Bright Zoom Maths

Logical Reasoning - Matching Definitions Read each definition and all four choices carefully, and find the answer that provides the best example of the given definition. Answer each question solely on the basis of the definition given. 1. A Tiebreaker is an additional contest or period of play designed to establish a winner among tied contestants. Which situation below is the best example of a Tiebreaker? A. At halftime, the score is tied at 28. B. Mary and Megan have each scored three goals in the game. C. The referee tosses a coin to decide which team will have possession of the ball first. D. The Sharks and the Bears each finished with 14 points, and they are now battling it out in a five-minute overtime. Answer: D. The Sharks and the Bears each finished with 14 points, and they are now battling it out in a five-minute overtime. Explanation :  This is the only choice that indicates that an additional period of play is taking place to determine the winner of a game that ended in ...

Logical Reasoning skills  Logical Reasoning - Essential Part 1. Choose the word that is necessary for the word given in the question: Saddle A. Horse B. Seat C. Stirrups D. Horn Answer : B. Seat Explanation :  A saddle is something one uses to sit on an animal, so it must have a seat (choice b). A saddle is often used on a horse (choice a), but it may be used on other animals. Stirrups (choice c) are often found on a saddle but may not be used. A horn (choice d) is found on Western saddles, but not English saddles, so it is not the essential element here. 2. Choose the word that is necessary for the word given in the question: Cell A. Running B. Swimming C. Winning D. Speaking Answer : C. Winning Explanation :  Without a first-place win, there is no champion, so winning is essential. There may be champions in running, swimming, or speaking, but there are also champions in many other areas. 3. Choose the word that is necessary for the word given in the question: Glacier A....

 Aptitude Solved Problems - Profit and Loss  1. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. Find his profit percent ?  Answer: 5 %  Explanation:  Cost Price of 26 kg of rice = ( 26 * 20 )  = Rs. 520  Cost Price of 30 kg of rice = ( 30 * 36 )  = Rs. 1080  Cost Price of 56 kg rice = Rs. ( 520 + 1080 )  = Rs. 1600  Selling Price of 56 kg rice = Rs. ( 56 * 30 )  = Rs. 1680  Gain = Selling Price - Cost Price  = 1680 - 1600  = 80  Gain % = ( Gain * 100 ) / Cost Price  = ( 80 * 100 ) / 1600  = ( 8000 / 1600 )  = ( 80 / 16 )  = 5 %  2. Vimal bought paper sheets for Rs. 7200 and spent Rs. 200 on transport. Paying Rs. 600, he had 330 boxes made, which he sold at Rs 28 each. Find his profit percentage ?  Answer: 15.5 %  Explanation  Total investments ( Cost Price ) = ( 7200 + 200 + 600 ...

Tricks to multiply a number by 39 Example: 1 26 * 39 Step 1: Multiply 26 by 4 26 * 4 = 104 Step 2: Multiply 104 by 10 104 * 10 = 1040 Step 3: Subtract 26 from 1040 1040 - 26 = 1014 26 * 39 = 1014  Example: 2 125 * 39 Step 1: Multiply 125 by 4 125 * 4 = 500 Step 2: Multiply 500 by 10 500 * 10 = 5000 Step 3: Subtract 5000 from 125 5000 - 125 = 4875 125 * 39 = 4875 Example: 3 342 * 39 Step 1: Multiply 342 by 4 342 * 4 = 1368 Step 2: Multiply 1368 by 10 1368 * 10 = 13680 Step 3: Subtract 342 from 13680 13680 - 342 = 13338 342 * 39 = 13338

Different types of Number Series Aptitude Notes Number Series What is Number Series? Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers. In competitive exams number series are given and where you need to find missing numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can . Different types of Number Series There are some format of series which are given in Exams. Perfect Square Series: This Types of Series are based on square of a number which is in same order and one square number is missing in that given series. Example :   1. 441, 484, 529, 576? Answer:  441 = 21^2, 484 = 22^2,  529 = 23^2, 576 = 24^2 ,  625 = 25^2. Perfect Cube Series:...

Problems on Trains - Aptitude Questions and Answers part -2  This is aptitude questions and answers section on "Problems on Trains" with explanation for various interview, competitive examinations and entrance tests. Candidates can practice the Problems on Trains Quiz, Problems on Trains MCQ, Problems on Trains Aptitude Questions, Problems on Trains Multiple Choice Questions and Answers from the below section. Problems on Trains Questions - Problems on Trains Quiz Details Test Name:   Problems on Trains Exam Type:  Multiple Choice Questions Category : Aptitude Quiz Number of Questions :  77 Problems on Trains Formulae: 1. km/hr to m/s conversion a km/hr = (a x5/18) m/s 2. m/s to km/hr conversion  a m/s = (a x18/5) km/hr 6. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? A. 120 m B. 240 m C. 300 m D. None of these Answer & Explanation A...

Problems on Trains - Aptitude Questions and Answers part -1 This is aptitude questions and answers section on "Problems on Trains" with explanation for various interview, competitive examinations and entrance tests. Candidates can practice the Problems on Trains Quiz, Problems on Trains MCQ, Problems on Trains Aptitude Questions, Problems on Trains Multiple Choice Questions and Answers from the below section. Problems on Trains Questions - Problems on Trains Quiz Details Test Name:   Problems on Trains Exam Type:  Multiple Choice Questions Category : Aptitude Quiz Number of Questions :  77 Problems on Trains Formulae: 1. km/hr to m/s conversion a km/hr = (a x5/18) m/s 2. m/s to km/hr conversion a m/s = (a x18/5) km/hr 1. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: A. 200 m B. 225 m C. 245 m D. 250 m Answer & Explanation Answer: Option C Explanation: Speed = [45 X 5/18] m/sec  = [25/2] m/sec Time...

Logical Reasoning Logical Deductions 1. Statement: Raman is always successful. No fool is always successful. Conclusions: I. Raman is a fool II. Raman is not a fool A. Only I follows B. Only II follows C. Either I or II follows D. Both I and II follow Answer : B. Only II follows Explanation :  Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, II follows.  2. Statement: All trucks fly. Some Scooters fly. Conclusions: I.All trucks are scooters II. Some scooters do not fly A. Only I follows B. Only II follows C. Neither I nor II follows D. Both I and II follow Answer : C. Neither I nor II follows  Explanation :  Since the middle term "fly" is not distributed even once in the premises, so no definition conclusion follows 3. Statement: All grasses are trees. No tree is shrub. Conclusions: I. No grasses are shrubs. II. Some shrubs are grasses. A. Only conclusion I follo...

Logical Reasoning skills  Logical Reasoning Essential Part 1 1. Choose the word that is necessary for the word given in the question: Antique A.prehistoric B. aged C. artifact D. rarity  Answer : B. aged Explanation :  An antique is something that belongs to, or was made in, an earlier period. It may or may not be a rarity, and it does not have to be an artifact, an object produced or shaped by human craft . An antique is old but does not have to be prehistoric. 2. Choose the word that is necessary for the word given in the question: Itinerary A. guidebook B. travel C. route D. map  Answer : C. route Explanation :  An itinerary is a proposed route of a journey. A map is not necessary to have a planned route. Travel is usually the outcome of an itinerary, but not always. A guidebook may be used to plan the journey but is not essential. 3. Choose the word that is necessary for the word given in the question: Dimension A. measure B. inch C. ruler D. compass Answer ...

Logical Reasoning skills  Find the missing letter  Logical Reasoning 1. Find the next term in this series : 11, 16, 23, 32, 43,...  Answer : 56 Explanation :  The pattern is + 5, + 7, + 9, + 11, + 13, ... Missing number = 43 + 13 = 56. 2. Find the missing letter : A, C, F, H, ____, M Answer : K Explanation :  The letters are alterntely moved two and three steps forward to obtain the successive terms. 3. Find the analogies pair:  RAIN : DRIZZLE A. run : jog B. juggle : bounce C. walk : run D. hop : shuffle Answer : A. run : jog Explanation :  To drizzle is to rain slowly; to jog is to run slowly. 4. Which of the following words will come fourth in the English dictionary? False, Follow, Faithfully, Fool, Fallible. Answer : Follow Explanation :  The given words can be arranged in the alphabetical order as: Faithfully, Fallible, False, Follow, Fool. Clearly, Follow comes fourth. 5. If SUCCESS is coded as VXFFHVV, how can VICTORY be coded ?  Ans...

Logical Reasoning skills  Logical Reasoning Seating Arrangements Read the following information carefully and answer the questions given below: (i) A, B, C, D, E and F are six students in a class. (ii) B and C are shorter than F but heavier than A. (iii) D is heavier than B and taller than C. (iv) E is shorter than D but taller than F. (v) F is heavier than D. (vi) A is shorter than E but taller than F. 1. Who among them is the tallest ? Answer : D is the tallest Explanation :  In terms of height, we have : B < F, C < F, C < D, E < D, F < E, A < E, F < A. So, C < F < E < D, B < F, F < A < E Thus, the sequence becomes : B < C < F < A < E < D or C < B < F < A < E < D. 2. Who is third from the top when they are arranged in descending order of heights ? Answer : A is third from the top when they are arranged in descending order of heights Explanation :  The descending order of height is : D > E > A ...

  Linear Algebra Symbols Symbol Symbol Name Meaning / definition Example · dot scalar product a  ·  b × cross vector product a  ×  b A ⊗ B tensor product tensor product of A and B A  ⊗  B inner product [ ] brackets matrix of numbers ( ) parentheses matrix of numbers |  A  | determinant determinant of matrix A det( A ) determinant determinant of matrix A ||  x  || double vertical bars norm A T transpose matrix transpose ( A T ) ij  = ( A ) ji A † Hermitian matrix matrix conjugate transpose ( A † ) ij  = ( A ) ji A * Hermitian matrix matrix conjugate transpose ( A * ) ij  = ( A ) ji A  -1 inverse matrix A A -1  =  I rank( A ) matrix rank rank of matrix A rank( A ) = 3 dim( U ) dimension dimension of matrix A rank( U ) = 3

  Algebra symbols Symbol Symbol Name Meaning / definition Example x x variable unknown value to find when 2 x  = 4, then  x  = 2 ≡ equivalence identical to ≜ equal by definition equal by definition := equal by definition equal by definition ~ approximately equal weak approximation 11 ~ 10 ≈ approximately equal approximation sin (0.01) ≈ 0.01 ∝ proportional to proportional to y  ∝  x  when  y  =  kx, k  constant ∞ lemniscate infinity symbol ≪ much less than much less than 1 ≪ 1000000 ≫ much greater than much greater than 1000000 ≫ 1 ( ) parentheses calculate expression inside first 2 * (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 { } braces set ⌊ x ⌋ floor brackets rounds number to lower integer ⌊4.3⌋ = 4 ⌈ x ⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉ = 5 x ! exclamation mark factorial 4! = 1*2*3*4 = 24 |  x  | single vertical bar absolute value | -5 | = 5 f  ( x ) function ...

  Geometry symbols Symbol Symbol Name Meaning / definition Example ∠ angle formed by two rays ∠ABC = 30° measured angle ABC = 30° spherical angle AOB = 30° ∟ right angle = 90° α = 90° ° degree 1 turn = 360° α = 60° deg degree 1 turn = 360deg α = 60deg ′ prime arcminute, 1° = 60′ α = 60°59′ ″ double prime arcsecond, 1′ = 60″ α = 60°59′59″ line infinite line AB line segment line from point A to point B ray line that start from point A arc arc from point A to point B  = 60° ⊥ perpendicular perpendicular lines (90° angle) AC ⊥ BC | | parallel parallel lines AB | | CD ≅ congruent to equivalence of geometric shapes and size ∆ABC≅ ∆XYZ ~ similarity same shapes, not same size ∆ABC~ ∆XYZ Δ triangle triangle shape ΔABC≅ ΔBCD | x - y | distance distance between points x and y |  x - y  | = 5 π pi constant π  = 3.141592654... is the ratio between the circumference and diameter of a circle c  =  π · d  = 2· π · r rad radians radians angle unit 360° = 2π rad c ...

  Basic math symbols Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 5 is equal to 2+3 ≠ not equal sign inequality 5 ≠ 4 5 is not equal to 4 ≈ approximately equal approximation sin (0.01) ≈ 0.01, x  ≈  y  means  x  is approximately equal to  y > strict inequality greater than 5 > 4 5 is greater than 4 < strict inequality less than 4 < 5 4 is less than 5 ≥ inequality greater than or equal to 5 ≥ 4, x  ≥  y  means  x  is greater than or equal to  y ≤ inequality less than or equal to 4 ≤ 5, x ≤ y  means  x  is less than or equal to  y ( ) parentheses calculate expression inside first 2 × (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)×(1+5)] = 18 + plus sign addition 1 + 1 = 2 − minus sign subtraction 2 − 1 = 1 ± plus - minus both plus and minus operations 3 ± 5 = 8 and -2 ± minus - plus both minus and plus operations 3 ± 5 = -2 and 8 * asterisk m...

Logical Reasoning skills  Logical Reasoning -Analogy  1. Complete analogous pair: Automobile : Petrol :: ? A. fire : fuel B. plane : propeller C. diesel : gas D. man : food Answer: D. man : food Explanation: An automobile needs petrol to function. Similarly, man needs food in order to function. 2. Complete analogous pair: Calf : cow :: Puppy : ? A. cub B. kitten C. dog D. snake Answer: C. dog Explanation: A calf's parent is cow and puppy's parent is dog. 3. Complete analogous pair: Tungsten : Filament :: Tree : ? A. graphite B. paper C. wool D. fabric Answer: B. paper Explanation: The first term is used in the production of the second. 4.Complete analogous pair: Letter : Word :: A. homework : school B. club : people C. product : factory D. page : book Answer: D. page : book Explanation: A group of letters form a word. Similarly, a group of pages combined together form a book. 5. Complete analogous pair. Brick : Clay :: Ruby : ? A. graphite B. corundum C. diamond D. pearl Answe...

 Logical Reasoning skills  Logical Reasoning -Solved Problems  1. Arrange the given words in a meaningful sequence. 1. Sentence, 2. Chapter, 3. Word, 4. Paragraph, 5. Book A. 2, 3, 1, 5, 4. B. 3, 2, 5, 4, 1. C. 5, 2, 4, 1, 3. D. 5, 3, 2, 4, 1. Answer: C. 5, 2, 4, 1, 3. Explanation: The correct order is: Book (5) - Chapter (2) - Paragraph (4) - Sentence (1) - Word (3). 2. In a row of 54 persons, A is 35th from the left side of the row and B is 22nd from the right side of the row. Find the no. of persons sitting between A and B? A. 1 B. 2 C. 3 D. 4 Answer: A. 1 Explanation:  Here Sum of positions of A & B from opposite ends = 35 + 22 = 57 > Total no. of persons ∴ No. of persons between A & B = (Position of A from left + Position of B from right) - Total no. of students - 2 No. of persons between A & B = (35+22) - 54 - 2  = 57 - 54 - 2 = 1. 3. Choose the pair in which the words are differently related. A. Cow : Fodder B. Crow : Carrion C. Poultry : F...

Logical Reasoning skills Logical Reasoning - Syllogism  1. Direction (1-7) : In each of the questions below three statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. 1. Statements: Some buildings are white. All whites are oranges. Some oranges are boxes. Conclusions: I. Some boxes are buildings. II. Some oranges are buildings. Answer: If only conclusion II follows. Explanation: Some buildings are white + All whites are oranges = I + A = I Some buildings are oranges - conversion - some oranges are buildings (I). Hence II follows. Some buildings are oranges + Some oranges are boxes = I + I = No Conclusions. Hence I does not follow.. 2. Statements: All desks are mirrors. All mirrors are chairs. Some chairs are...