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ARITHMETIC APTITUDE / REASONING APTITUDE / CREATIVITY APTITUDE / VERBAL APTITUDE Soft Skills Training – Aptitude/Verbal Training – Finance Training – Faculty Development Program – Technical Training – `Guest Lectures & Seminars ARITHMETIC APTITUDE .................................................................................2 NUMBERS .......................................................................................................2 PROBLEMS ON TRAINS.....................................................................................18 TIME AND DISTANCE .......................................................................................22 HEIGHT AND DISTANCE ...................................................................................24 TIME AND WORK............................................................................................26 PROBLEMS ON AGES .......................................................................................31 ALLIGATION OR MIXTURE ................................................................................33 CHAIN RULE .................................................................................................36 SIMPLE INTEREST ..........................................................................................39 COMPOUND INTEREST .....................................................................................41 PROFIT AND LOSS ..........................................................................................43 PARTNERSHIP................................................................................................45 PERCENTAGE ................................................................................................47 TRUE DISCOUNT ............................................................................................49 RATIO AND PROPORTION..................................................................................51 SIMPLIFICATION.............................................................................................54 PROBLEMS ON H.C.F AND L.C.M .....................................................................57 SQUARE ROOT AND CUBE ROOT ........................................................................59 LOGARITHM ..................................................................................................62 VOLUME AND SURFACE AREA............................................................................63 PERMUTATION AND COMBINATION......................................................................66 PROBABILITY.................................................................................................68 AVERAGE .....................................................................................................70 AREA ..........................................................................................................72 RACES AND GAMES ........................................................................................75 BOATS AND STREAMS......................................................................................77 SURDS AND INDICES........................................................................................79 PIPES AND CISTERN........................................................................................82 CALENDAR....................................................................................................84 CLOCK.........................................................................................................86 GEOMETRY ...................................................................................................89 REASONING APTITUDE .................................................................................92 ANALYTICAL REASONING..................................................................................92 PIPES AND CISTERN......................................................................................100 LOGICAL PROBLEMS .....................................................................................101 LOGICAL GAMES ..........................................................................................108 LOGICAL DEDUCTION ....................................................................................111 DATA SUFFICIENCY ......................................................................................115 ARITHMETIC REASONING ...............................................................................119 DATA INTERPRETATION .................................................................................123 TABLE CHARTS............................................................................................123 BAR CHARTS...............................................................................................134 PIE CHARTS................................................................................................139 LINE CHARTS ..............................................................................................142 DATA SUFFICIENCY (DS) PROBLEMS ON TRAINS.................................................146 TIME AND DISTANCE .....................................................................................148 TIME AND WORK..........................................................................................149 SIMPLE INTEREST ........................................................................................151 COMPOUND INTEREST ................................................................................... 152 PROFIT AND LOSS ........................................................................................ 154 PARTNERSHIP ............................................................................................. 156 PROBLEMS ON AGES ..................................................................................... 157 AVERAGE ................................................................................................... 159 AREA ........................................................................................................ 161 VOLUME AND SURFACE AREA ......................................................................... 163 PROBLEMS ON NUMBERS ............................................................................... 165 STATEMENT AND ASSUMPTION ........................................................................ 166 MAKING ASSUMPTIONS ................................................................................. 170 COURSE OF ACTION...................................................................................... 172 CAUSE AND EFFECT ..................................................................................... 176 STATEMENT AND CONCLUSION ........................................................................ 180 STATEMENT AND ARGUMENT .......................................................................... 184 CREATIVITY APTITUDE .............................................................................. 188 VENN DIAGRAM ANSWERS.............................................................................. 188 CUBE AND CUBOIDS ..................................................................................... 191 DICE ......................................................................................................... 193 CUBES AND DICE ANSWERS............................................................................ 196 FIGURE MATRIX .......................................................................................... 201 SEATING ARRANGEMENT ............................................................................... 205 DIRECTION SENSE TEST................................................................................ 208 MIRROR AND WATER IMAGES......................................................................... 214 EMBEDDED IMAGES...................................................................................... 216 GROUPING OF IMAGES .................................................................................. 219 IMAGE ANALYSIS ......................................................................................... 224 PATTERN COMPLETION ................................................................................. 226 PAPER CUTTING .......................................................................................... 230 SHAPE CONSTRUCTION.................................................................................. 233 PAPER FOLDING .......................................................................................... 237 CHARACTER PUZZLES ................................................................................... 239 MISSING LETTERS PUZZLES ........................................................................... 244 LOGICAL PUZZLES ........................................................................................ 248 PLAYING CARDS PUZZLES .............................................................................. 253 CLOCK PUZZLES .......................................................................................... 255 NUMBER PUZZLES ........................................................................................ 260 DOT SITUATION........................................................................................... 266 RULE DETECTION ........................................................................................ 270 VERBAL APTITUDE ..................................................................................... 271 CLOSET TEST ............................................................................................. 271 IDIOMS AND PHRASES ................................................................................... 274 SYNONYMS ................................................................................................. 276 ANTONYMS ................................................................................................. 278 CHANGE OF VOICE....................................................................................... 280 CHANGE OF SPEECH .................................................................................... 281 LETTER AND SYMBOL SERIES ......................................................................... 282 ESSENTIAL PART ......................................................................................... 283 SPELLINGS ................................................................................................. 285 SPOTTING ERRORS....................................................................................... 287
2 ORDERING OF WORDS ..................................................................................288 SENTENCE CORRECTION ................................................................................291 SENTENCE IMPROVEMENT ..............................................................................292 COMPLETING STATEMENTS.............................................................................293 SENTENCE FORMATION .................................................................................295 PARAGRAPH FORMATION ...............................................................................296 ORDERING OF SENTENCES .............................................................................297 COMPREHENSION .........................................................................................298 ONE WORD SUBSTITUTES ..............................................................................301 VERBAL ANALOGIES......................................................................................302 SYLLOGISM .................................................................................................303 CLASSIFICATION ..........................................................................................306 LOGICAL SEQUCENCE ....................................................................................309 VERBAL REASONING .....................................................................................312 ANALYSING ARGUMENTS ................................................................................314 VERIFICATION OF TRUTH ..............................................................................317 BLOOD RELATIONS .......................................................................................318 MATCHING DEFINITION .................................................................................321 THEME DETECTION ......................................................................................323 Arithmetic Aptitude Numbers 1.1397 x 1397 = ? Answer: 1951609. Explanation: 1397 x 1397= (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. 2. (112 x 54 ) = ? Answer: 70000 Explanation: (112 x 54 ) = 112 x104 = 112 x 104 = 1120000= 70000 2 2 4 16 3. It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number? Answer: (x + 1) Explanation: Let 232 = x. Then, (232 + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(232) 3 + 1] = (x 3 + 1) = (x + 1)(x 2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N. 4.Which one of the following is not a prime number? Answer: 91 Explanation: 91 is divisible by 7. So, it is not a prime number. 5.What least number must be added to 1056, so that the sum is completely divisible by 23 ? Answer: 2 Explanation: 23) 1056 (45 92 --- 136 115 ---
3 21 --- Required number = (23 - 21) = 2. 6. How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 Answer: 4 Explanation: 132 = 4 x 3 x 11 So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also. 264 11,3,4 (/) 396 11,3,4 (/) 462 11,3 (X) 792 11,3,4 (/) 968 11,4 (X) 2178 11,3 (X) 5184 3,4 (X) 6336 11,3,4 (/) Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. 7.(935421 x 625) = ? Answer: 584638125 Explanation: 935421 x 625 = 935421 x 54 = 935421 x 10 4 2 = 935421 x 104 = 9354210000 2 4 16 = 584638125 8. The largest 4 digit number exactly divisible by 88 is: Answer: 9944 Explanation: Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944. 9.On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ? Answer: 4 Explanation: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder. x = 5k + 3 x 2 = (5k + 3)2 = (25k 2 + 30k + 9) = 5(5k 2 + 6k + 1) + 4 On dividing x 2 by 5, we get 4 as remainder. 10.How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 Answer: 6 Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 9 (X) 2343 12 (/)
4 3474 18 (X) 4131 9 (X) 5286 21 (/) 5340 12 (/) 6336 18 (X) 7347 21 (/) 8115 15 (/) 9276 24 (/) Required number of numbers = 6. 11.(x n - a n ) is completely divisible by (x - a), when Answer: For every natural number n, (x n - a n ) is completely divisible by (x - a). Explanation: For every natural number n, (x n - a n ) is completely divisible by (x - a). 12.A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ? Answer: 10 Explanation: 4 a 3 | 9 8 4 } ==> a + 8 = b ==> b - a = 8 13 b 7 | Also, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b) (9 - b) = 0 b = 9 (b = 9 and a = 1) (a + b) = 10. 13.Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ? Answer: (47 + 43). Explanation: When n is odd, (x n + a n ) is always divisible by (x + a). Each one of (4743 + 4343) and (4747 + 4343) is divisible by (47 + 43). 14.(963 + 476)2 + (963 - 476)2 = ? (963 x 963 + 476 x 476) Answer: 2 Explanation: Given Exp. =(a + b) 2 + (a - b) 2 = 2(a 2 + b 2 )= 2 (a 2 + b 2 ) (a 2 + b 2 ) 15.8597 - ? = 7429 - 4358 Answer: 5526 Explanation: 7429 Let 8597 - x = 3071 -4358 Then, x = 8597 - 3071 ---- = 5526 3071 ---- 16.(12345679 x 72) = ? Answer: 888888888 Explanation: 12345679 x 72= 12345679 x (70 +2) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888 17.What smallest number should be added to 4456 so that the sum is completely divisible by 6 ? Answer: 2 Explanation: 6) 4456 (742 42 --- 25 24 Therefore, Required number = (6 - 4) = 2. --- 16 12 --- 4 18.Which of the following numbers will completely divide (4915 - 1) ? Answer: 8 Explanation: (x n - 1) will be divisibly by (x + 1) only when n is even. (4915 - 1) = {(72 ) 15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8. 19.(112 + 122 + 132 + ... + 202 ) = ? Answer: 2485