Tag: CSAT Numerical Ability

APSC Prelim 2018 GS Paper – Analysis of General Mental Ability & Aptitude Section Questions

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APSC Prelim 2018 GS Paper – General Mental Ability & Aptitude Section Questions Analysis

General Mental Ability & Aptitude is an important section in erstwhile General Studies paper in APSC GS Paper. In the revised exam pattern of APSC CC (Prelim) Exam, Questions of Aptitude and Mental Ability (along with Comprehension) has a whole paper in the form of GS-2 (CSAT) Paper.

Analyzing the previous year’s Qs from this section can be very helpful to understand Focus Areas to study more extensively for the GS-2 (CSAT) Paper.

 

Q22. If LIGHT is called MORNING, MORNING is called DARK, DARK is called NIGHT, NIGHT is called SUNSHINE and SUNSHINE is called DUSK, when do we sleep?

  1. At night
  2. At sunshine
  3. In dusk
  4. At dark

Area: code – reasoning

 

Q23. If MINERAL is written as QRSTUVW and SOUND is written as ABCSD, then how will READER be written in the same code ?

  1. SBFEFS
  2. UTVDTU
  3. TUDVUT
  4. QDZCDQ

Area: code letter

 

Q24. Arun said, “This girl is the wife of the grandson of my mother.” Who is Arun to the girl?

  1. Father
  2. Grandfather
  3. Husband
  4. Father-in-law

Area: Relationship

APSC Prelims 2020 Test Series

 

Q25. If P is taller than Q and R is taller than S but shorter than Q, then who among them is the tallest?

  1. P
  2. Q
  3. S
  4. T

Solution

P is taller than Q.
R is taller than S but shorter than Q, which means Q is taller than R and therefore S is shortest.
Decreasing order P>Q>R>S

Area: Puzzle – comparative taller

 

Q26. In the numbers from 100 to 1000 how many times digit 1 comes at the 10’s place?

  1. 9
  2. 10
  3. 90
  4. 900

Solution

The digit 1 comes at the ten’s place in numbers from 110 to 119, 210 to 219, 310 to 319, 410 to 419, 510 to 519, 610 to 619, 710 to 719, 810 to 819, 910 to 919.

∴ Required number=10×9=90.

Area: Numbers

 

Q27. If second and fourth Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in the month?

  1. 20
  2. 21
  3. 22
  4. 23

Solution

The month of 30 days starts with a Saturday.

There will be 4 weeks and 2 days.

This means that there are 4 Sundays and 1 second and 1 fourth Saturdays.

In the two days left, one will be a Sunday and the other a Monday.

So total holiday will be 5 Sundays and 1 second and 1 fourth Saturdays=7 days

Working days =30−7=23 days.

Area: Calendar

 

Q28. Arrange the given words in a meaningful sequence and then choose the most appropriate sequence from among the alternatives:

1. Probation, 2. Interview, 3. Selection,

4. Appointment, 5. Advertisement, 6. Application

5, 6, 2, 3, 4, 1

Area: ordering of business processes

 

APSC Prelims 2020 Test Series

 

Q29. In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2:3 then what percent of the population is literate?

  1. 20%
  2. 25%
  3. 50%
  4. 75%

Solution

Let the Adults be 2x and Students be 3x.

Given that 40% of students are illiterate i.e 60% of the students are literate.

According to the given condition,

⇒ 60% of 2x + 85% of 3x

⇒ (60/100) * 2x + (85/100) * 3x

⇒ (120x/100) + (255x/100)

⇒ (6x/5) + (51x/20)

⇒ (24x + 51x)/20

⇒ (75x/20)

⇒ (15/4)x

∴ Required % = [ (15/4)x % (1/5x) ] x 100

= (3/4) * 100

= 75%.

Therefore, 75% of the population is literate.

Area: % and ratio



Q30. A hill always has

  1. Trees
  2. animals
  3. water
  4. height

Area: Item properties

 

Q31. The population of a town 2 years ago was 62,500. Due to migration to cities, it decreases at the rate of 4% per year. Therefore, the present population will be

  1. 56700
  2. 57600
  3. 58800
  4. 60000

Area: Compound Interest

Geometry and Mensuration Formulas & Properties – APSC PrelimCSAT Paper Notes, formulas

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Geometry and Mensuration Important Formulas

& Properties – 

Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams

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Circle
  • Area of a circle = R2, where R is the radius.
  • Circumference of a circle = 2πR.
  • Length of an arc =  2 π r ×  (θ/360°), where θ is the central angle.
  • Area of a sector = θ/2 × r2.
  • Perimeter of a semi-circle =πR + 2R.

 

Quadrilaterals

Parallelogram

  • Area of parallelogram = (Base x Height).
  • The diagonals of a parallelogram bisect each other.
  • Each diagonal of a parallelogram divides it into triangles of the same area.
  • A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
  • Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

Rectangle

  • Area of a rectangle = (Length x Breadth).
  • Perimeter of a rectangle = 2(Length + Breadth).
  • The diagonals of a rectangle are equal and bisect each other.

Square

 

  • Area of a square = (side)2 = (diagonal)2.
  • Area of 4 walls of a room = 2 (Length + Breadth) x Height.
  • The diagonals of a square are equal and bisect each other at right angles.

Rhombus

  • Area of a rhombus = x (Product of diagonals).
  • The diagonals of a rhombus are unequal and bisect each other at right angles.

Trapezium

  • Area of a trapezium =  (sum of parallel sides)/2 x distance between them.

 

Triangle

 

  • Sum of the angles of a triangle is 180°.
  • The sum of any two sides of a triangle is greater than the third side.
  • Area of a triangle = x Base x Height.
  • Area of a triangle = s(s-a)(s-b)(s-c), where a, b, c are the sides of the triangle and s = (a + b + c).
  • Area of an equilateral triangle = sqrt(3)/4 x (side)2.

Pythagoras Theorem

In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.

  • Median – The line joining the mid-point of a side of a triangle to the opposite vertex is called the median.
  • Centroid – The point where the three medians of a triangle meet. The centroid divided each of the medians in the ratio 2 : 1.
  • In an isosceles triangle, the altitude from the vertex bisects the base.
  • The median of a triangle divides it into two triangles of the same area.
  • The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.

Probability – Important Formulas – APSC Prelim CSAT Paper Notes

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Probability – Important Formulas & Notes

Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams

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Probability

A quantitative measure of the chance of occurrence of a particular event. The likelihood of the occurrence of a particular event. The probability of event A is often written as P(A).

The probability of an event can only be between 0 and 1 and can also be written as a percentage. 

Probability of Occurrence of an Event

Let S be the sample and let E be an event.

P(E) = n(E) /n(S)


Results on Probability

P(S) = 1

0 <= P (E) <= 1

P() = 0

For any events A and B, P(A B) = P(A) + P(B) – P(A  B)

 

Experiment – An operation which can produce some well-defined outcomes is called an experiment.

Random Experiment – An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment. Like drawing a card from a pack of well-shuffled cards.

Sample Space – When we perform an experiment, then the set S of all possible outcomes is called the sample space.

In tossing a coin, S = {H, T}

If two coins are tossed, S = {HH, HT, TH, TT}.

In rolling a dice, S = {1, 2, 3, 4, 5, 6}.

Event – Any subset of a sample space is called an event.

Equally Likely Events  – Events are said to be equally likely if there is no preference for a particular event over the other.

Mutually Exclusive Events  – Two or more than two events are mutually exclusive if the occurrence of one of the events excludes the occurrence of the other.

Independent Events – If the occurrence or non-occurrence of one event does not influence the occurrence or non-occurrence of the other.

Simple Events – Events where one experiment happens at a time and it has a single outcome.

Compound Event – An event in which there is more than one possible outcome.

Exhaustive Events – The mutually exclusive events that form the sample space collectively are called the exhaustive events. Example, when a coin is tossed, either Head or Tail appears and they collectively form the sample space.

 

 

L.C.M and H.C.F based Questions – Important Formulas for APSC Prelim CSAT Paper

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L.C.M  and H.C.F based Questions – Important Formulas

Numerical Aptitude Notes for APSC Prelim CSAT Paper, SSC and Competitive Exams

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Factors and Multiples:

If number a divided another number b exactly, we say that a is a factor of b.

b is also a multiple of a.

 

Highest Common Factor (H.C.F.) or Greatest Common Divisor (G.C.D.)

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

Two methods of finding the H.C.F. of a given set of numbers:

Factorization Method: Express the each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

Division Method: To find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the H.C.F.

 

Least Common Multiple (L.C.M.)

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

There are two methods of finding the L.C.M. of a given set of numbers:

Factorization Method Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.

Division Method: Arrange the given numbers in a rwo in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.

 

H.C.F. and L.C.M. of Fractions

H.C.F. = (H.C.F. of Numerators)/(L.C.M. of Denominators)

L.C.M. = (L.C.M. of Numerators)/(H.C.F. of Denominators)

 

Product of two numbers = Product of their H.C.F. and L.C.M.

Co-primes: Two numbers are said to be co-primes if their H.C.F. is 1.

 

 

Comparison of Fraction numbers

  1. Find the L.C.M. of the denominators of the given fractions.
  2. Convert each of the fractions into an equivalent fraction with L.C.M as the denominator, by multiplying both the numerator and denominator by the same number.
  3. The resultant fraction with the greatest numerator is the greatest.

 

Downstream/Upstream Boat Speed – Important Formulas – APSC PrelimCSAT Paper Notes

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Downstream/Upstream Boat Speed – Important Formulas

Numerical Aptitude Notes for APSC Prelim CSAT Paper, SSC and Competitive Exams

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Still Water: If the speed of the water is zero, i.e. water is stationary, then it is called still water.

Stream: The moving water in the river is known as a stream.

  • Upstream: If a boat or a swimmer moves in the opposite direction of the stream, then it is called upstream, i.e. direction against the stream.
  • Downstream: If a boar or a swimmer moves in the same direction of the stream, then it is called downstream, i.e. direction along the stream

 

If the speed of a boat in still water is u km/hr and Speed of the stream is v km/hr,

  • Speed downstream = (u + v) km/hr.
  • Speed upstream = (u – v) km/hr.


If the speed downstream is a km/hr and the speed upstream is b km/hr, then

  • Boat Speed in still water = ½ (Downstream Speed + Upstream Speed) = 1/2 x (a + b) km/hr.
  • Rate of stream = ½ (Downstream Speed – Upstream Speed) = 1/2 x (a – b) km/hr.
  • Average Speed of Boat = {(Upstream Speed × Downstream Speed) / Boat’s Speed in Still Water}

 

 

If it takes “T” hours for a boat to reach a point in still water and comes back to the same point then,
the distance between the two points = {(u2-v2) × T} / 2u,
where “u” is the speed of the boat in still water and “v” is the speed of the stream.


If it takes “T” hours more to go to a point in upstream than downstream for the same distance, then
the distance = {(u2-v2) × t} / 2v,
where “u” is the speed of the boat in still water and “v” is the speed of the stream.

If a boat travels a distance downstream in “t1” hours and returns the same distance upstream in “t2” hours, then,
the speed of the man in still water = [v × {(t2+t1) / (t2-t1)}] km/hr,
where “v” is the speed of the stream

Calendar, Odd days, Leap years – Important Formulas – APSC Prelim CSAT Paper Notes, Qs, Formulas

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Calendar, Odd days, Leap years – Important Formulas & Notes

Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams

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Odd Days

To find the day of the week on a given date, use the concept of ‘odd days’.

Number of days more than the complete weeks are called odd days in a given period.

 

Finding No. of odd Days

1 ordinary year = 365 days = (52 weeks + 1 day.) i.e. 1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days) i.e. 1 leap year has 2 odd days.

1 Century = 100 years = 76 ordinary years + 24 leap years = (76 x 1 + 24 x 2) odd days = 124 odd days. = (17 weeks + days) 5 odd days = 5 odd days in 100 years

Odd days in 200 years = (5 x 2) %7 =3 odd days.

Number of odd days in 300 years = (5 x 3) %7 = 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) %7 = 0 odd day.

Similarly, 800 years, 1200 years, 1600 years, 2000 years  has 0 odd days.

Last day of a century cannot be Tuesday or Thursday or Saturday as odd days of any century can be one 0, 1, 3 and 5 days. 

For the calendars of two different years to be the same, the conditions to be satisfied are

  • Both years must be of the same type. i.e., both years must be ordinary years or both years must be leap years.
  • 1st January of both the years must be the same day of the week.

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Profit and Loss – Important Formulas – APSC CSAT Paper Notes

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Profit and Loss – Important Formulas

Numerical Aptitude Notes for CSAT Paper, SSC and Competitive Exams

 

Go to Aptitude, Reasoning and Quants Formulas & Notes

 

Cost Price – The price, at which an article is purchased.

Selling Price – The price, at which an article is sold.

Profit – If S.P. is greater than C.P., the seller is said to have a profit.
Profit = S.P. – C.P.

Loss – If S.P. is less than C.P., the seller is said to have incurred a loss.
Loss = C.P. – S.P.

Loss and Profit are always calculated on Cost Price.

Profit Percentage

    Profit % =

 Profit x 100
————–
C.P. 

                                                                                            

  

                                                                                                            

Loss Percentage

    Loss % =

 Loss x 100
————
C.P.   

 

                                                                                         

  

Selling Price

            (100 – Loss %)
SP =  ——————  x C.P  
               100

            (100 + Gain %)
SP =  ——————   x  C.P  
               100

 

Cost Price

            100
CP =  ——————–  x SP  
            ( 100 + Gain %)

            100
CP =  ——————–  x SP  
            ( 100 – Loss %)

   

Whenever two similar items are sold, one at a gain of L %, and the other at a loss of L %, then the seller always incurs a loss of

                     Common Loss and Gain %
Loss % = [  ———————————– ] 2 =  (L/10) 2
                     10

   

If a dishonest trader shows as if he sell goods at cost price, but uses false weights, then

                    Error
Gain % = [  —————————] x 100 
                    (True Value) – (Error)

Simple Interest & Compound Interest – Important Formulas – APSC CSAT Paper Notes

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Simple Interest (SI) & Compound Interest (CI) – Important Formulas

Numerical Aptitude Notes for CSAT Paper, SSC and Competitive Exams

 

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Principal – The money borrowed or lent out for a certain period is called the principal or the sum.

Interest – Extra money paid for using other’s money is called interest.

Simple Interest (S.I.) – If the interest on a sum borrowed for certain period is reckoned uniformly

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

Simple Interest =

  

P x R x T
———–

                                                                         

100

 

P =

  

100 x S.I.
———–

  

;                       R =

  

100 x S.I.
———–

  

 ;                and  T =

  

100 x S.I.
———–       

  

.

R x T

P x T

P x R            

Compound Interest – the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Let Principal = P, Rate = R% per annum, Time = n

When interest is compound Annually:

   Amount = P

(

1 +

R
—-

)

n                                                                                             

100

When interest is compounded Half-yearly:

    Amount = P

(

1 +

(R/2)
——

)

2n                                                                               

100

When interest is compounded Quarterly:

    Amount = P

(

1 +

(R/4)
—–

)

4n                                                                           

100

When Rates are different for different years, say r1%, r2%, r3% for 1st, 2ndand 3rd year respectively.

    Then, Amount = P

(

1 +

r1
—-

)(

  

1 +

r2
—

)(

  

1 +

r3
—–

)                 

.

100

100

100

Present worth of Rs. P due n years hence is given by:

    Present Worth =

        P
———————–                                                                               

(

1 +

r
—-

)

n                                                                                                

100

 

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Speed, Time and Distance – Important Formulas – APSC CSAT Paper Notes

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Speed, Time and Distance – Important Formulas

Numerical Aptitude Notes for CSAT Paper, SSC and Competitive Exams

 

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Basic Formulas

  • Speed = Distance/Time
  • Time = Distance/Speed
  • Distance = (Speed x Time).

Ratio of Speed to Ratio of Time

  • If the ratio of the speeds of A and B is a: b, then the ratio of the times taken by them to cover the same distance is 1/a: 1/b or b:a

Average Speed Formula

  • Suppose a car covers a certain distance at a km/hr and an equal distance at b km/hr. The average speed for the whole journey is = 2ab/(a + b) km/hr.

km/hr to m/sec conversion

  • 10 km/hr = 10 x(5/18) m/sec.

m/sec to km/hr conversion

  • 10 m/sec = 10 x(18/5) km/hr.

 

Important Formulas for Train base Questions

  • Time taken by a train of length K metres to pass an object be negligible length like a pole or standing man or an electric post is equal to the time taken by the train to cover K metres

 

  • Time taken by a train of length K metres to pass a stationery object of length L metres is the time taken by the train to cover (K + L) metres.

 

  • Suppose two trains or two objects bodies are moving in the same direction at S m/s and T m/s, where S > T, then their relative speed is = (S – T) m/s.

 

  • Suppose two trains or two objects bodies are moving in opposite directions at S m/s and T m/s, then their relative speed is = (S + T) m/s.

 

  • If two trains of length K metres and L metres are moving in opposite directions at S m/s and T m/s, then
  • The time taken by the trains to cross each other = (K + L)/(S + L) sec.

 

  • If two trains of length K metres and L metres are moving in same directions at S m/s and T m/s, then
  • The time taken by the trains to cross each other = (K + L)/(S – L) sec.

 

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