The document provides information on preparing for competitive exams by focusing on developing strong fundamentals in various math topics like percentages, averages, time and work problems. It lists common math-based question types seen in exams and provides examples of questions and step-by-step solutions for practice. Key advice includes practicing frequently, understanding questions thoroughly, and mastering techniques for simplification and conversions.

2. 1.Competitive Exams-MPSC/UPSC
2.Railway/Post Office
3.Banking Exams-100 Marks
4.MBA/MCA Entrance-200 Marks

3.  Build your basics strong....
 Know your strengths. ...
 Work on shortcut techniques. ...
 Get the formulas right. ...
 Work on conversions…….
 Practice and practice. ...
 Understand the Question

4.  Age
 Volume and Area
 Average
 Clock
 Time and Distance
 Partnerships
 Ratio and Proportion
 Time and Distance
 Time and Work
 Simplification
 Square Root and
Cube Root
 Probability
 Train

6.  Type I: Basic Math
 Type II: %/ of
 Type III: Square or Cube and Roots
 Type IV Mixed Fractions

7. Ten years ago, P was half of Q's age. If
the ratio of their present ages is 3:4,
what will be the total of their present
ages?
Let the present age of P and Q be 3x and 4x
respectively.
A. 45 B. 40
C. 35 D. 30
And : C. 35
 Ten years ago,(3x – 10) = (4x – 10)
 P was half of Q
 > (3x – 10) = 1/ 2(4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
lf of
 total of their present ages = 3x +
4x = 7x
 = 7 × 5 = 35 Q's age.
Age

8. The word 'JUDGE' has 5 letters. It has 2
vowels (UE) in it
2 vowels can be grouped and considered
as a single letter. That is, JDG(UE).
Number of ways to arrange these letters
= 4!= 4 x 3 x 2 x 1 = 24
To arrange these vowels among
themselves = 2! = 2
Total number of ways = 24 x 2 =48
Permutations : Arrangement of Objects
Combinations : Selection of Objects
In how many different ways can the
letters of the word 'JUDGE' be
arranged such that the vowels always
come together?
A. None of these B. 48
C. 32
Option B. 48
D. 64
Permutations & Combinations

9. Total number of outcomes possible when a
die is rolled = 6
 Hence, total number of outcomes
possible when a die is rolled twice,
n(S) T= 6 × 6 = 36
E =Getting a sum of 9 when the two
dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
 E= 4
 P(E) = (E)/ (T)=4/36=1/9
 P(E) =1/9
Probability = Favorable No. of
Outcomes
Total Outcomes
A die is rolled twice. What is the
probability of getting a sum equal to 9?
A. 2/3 B. 2/9
C. 1/3
Ans: Option D
D. 1/9
Probability

10.  Amount of work P can do in 1
day = 1/15
Amount of work Q can do in 1
day = 1/20
Amount of work P and Q can do
in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can
together do in 4 days = 4 × (7/60)
= 7/15
Fraction of work left = 1 – 7/15=
8/15
P is able to do a piece of work in 15 days and
Q can do the same work in 20 days. If they
can work together for 4 days, what is the
fraction of work left?
A. 8/15 B. 7/15
C. 11/15
Option A: 8/15
D. 2/11
Work

11.  v = 240/24 (where v is the speed of
the train)
= 10 m/s (length/time)
t = (240+650)/10 = 89 seconds
A train having a length of 240 m passes
a post in 24 seconds. How long will it
take to pass a platform having a length
of 650 m?
A. 120 sec B. 99 sec
C. 89 sec
Option : C. 89 sec
D. 80 sec
Train

12. 1. Family Relationship
2. Series Completion
3. Coding-Decoding
4. Direction Sense
5. Seating Arrangement
6. Syllogism
7. Ranking
8. Calendar
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13.  ALPHABET SERIES
1. Regular order
2. Increasing Order
3. Decreasing Order
4. Combination Series
 NUMBER SERIES
1 . Consecutive odd-even Numbers
2. Consecutive Prime Numbers
3. Square or Cube of some number with or without
addition/subtraction
4. Sum/Product/ difference of preceding numbers
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Series Completion Test

14. Example 1. which of the alternative figures would correctly fill in the
blank space in the following series of numbers?
6,13,27,55,111, ___ 2, 12, 72, 432, ?
(A) 225 (B) 224
(C) 223 (D)231
(E) 230
Answer with Explanation :- 13 is greater than the double of 6 by 1.
similarly 27 is greater than the double of 13 by 1. 55 is greater than
the double of 27 by 1. 111 is greater than the double of 55 by 1. thus,
in blank space there would be 2*111+1= 223
Hence the correct answer is (C).
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15.  The pattern is 13, 23, 33, 43, 53, 63,
73.
196 is not a perfect cube
Find the odd man out.
1, 8, 27, 64, 125, 196, 216, 343
A. 64 B. 196
C. 216 D. 1
Option B: 196

16.  We have two series here
34, 37, 40, 43, ... (Increase by 3)
7, 14, 28, ... (Multiply by 2)
 Hence, next term is 28 × 2 = 56
Insert the missing number.
34, 7, 37, 14, 40, 28, 43, (...)
A. 312 B. 42
C. 46 D. 56
Ans: Option D

17.  Example 2. which one of the letter groups given below would replace the
question mark (?) in the letter series?
 YCL, MQZ, AEN, ?
(A) OSB (B) PUE
(C) MPX (D) OTC
(E) PVF
 Answer with explanation :- Last letter of the firs group is L and the first letter of second
group is M. Here, M is the next letter of L in alphabet. Similarly the last letter of the
second group is Z and the first letter of the third group is A. here A is the next letter of Z
in alphabet. Therefore, the first letter of blank space should be the next letter of N, which
is O. Besides, there is a gap of three letters between the first and second letters of each
group. therefore, second letter of blank space should be fourth letter after O. i.e it should
be S. in given alternatives only (A) is such alternative that has first letter as O and
second as S. Hence (A) is the correct answer.

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18. 18

19. Example 1 : A man Started to walk in West. After moving a distance he turned to
his right. After moving a distance he turned To his right. After moving a little he
turned in the end to his left. Now in which direction was he going?
(A) North
(B) South
(C) East
(D) West
Answer With Explanation : (A) The man started to walk from A towards West and
reached to B after moving a little distance. Then From B he turned to his right
(C) From (C) he turned to his right and reached at (D). at D he turned to his
left. So, he Was going in the north direction. See Below Image for better idea.
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20.  If DELHI is coded as FGNJK how MADRAS is coded?
 If BHOPAL is coded as EERMDI how POWDER is coded
20

21.  Find and draw a line of direction. (North, South, East,
West)
 note down right side and left side in the top of the line
which you drawn
 Arrange the seat
21

22.  A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting next
to D, D is not sitting with E who is on the left end of the bench. C is on the
second position from the right. A is to the right of B and E. A and C are sitting
together. In which position A is sitting ?
 draw a line and find out who is on the last, in this question “E” is the left end
of the bench. another placement would of “A” which is right of “B” and “E”.
 Ans. EBACD
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23. Statement : All plants are trees.
No trees are green.
Conclusions : I. Some plants are green.
II. No plants are green.
 1) Only I follows
 2) Only II follows
 3) Both I and II follow
 4) Either I or II follows
 5) Neither I nor II follows
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24. 24
Pointing to a photograph, Vipul said, "She is the daughter of my
grandfather's only son." How is Vipul related to the girl in the photograph ?
Option :
A. Father
B. Brother
C. Cousin
D. Uncle
E. Grandson