# Practice Test

Q1) If a+b = 9 and ab=19.25, then which of these is a possible value of (a-b)? Show Answer

Q2) Find the value of m, from the following simultaneous equations.
15m+17n=21
17m+15n=11

Q3) 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? Show Answer

Q4) 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. Show Answer

Q5) 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.

Q6) 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? Show Answer

Q7) 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? Show Answer

Q8) 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? Show Answer

Q9) 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.

Q10) 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. Show Answer

Q11) 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?

Q12) 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? Show Answer

Q13) 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. Show Answer

Q14) 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. Show Answer

Q15) 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.

Q16) The difference between two numbers is 3 and the sum of their squares is 29. Find the product of those two numbers. Show Answer

Q17) If -2 < x < 7 and 3 < y < 5, then which of the following is true?

Q18) If x and y are two unequal positive numbers, then which of the following is definitely true? Show Answer

Q19) If a + b = 11 and ab = 30 then the value of (a - b) could be : Show Answer

Q20) find the value of x,if 7x+8(2 - x) + 10 = 4x - 4 Show Answer

Q21) 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 Show Answer

Q22) 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. Show Answer

Q23) A two digit number when reversed becomes one less than thrice the original number. Find the original number. Show Answer

Q24) 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. Show Answer

Q25) How many two digit numbers are 72 less than the number obtained by reversing the digit of the original number? Show Answer

Q26) 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? Show Answer

Q27) A two digit number when reversed becomes three less than the four times the original value. Find the original number Show Answer

Q28) 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. Show Answer

Q29) 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? Show Answer

Q30) For general n, how many enemies will each member of S have? Show Answer

Q31) For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members? Show Answer

Q32) Consider the set S = {1, 2, 3, ..., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements? Show Answer

Q33) 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? Show Answer

Q34) 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? Show Answer

Q35) 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 Show Answer

Q36) 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? Show Answer

Q37) The total number of integer pairs (x, y) satisfying the equation x + y = xy is Show Answer

Q38) 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. Show Answer

Q39) 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 Show Answer

Q40) If the product of n positive real numbers is unity, then their sum is necessarily Show Answer

Q41) If x and y are integers, then the equation 5 x + 19 y = 64 has Show Answer

Q42) 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? Show Answer

Q43) Amol was asked to calculate the arithmetic mean of ten positive integers each of which had two digits. By mistake, he interchanged the two digits, say a and b, in one of these ten integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then b - a equals Show Answer

Q44) 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 Show Answer

Q45) 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? Show Answer

Q46) If x > 5 and y < - 1, then which of the following statements is true? Show Answer

Q47) 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? Show Answer

Q48) 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? Show Answer

Q49) 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? Show Answer

Q50) 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)

Q51) 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? Show Answer

Q52) 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? Show Answer

Q53) x > 2, y > - 1 then which of the following holds good? Show Answer

Q54) 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? Show Answer

Q55) What is the maximum possible value of m? Show Answer

Q56) If m is maximum, then what is minimum number of white vessels required to empty it? Show Answer

Q57) If m is maximum, then what is range of the volume remaining empty in the vessel with the maximum empty space Show Answer

Q58) 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 Show Answer

Q59) 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? Show Answer

Q60) P and Q are two integers such that (PQ) = 64. Which of the following cannot be value of P + Q? Show Answer

Q61) If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13, then the numbers could be in the ratio Show Answer

Q62) Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression? Show Answer

Q63) 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. Show Answer

Q64) A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Show Answer

Q65) There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: Show Answer

Q66) The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: Show Answer

Q67) The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? Show Answer

Q68) One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ? Show Answer

Q69) Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: Show Answer

Q70) A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: Show Answer

Q71) To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ? Show Answer

Q72) In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? Show Answer

Q73) Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ? Show Answer

Q74) A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: Show Answer

Q75) David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ? Show Answer