Practice Test

1) An employer recruits experienced (x) and fresh (y) workmen for his firm. If he cannot afford to employ more than 9 people, then

2) On an average, an experienced person does 5 units of work while a new recruit does only 3 units of work daily. If their employer has to maintain an output of at least 30 units of work per day, then, with usual notations,

3) If the worker's union demands that an employer should not hire more than 5 experienced hands to 1 fresh one, then

4) If the union forbids an employer to hire less than 2 experienced persons to each fresh person, then

5) A solution of the inequality 3x-2y>3 is

6) If -2 < x < 7 and 3 < y < 5, then which of the following is true?

7) If x and y are two unequal positive numbers, then which of the following is definitely true?

8) If x and y are integers, then the equation 5 x + 19 y = 64 has

9) x > 2, y > - 1 then which of the following holds good?

10) If a+b = 9 and ab=19.25, then which of these is a possible value of (a-b)?

11) Find the value of m, from the following simultaneous equations.

12) Carla had Rs.2,750 in her purse in denominations of hundred and fifty. She has 32 notes in all counting both hundred and fifty. How many hundred rupee notes does she have in her purse?

13) If 1 added to the numerator of a certain fraction, its value becomes 7/19 and if 1 is added to the denominator of the original fraction, its value becomes 1/3. Find the original fraction.

14) Aishwarya's age 10 years hence will be twice Deepika's present age. Six years back Aishwarya's age was 5/3 times Deepika's age at that time. Find the present age of Aishwarya and Deepika respectively.

15) Amar bought bananas to school. He gave one-fourth of the bananas to the Physics teacher and one-sixth of the bananas to his Chemistry teacher. The Chemistry teacher gave the head-master 2 bananas and now has 4 bananas left. How many bananas did Amar give to the Physics teacher?

16) There are three cities: A,B and C. Three friends are discussing the population (in millions) of the three cities. One says A has 9 million people. The second says: B has as many people as A and C combined. The third says: The number of people in A added to half of the number of people in B is the number of people in C. What is the total number of people (in millions) in all three cities combined?

17) Sam, Harry and Jake had some candies each. Together Sam and Harry had 19 candies. Even after giving three candies to Jake, Sam had two more candies than him. Then Harry gave two of his candies to Jake and was also left with two more candies than him. How many candies does Jake have now?

18) Students were standing in rows for exercise. Each row had an equal number of students. If 5 students less were to stand in each row, 6 more rows would be required and if 5 students more were to stand in each row than the number of rows required would be reduced by 2. Find the total number of students.

19) A three digit number is equal to 17 times the sum of the digits. Of 198 is added to the number, the digits get reversed; also the sum of the extreme digits of the original number is less than the middle digit by unity. Find the sum of digits of the original number.

20) In an MBA entrance exam, 1 mark is awarded for every correct answer and 1/4 mark is deducted for each incorrect answer. There are two sections in the exam. A student gets an accuracy of 75% across each section. What is the minimum number of questions that he should attempt in all to clear the test, if the sectional cut-offs for the sections are 22 and 11 marks respectively?

21) Hermoine purchases 3 apples, 7 mangoes and 1 orange for a total of Rs.120. Ron buys 4 apples, 5 mangoes and an orange for Rs.164.50 from the same shop. If Harry picks 1 apple, 11 mangoes and an orange from the same shop, then how much does he have to pay?

22) 5 candles, 3 packets of chips and 2 pastries cost Rs.140. The difference between the costs of 1 packet of chips and 1 pastry is Rs.10 and the difference between the costs of 1 packet of chips and 1 candy is Rs.28. How much will Anil need to pay if he had to buy 10 candies, 1 packet of chips and 5 pastries? Assume that the chips are the costliest of an individual basis.

23) When a two digit number is divided by the sum of the digits, the quotient is 4. If the digits are reversed, the new number is 6 less than twice the original. Find the number.

24) A man earns Rs.800/- more than his wife. One-fourth of the man's salary and one-eighth of the wife's salary amount to Rs.500/- which is saved every month. Find their monthly expenditure.

25) The difference between two numbers is 3 and the sum of their squares is 29. Find the product of those two numbers.

26) If -2 < x < 7 and 3 < y < 5, then which of the following is true?

27) If x and y are two unequal positive numbers, then which of the following is definitely true?

28) If a + b = 11 and ab = 30 then the value of (a - b) could be :

29) find the value of x,if 7x+8(2 - x) + 10 = 4x - 4

30) Suresh wins one million in a lottery. He spends half the money to buy a house, half of the remaining amount to buy a car and 20% of the remaining amount to buy the motorcycle. Find the amount left with suresh

31) Ramesh travelled 60% of a journey by train and the remaining by road, thus taking 8 hours to complete the journey. If he travels 30% of the journey by train and 70% by road, he requires 12 hours to complete the same journey. If the average speed of the trains journey and road journey remain constant, find the ratio of the average speed of the train journey to the average speed of the train journey to the average speed of the road journey.

32) A two digit number when reversed becomes one less than thrice the original number. Find the original number.

33) In a management test, 3 marks are awarded for a correct answer and 1 mark is deducted for an incorrect one. There is no negative marking. Suresh attempted 70 out of 100 questions and managed to score 170 marks. Find the number of question correctly answered by Suresh.

34) How many two digit numbers are 72 less than the number obtained by reversing the digit of the original number?

35) On a certain island, there are coins available in only two denomination - Rs. 2 and Rs. 5. Suresh has 100 coins with him, such that the total amount is Rs. 350. How many Rs.2 coins does Suresh have?

36) A two digit number when reversed becomes three less than the four times the original value. Find the original number

37) The units digit of a certain two digit number is three more than the tens digit. Find the difference between the number and the number obtained by reversing the number.

38) Ramesh had twice as many 2 rupee coins as 5 rupee coins. Had the number of coins been interchanged, he would have had 30 rupees extra. How many coins did Ramesh have n all?

39) A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wages of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operator should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

40) Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English and only one Englishmen knows French. What is the minimum number of phone calls needed for the above purpose?

41) Consider a triangle drawn on the X - Y plane with its three vertices at (41, 0), (0, 41) and (0, 0) each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

42) The digits of a three-digit number A are written in the reverse order to form another three digit number B. If B > A and B - A is perfectly divisible by 7, then which of the following is necessarily true?

43) The total number of integer pairs (x, y) satisfying the equation x + y = xy is

44) The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the progression. Then, which element of the series should necessarily be equal to zero.

45) There are 8436 steel balls, each with a radius of 1 cm, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth and so on. The number of horizontal layers in the pile is

46) If the product of n positive real numbers is unity, then their sum is necessarily

47) If x and y are integers, then the equation 5 x + 19 y = 64 has

48) If x, y and z are real numbers such that, x + y + z = 5 and xy + y z + zx = 3. What is the largest value of that x can have?

49) A child was asked to add first few natural numbers (that is, 1 + 2 + 3 +...) so long his patience permitted. As he stopped he gave the sum as 575. When the teacher declared the result wrong the child discovered he had missed one number in the sequence during addition. The number he missed was

50) Let x, y and z be distinct integers. x and y are odd positive and z is even and positive. Which one of the following statements cannot be true?

51) If x > 5 and y < - 1, then which of the following statements is true?

52) Two men X and Y started working for a certain company at similar job on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?

53) x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < -7. Which of the following expressions will have the least value?

54) All the pages numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?

55) If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a) (1 + b) (1 + c)
(1 + d)?

56) For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?

57) Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

58) x > 2, y > - 1 then which of the following holds good?

59) A, B and C are 3 cities that form a triangle and where every city is connected to every other one by at least one direct root. There are 33 routes direct and indirect from A to C and there are 23 direct routes from B to A. How many direct routes are there from A to C?

60) One year payment to the servant is Rs. 90 plus one turban. The servant leaves after 9 months and receives Rs. 65 and a turban. Then, find the price of the turban

61) You can collect rubies and emeralds as many as you can. Each ruby is worth Rs. 4 crores and each emerald is worth of Rs. 5 crore. Each ruby weights 0.3 kg and each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What you should collect to get the maximum wealth?

62) P and Q are two integers such that (PQ) = 64. Which of the following cannot be value of P + Q?

63) If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13, then the numbers could be in the ratio

64) Once I had been to the post-office to buy stamps of five rupees, two rupees and one rupee. I paid the clerk Rs. 20 and since he did not have change, he gave me three more stamps of one rupee. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought.

65) When an inequation is multiplied or divide by same negative number, inequation —direction.

66) X < -3 implies -

67) A car manufacturing company manufactures cars of two types A and B. Model A require 150 man-hours for assembling, 50 man-hours for painting and 10 man-hours for checking and testing. Model B requires 60 man-hours for assembling, 40 man-hours for painting and 20 man-hours for checking and testing. There are available 30 thousand man-hours for assembling, 13 thousand man-hours for painting and 5 thousand man-hours for checking and testing. Express the above situation using linear inequalities. Let the company manufacture x units of type A model of car and y units of type B model of car. Then, the inequalities are:

68) The linear relationship between two variables in an inequality:

69) On the average an  experienced person does 7 units of work while a fresh one work 5 units of work daily but the employer has to maintain an output of at least 35 units of work per day. The situation can be expressed as:

70) An employer recruits experienced (x) and fresh (y) workmen for his under the condition that he cannot afford to employ more than 11 people. x and y can related by the inequality.

71) XYZ company has a policy for its recruitment as: it should not recruit more than 8 men (x) to 3 women (y). How can this fact be expressed in inequality?