SIXPHRASE

AMCAT TRAININGC.S.VEERARAGAVAN

SIXPHRASE

AMCAT

NAC

AMCAT QUANTITATIVE ABILITY

AMCAT LOGICAL ABILITY

15 08 13

AMCAT LOGICAL ABILITYDeduction. Rule: All the beans from this bag are white.

Case: These beans are from this bag.

Result: These beans are white.Induction. Case: These beans are [randomly selected] from this bag.

Result: These beans are white.

Rule: All the beans from this bag are white.AbductionRule: All the beans from this bag are white.

Result: These beans [oddly] are white.

Case: These beans are from this bag.

DECIMALS & FRACTIONS

DECIMALS & FRACTIONSWhich pair of rational numbers lie between 1/5 and 2/5 -a. 262/1000, 275/1000b. 362/1000, 562/1000 c. 451/1000, 552/1000 d. 121/1000,131/1000BETWEEN 0.2 AND 0.4 ANS A.

BASIC ALGEBRAA, B and C are three typists, who working simultaneously can type 216 pages in four hours. In one hour, C can type as many pages more than B as B can type more than A. During a period of five hours, C can type as many pages as A can during seven hours. How many pages does each of them type per hour respectively?

A.14,17,20B.16,18,22C.15,17,22D.15,18,21

BASIC ALGEBRAA man arranges to pay off a debt of Rs 3600 by 40 annual instalments which are in A.P. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid. The value of the 8th instalment is:A.Rs 35B.Rs 50C.Rs 65D.Rs 70

BASIC ALGEBRAA student was asked to divide a number by 6 and add 12 to the quotient. He, however first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been:

A.122B.118C.114D.124

FACTORIZATION

DIVISIBILITY

DIVISIBILITYWhat least number must be subtracted from 9400 to get a number exactly divisible by 65?a. 40 b. 20c. 80 d. none of these65 = 5 X 13Last digit should be zero or 5.940040=9360 divisible by 13 & 5940020=9380, 940080=9320. none of these divisible by 13.Hence answer is A.

HCF & LCM

HCF & LCMThe H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:A. 276 B. 299 C. 322 D. 345 Numbers are 23 x 13 = 299 and 23 x 14 = 322.So, Larger number = (23 x 14) = 322.

HCF & LCMThe product of three natural number is 24000 and HCF is 10. How many such a triplets exists ?Let the numbers be 10x,10y and 10z.Given xyz = 24 and x,y,z are coprime.The possible values of x,y,z are (1,2,12),(1,3,8),(1,4,6),(2,3,4).only four triplets are possible. they are 10,20,120;10,30,80;10,40,60 and 20,30,40

ODD, EVEN,PRIME, RATIONAL NUMBERSA school purchased x computers at y dollars each for a total of $640,000. Both x and y are whole numbers and neither is a multiple of 10. Find the absolute value of the difference between x and y.The prime factorization of 640,000 is 21054.210 = 1024 and 54 = 625.Hence the absolute difference is 399.

ODD, EVEN, PRIME4^125 + 125^4 is - 1) prime2) composite even 3) composite odd4) not possible to decide 5) none of these4^125 IS EVEN AND OF THE FORM 4K.1254 IS MULTIPLE OF 5 AND OF THE FORM 5M1254 = 512. it is in the form of 4k+1.Hence the number is in the form of 4k+1.

APPLICATION OF ALGEBRA TO REAL WORLD

ALGEBRAThree consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number.a. 6b. 18c. 12d. All of theseLet the numbers be x1, x, x + 1. Since x2 = (x1) * (x+1) + 1 it is true for any values of x.

A, B, C and D play a game of cards. A says to B "If I give you 8 cards, you will have as many as C has and I shall have 3 less than what C has. Also if I take 6 cards from C, I shall have twice as many as D has". If B and D together have 50 cards, how many cards have A got?

A.40B.37C.23D.27

B+8=CA8=C3A+6=2DB+D=50solving these we get A= 40

BASIC ALGEBRANaveen purchased two oranges, 3 apples and 5 bananas and paid Rs 40. Had Naveen purchased 3 oranges, 5 apples and 9 bananas, He would have to pay Rs 64. Gagan demanded only 1 orange, 1 apple and 1 banana. If Naveen purchased only what was demanded by Gagan, then how much would he have paid (in Rs)?

A.16B.28C.36D.24

Let the cost of each orange, apple and banana be o, a and b respectively.Given, 2(o)+3a+5b=40 -------- (i) 3(o)+5a+9b=64-------- (ii)2(i) - (ii): o+a+b= 16

BASIC ALGEBRAA,B,C and D each had some money. D doubled the amounts with the others. C then doubled the amounts with the others. B then doubled the amounts with the others. A then doubled the amounts with the others. At this stage, each of them has Rs 80. Find the initial amount with C (in Rs).

A.75B.80C.95D.85

A man purchased 40 fruits; apples and oranges for Rs 17. Had he purchased as many as oranges as apples and as many apples as oranges, he would have paid Rs 15. Find the cost of one pair of an apple and an orange.

A.70 paiseB.60 paiseC.80 paiseD.1 rupee

DIRECT & INVERSE PROPORTION

COMMON APPLICATIONS

SPEEDTIMEDISTANCE

TRAINSTwo trains start from stations Chennai and Villupuram spaced 150 km apart at the same time and speed. As the trains start, a bird flies from one train towards the other and on reaching the second train; it flies back to the 1st train. This is repeated till the trains collide. If the speed of the train is 75kmph and that of the bird is 100kmph. How much did the bird travel till collision?(a) 100km(b) 120km(c) 220km(d) 175km

distance between trains is 150 km. one train travels 75 km / hr. other train travels 75 km / hr. they will meet when the total distance traveled by both of them is equal to 150 km. rate * time = distance. We know that the time that each train travels will be the same. We let h = the time each train travels. train 1 travels 75 km / hr * h hours.train 2 travels 75km / hr * h hours. the total distance they travel is 150 km. 75 * h + 75 * h = 150 h = 1They will meet in 1 hour. the bird was flying at 100 km/h. in the same 1 hour the bird flew a total of 100 km. bird flies 50 km in one direction, then travels back 50 km when the trains meet.

PROFIT & LOSS

PROFIT/ LOSS

PROFIT / LOSS

PROFIT / LOSS

PROFIT / LOSSA man buys a watch for Rs.135. His overhead expenses were Rs.50. If he sells the watch for Rs.254, what is his approximate profit/loss in percent?A) 39% profit B) 37% profit C) 37% loss D) 39% lossC.P = 135+50 = 185.PROFIT % = 37%

PROFIT / LOSS

PROFIT / LOSSAfter giving a discount of Rs.45 the shopkeeper still gets a profit of 20%, if the cost price is Rs.180. Find the mark up percent.A) 0.4 B) 0.55 C) 0.45 D) 0.48LET THE S.P = XC.P = 180. S.P = 180 + 36 = 216.M.P = S.P + 45 = 216+45 = 261.M.P% = 0.48PROFITCOST PRICEDISCOUNTMARKED PRICESELLING PRICE

PROFIT / LOSS

PERCENTAGE

PERCENTAGE

PERCENTAGEIf 7% of A is 42, then find 27% of A.A) 162 B) 62 C) 600 D) 126Ans: 162Another method7 is prime number and the last digit of given number is 2. Hence 27% of A also should have last digit is 2 and so C and D are not possible.B is also not possible because it is not divisible by 9(ie 27).

PERCENTAGE

PERCENTAGE

PERCENTAGE

PERCENTAGE4% is equal to one out of every:A) 12 B) 20 C) 40 D) 25Answer25

PERCENTAGEFind the percentage of prime numbers present between 1 and 100 (including both).A) 20 B) 25 C) 24 D) 232,3,5,7, 11,13,17,19 =823,29,31,37,41,43,47,53 =861,67,71,73,79,83,89,97 =824%

AGE RELATIONS

AVERAGEThe average age of a group of nine men today is the same as it was six years ago, with one of the men having been replaced by another much younger man. The difference in ages of the man being replaced and the man replacing him is how many years?(a) 53(b) 54 (c) 55 (d) 56Six years ago the average is x and now also x. the number is same. HenceNo of persons * time elapsed = 9 * 6 = 54.

MIXTURES

MISCELLANEOUS

RACES & GAMES

PIPES & CISTERNSPipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill another tank twice as big as the first. If A has a cross-sectional circumference that is one-third of C, how long will it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross-sectional area is same for all the three pipes.)a. 66/13 b. 40/13 c. 16/13 d. 32/13If A has a cross sectional circumference x and area will be proportional to x2 cross section of C is 3x and area will be proportional to 9x2 .Hence cross sectional circumference of B will be (2/3)*3x = 2x so area is proportional to 4x2. Pipe A fills in 16 min. Pipe B and C sum of area is proportional to 13x2. will fill the same tank in 16/13 min.The second tank is twice big in size require 2 * 16 / 13 = 32/13 min

A.M & G.M

PERMUTATIONThe letters of the word WOMAN are written in all possible orders and these words are written out as in a dictionary ,then the rank of the word 'WOMAN' isa. 117b. 120c. 118d. 1195!=120120/5=24 Since W is the last in rank WOMAN is in the last 24.O is in the last rank of the remaining 4 letters. 24/4 = 6Therefore WOMAN is in the last 6 in rank.M is between A and N so WOMAN is in rank 117 or 118.A is before N so WOMAN's rank is 117.There are 120 possible arrangements of the letters in WOMAN. Since WOMAN is near the end, I'll list out the ones after WOMAN:

WONMAWONAMWOMNA

There are only three, so these account for the 118th, 119th, 120th words, and it places WOMAN 117th.

PERMUTATIONA father with 8 children takes 3 children at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. Then:A.number of times he will go to zoological garden is 56.B.number of times each child will go to the zoological garden is 21.C.number of times a particular child will not go to the zoological garden is 35.D.All of the above.

PROBABILITY

PROBABILITY

Permutation with restriction

Probability what is the probability of 2 man will be born in a same month ?1/12 is the probability of 2 man will be born in a same month as first person can be born in any month and second person has 1/12 probability of birth in same month.

Probability What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'? Total two digit numbers = 90The numbers multiple of 3 but not 5 12,18,21,24,27,33,36,39,42,48,51,54,57,63,66,69,72,78,81,84,87,93,96,99 = 24 numbersHence probability = 24/90 = 4/15

ProbabilityThe bacteria had a probability of splitting into three and a probability to die is one third of total bacteria. Let the probability be P. Some of them survived with probability 1/5 than which among the following relation is true?(a) P=1/3+1/5*3(b) P=1/5*(1/8-3)here prob for dying = 1/3prob of survival = 1/5if they survive, they will be splited into 3 more bacteriahence, p = (1/3) + (3* 1/5)

POWERSIf x increases linearly, how will a-x behave (a>1) ?a. Increase linearlyb. Decrease linearlyc. Increase exponentiallyd. Decrease exponentiallySince x increases linearly, x decreases linearly and ax also decreases linearly. Ans b.

LOGARITHMWhat is the value of the following expression: 2 log105 + log104 ?a. 2b. 2.5c. 3d. None of theseLog10 25*4 = log10100 = 2.

POWERSWhat is x if

Rewrite each term as a power of three, then combine exponents:

Since the bases are the same, the exponents must be equal:

which has the solution x = 94

Power graphicalwhat is maximum no. of point of intersection of graph of 2 different cubic polynomial function with leading coefficient equal to 1a.)2b.)3c.)9d.)6 Finding the number of solutions to p(x) = q(x) will find the number of intersections of the two graphs.This is also equivalent to the number of roots of p(x) - q(x) = 0. Since p(x) and q(x) are both third degree polynomials with a leading term of x^3, the x^3 term will drop out, leaving at most a second degree polynomial (quadratic) on the left side. By the Fundamental Theorem of Algebra, a 2nd degree polynomial can have at most 2 real solutions, leading to an answer of 2.