2580 * 0.25 = 645
645 * 0.5 = 322.5
322.5 * 0.25 = 80.62
80.62 * 0.5 = 40.31 …..
91. B
Explanation :
21 – 14 = 7
35 – 21 = 14
57 – 35 = 22 14 – 7 = 7; 22 – 14 = 8…..
92. B
Explanation :
21 – 13 = 8
37 – 21 = 16
61 – 37 = 24….
93. D
Explanation :
9 * 1 + 1 = 10
10 * 2 – 2 = 18
18 * 3 + 3 = 57
94. A
Explanation :
14 * 0.5 + 1 = 8
8 * 1 – 1 = 7
7 * 1.5 + 1 = 11.5
95. D

Explanation :
13 * 1 + 1 = 14
14 * 2 – 2 = 26
26 * 4 + 4 = 108
108 * 8 – 8 = 856
856 * 16 + 16= 13712
96. E
Explanation :
12 + 1² + 1= 14
14 + 2² + 1= 19
19 + 4² + 1= 36……..
97. C
Explanation :
4*1 – 1 = 3
3*2 – 2 = 4
4*3 – 3 = 9.
98. D
Explanation :
34 + 1³ – 1 = 34
34 + 2³ + 1 = 43
43 + 3³ – 1 = 69
99. A
Explanation :
12*2 – 1 = 23
23*2 – 11 = 35
35*2 – 21 = 49
100. C

25*0.5 + 0.5 = 13
13*1 + 1 = 14
14*1.5 + 1.5 = 22.5
Letter Series Tricks with Questions
To understand the trick of letter series, first of all we must have the knowledge of
alphabetical order, its numerical position and its opposite letters' positions. Lets know more
about this trick.
o From the above diagram you can easily see the position and opposite word of each
alphabet.
o For Example - Position of D is 4 and opposite letter to D is W and position of W is 23.
o Position of J is 10 and opposite letter of J is Q and position of Q is 17 and so on.
==>> Must read Alphabet Series Shortcut Techniques
here

Mathematical Reasoning and Aptitude
DIWAKAR EDUCATION HUB Page 25
Find the letter in place of question mark (?) In the series given below:
Q1. B, F, .........., N, R
a) G
b) K
c) J
d) L
e) None of The Above
Solution :-
Option C

Q2. P, .........., J, G, D, A
a) Q
b) N
c) K
d) M
Solution :-
Option D

Q3. .........., E, G, J, N
a) A
b) B
c) D
d) Z
Solution :-
Option C
Q4. X, F, Y, G, .............., H
a) Z
b) A
c) B

d) Y
Solution :-
Option A
Q5. B, B, A, D, ............, F
a) B
b) A
c) Z
d) C
Solution :-
Option C

Q6. LMD, MKG, NIJ, ............
a) PKM
b) MGO
c) LGM
d) OGM
Solution :-
Option D

Q7. D, DD, DDDD, DDDDDDD, ......................
a) DDDDDDDDD
b)DDDDDDDDDD
c) DDDDDD
d) DDDDDDDDDDD
Solution :-
Option D
Q8. 2B, ..........., 8E, 14H, 22L
a) 4C
b) 4D
c) 6E
d) 9F
Solution :-
Option A

Q9. 1 C V, 5 F U, 9 I T, .............., 17 O R
a) 11LS
b) 14JS
c) 15JS
d) 13LS
Solution :-
Option D
Q10. K M 5, 1 P 8, G S 11, E V 14 , ..............
a) C Y 17
b) B Y 17
c) B X 17

d) C Z 17
Solution :-
Option A
MCQ Of Letter Series -

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