Practice Test

Q1) How many terms are there in AP 20, 25, 30, .....130. Show Answer

Q2) Bobby was appointed to AMS Careers in the pay scale of Rs. 7000-500-12,500. Find how many years he will take to reach the maximum of the scale. Show Answer

Q3) Find the 1st term of an AP whose 8th and 12th terms are respectively 39 and 59. Show Answer

Q4) A number of squares are described whose perimeters are in GP. Then their sides will be in: Show Answer

Q5) There is an AP 1, 3, 5 .....Which term of this AP is 55 ? Show Answer

Q6) How many terms are identical in the two APs 1, 3, 5, ....upto 120 terms and 3, 6, 9, .... upto 80 terms ? Show Answer

Q7) Find the lowest number in an AP such that the sum of all the terms is 105 and greatest term is 6 times the least. Show Answer

Q8) Find the 15th term of the sequence 20, 15, 10..... Show Answer

Q9) A sum of money kept in a bank amounts to Rs. 1240 in 4 years and Rs. 1600 in 10 years at simple Interest. Find the sum. Show Answer

Q10) A number 15 is divided into three parts which are in AP and the sum of their squares is 83. Find the smallest number. Show Answer

Q11) The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is Show Answer

Q12) The number of terms of series 54 + 51 + 48 + .....such that the sum is 513 is Show Answer

Q13) The least value of n for which the sum of the series 5 + 8 + 11 .... n terms is not less than 670 is Show Answer

Q14) A man receives Rs.60 for the first week and Rs.3 more each week than the proceeding week. How many does he earn by the 20th week ? Show Answer

Q15) How many terms are there in the GP 5, 20, 80, 320, .....20480 ? Show Answer

Q16) A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on the third day and so on. How much will the boy get if he starts working on the 1st of February and finishes on the 20th of February ? Show Answer

Q17) If the fifth term of GP is 81 and first term is 16, what will be the 4th term of the GP ? Show Answer

Q18) The seventh term of a GP is 8 times the fourth term. What will be the first term when its fifth term is 48 ? Show Answer

Q19) The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this AP ? Show Answer

Q20) The sum of three numbers in a GP is 14 and the sum of their squares is 84. Find the largest number. Show Answer

Q21) How many natural numbers between 300 to 500 are multiples of 7? Show Answer

Q22) The sum of the first and the third term of a geometric progression is 20 and the sum of its first three terms is 26. Find the progression. Show Answer

Q23) If a man saves Rs.4 more each year than he did the year before and if he saves Rs.20 in the first year, after how many years will his savings be more than Rs.1000 altogether ? Show Answer

Q24) A man's salary is Rs.800 per month in the first year. He has joined in the scale of 800-40-600. After how many years will his savings be Rs.64,800 ? Show Answer

Q25) The 4th and the 10th term of an GP are 1/3 and 243 respectively. Find the 2nd term. Show Answer

Q26) The 7th and 21st terms of an AP are 6 and -22 respectively. Find the 26th term. Show Answer

Q27) The sum of 5 numbers in AP is 30 and the sum of their squares is 220. Which of the following is the third term ? Show Answer

Q28) Find the sum of all numbers in between 10-50 excluding all those numbers which are divisible by 8. (include 10 and 50 for counting). Show Answer

Q29) Find the general term of the GP with with the third term 1 and the seventh term 8. Show Answer

Q30) Find the number of terms of the series 1/81, -1/27, 1/9,....-729. Show Answer

Q31) Four geometric means are inserted between 1/8 and 128. Find the third geometric mean. Show Answer

Q32) A and B are two numbers whose AM is 25 and GM is 7. Which of the following may be a value of A? Show Answer

Q33) Two numbers A and B are such that their GM is 20% lower than their AM. Find the ratio between the numbers. Show Answer

Q34) A man saves Rs.100 in January 2002 and increases his saving by Rs.50 every month over the previous month. What is the annual saving for the man in the year 2002 ? Show Answer

Q35) In a nuclear power plant a technician is allowed an interval of maximum 100 minutes. A timer with a bell rings at specific intervals of time such that the minutes when the timer rings are not divisible by 2, 3, 5 and 7. The last alarm rings with a buzzer to give time for decontamination of the technician. How many times will the bell ring within these 100 minutes and what is the value of the last minute when the bell rings for the last time in a 100 minute shift ? Show Answer

Q36) The 1st, 8th and 22nd terms of an AP are three consecutive terms of a GP. Find the common ratio of the GP, given that the sum of the first twenty-two terms of the AP is 385. Show Answer

Q37) After striking a floor a rubber ball rebounds (7/8)th of the height from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of 420 meters ? Show Answer

Q38) Each of the series 13 + 15 + 17 + .... and 14 + 17 + 20 + .... is continued to 100 terms. Find how many terms are identical between the two series ? Show Answer

Q39) Jack and Jill were playing mathematical puzzles with each other. Jill drew a square of sides 8 cm and then kept on drawing squares inside the squares by joining the mid points of the squares. She continued this process indefinitely. Jill asked Jack to determine the sum of the areas of all the squares that she drew. If Jack answered correctly then what would be his answer ? Show Answer

Q40) How many terms of series 1 + 3 + 5 + 7 + .... amount to 123454321 ? Show Answer

Q41) A student takes a test consisting of 100 questions with differential marketing is told that each question after the first is worth 4 marks more than the preceding question. If the third question of the test is worth 9 marks. What is the maximum score that the student can obtain by attempting 98 questions ? Show Answer

Q42) In an infinite geometric progression, each term is equal to 3 times the sum of the terms that follow. If the first term of the series is 8, find the sum of the series ? Show Answer

Q43) What is the maximum sum of the terms in the arithmetic progression 25, 24 1/2, 24, .....? Show Answer

Q44) An equilateral triangle is drawn by joining the mid-points of the sides of another equilateral triangle. A third equilateral triangle is drawn inside the second one joining the midpoints of the sides of the second equilateral triangle, and the process continues infinitely. Find the sum of the perimeters of all the equilateral triangles, if the side of the largest equilateral triangle is 24 units. Show Answer

Q45) The sum of the first two terms of an infinite geometric series is 18. Also, each term of the series is seven times the sum of all the terms that follow. Find the first term and the common ratio of the series respectively. Show Answer

Q46) Find the 33rd term of the sequence: 3, 8, 9, 13, 15, 18, 21, 23.... Show Answer

Q47) Find the sum of the series till the 33rd terms of the sequence: 3, 8, 9, 13, 15, 18, 21, 23.... Show Answer

Q48) The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88. Find the sum of the first 16 terms of the AP ? Show Answer

Q49) If a times the ath term of an AP is equal to b time the bth term, find the (a+b)th term. Show Answer

Q50) A number 20 is divided into four parts that are in AP such that the product of the first and fourth is to the product of the second and third is 2:3. Find the largest part. Show Answer

Q51) Find the value of the expression: 1 - 4 + 5 - 8 ....to 50 terms Show Answer

Q52) If a clock strikes once at one o'clock, twice at two o'clock and twelve times at 12 o'clock and again once at one o'clock and so on, how many times will the bell be struck in the course of 2 days ? Show Answer

Q53) What will be the maximum sum of 44, 42, 40 ....? Show Answer

Q54) Find the sum of the integers between 1 and 200 that are multiples of 7 ? Show Answer

Q55) If the mth term of an AP is 1/n and nth term is 1/m, then find the sum to mn terms. Show Answer

Q56) find the sum of all odd numbers lying between 100 and 200. Show Answer

Q57) Find the sum of all integers of 3 digits that are divisible by 7. Show Answer

Q58) The first and the last terms of an AP are 107 and 253. If there are five terms in this sequence, find the sum of sequence. Show Answer

Q59) Find the value of 1 - 2 - 3 + 2 - 3 - 4 +...+ upto 100 terms. Show Answer

Q60) What will be the sum to n terms of the series 8 + 88 +888 + .... ? Show Answer

Q61) If a, b, c are in GP, then log a, log b, log c are in Show Answer

Q62) After striking the floor, a rubber ball rebounds to 4/5th of the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres. Show Answer

Q63) The sum of an infinite GP whose common ratio is numerically less than 1 is 32 and the sum of the first two terms is 24. What will be the third term ? Show Answer

Q64) Determine the first term of the geometric progression, the sum of whose first term and third term is 40 and the sum of the second term and fourth term is 80. Show Answer

Q65) Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to -3. Show Answer

Q66) The sum of the second and the fifth term of an AP is 8 and that of the third and the seventh term is 14. Find the eleventh term. Show Answer

Q67) How many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and the difference between the seventh and the second term is 20 ? Show Answer

Q68) Four numbers are inserted between the numbers 4 and 39 such that an AP results. Find the biggest of these four numbers. Show Answer

Q69) Find the sum of all three digit natural numbers, which on being divided by 5, leave a remainder equal to 4. Show Answer

Q70) The sum of the first three terms of the arithmetic progression is 30 and the sum of the squares of the first term and the second term of the same progression is 116. Find the seventh term of the progression if its fifth term is known to be exactly divisible by 14. Show Answer

Q71) A and B set out to meet each other from two places 165 km apart. A travels 15 km the first day, 14 km the second day, 13 km the third day and so on. B travels 10 km the first day, 12 km the second day, 14 km the third day and so on. After how many days will they meet ? Show Answer

Q72) If a man saves Rs.1000 each year and invests at the end of the year at 5% compound interest, how much will the amount be at the end of 15 years ? Show Answer

Q73) If sum to n terms of a series is given by (n+8), then its second term will be given by Show Answer

Q74) If A is the sum of the n terms of the series 1+ 1/4 + 1/6 + .... and B is the sum of 2n terms of the series 1 + 1/2 + 1/4 + ....., then find the value of A/B. Show Answer

Q75) A man receives a pension starting with Rs. 100 for the first year. Each year he receives 90% of what he received the previous year. Find the maximum total amount he can receive even if he lives forever. Show Answer

Q76) The sum of the series represented as: 1/1 x 5 + 1/5 x 9 + 1/9 x 13 ...... + 1/221 x 225 is Show Answer

Q77) Find the infinite sum of the series 1/1 + 1/3 + 1/6 + 1/10 + 1/15 ..... Show Answer

Q78) The sum of the series 5 x 8 + 8 x 11 + 11 x 14 upto n terms will be : Show Answer

Q79) The sum of the series: 1/2 + 1/6 + 1/12 + 1/20 + ......1/156 + 1/182 is: Show Answer

Q80) What is the sum of the series if taken to infinite terms: 1/2 + 1/6 + 1/12 + 1/20 + ......1/156 + 1/182 is: Show Answer

Q81) All values in A are changed in sign, while those in B remain unchanged. Which of the following statements is true ? Show Answer

Q82) Every element of A is made greater than or equal to every element of B by adding to each element of A an integer x. then, x cannot be less than: Show Answer

Q83) Rohit drew a rectangular grid of 529 cells, arranged in 23 Rows and 23 columns, and filled with a number. The numbers with which he filled each cell were such that the numbers of each taken from left to right formed an arithmetic series and the numbers of each column taken from top to bottom also formed an arithmetic series. The seventh and the seventeenth number of he fifth row were 47 and 63 respectively, while the seventh and the seventeenth numbers of the fifteenth row were 53 and 77 respectively. What is the sum of all the numbers in the grid ? Show Answer

Q84) How many three digit numbers have the property that their digits taken from left to right form an Arithmetic or a Geometric Progression ? Show Answer

Q85) How many burgers per day are made with cheese and tomato as fillings ? Show Answer

Q86) How many burgers are made with all three fillings chicken, vegetable and mushroom ? Show Answer

Q87) If in any decreasing arithmetic progression, sum of all its terms, except for the first term, is equal to -36, the sum of all its terms, except for the last term, is zero and the difference of the tenth and the sixth term is equal to -16, then what will be first term of this series ? Show Answer

Q88) The sum of all terms of the arithmetic progression having ten terms except for the first term, is 99, and except for the sixth term, 89. find the third term of the progression if the sum of the first and the fifth term is equal to 10. Show Answer

Q89) Product of the fourth term and the fifth term of an arithmetic progression is 456. Division of the ninth term by the fourth term of the progression gives quotient as 11 and the remainder as 10. Find the first term of the progression. Show Answer

Q90) A number of saplings are lying at a place by the side of a straight road. These are to be planted in a straight line at a distance interval of 10 metres between two consecutive saplings. Mithilesh, the country's greatest forester, can carry only one sapling at a time and has to move back to the original point to get the next sapling. In this manner he covers a total distance of 1.32 kms. How many saplings does he plant in the process if he ends at the starting point ? Show Answer

Q91) The first and the third terms of the arithmetic progression are equal, respectively, to the first and the third term of the geometric progression and the second term of the arithmetic progression exceeds the second term of the geometric progression by 0.25. Calculate the sum of the first five terms of the arithmetic progression if its first term is equal to 2. Show Answer

Q92) If (2 + 4 + 6 + ....50 terms)/(1 + 3 + 5 + ...... n terms) = 51/2, then find the value of n. Show Answer

Q93) Find the sum to n terms of the series 11 + 103 + 1005 + ...... Show Answer

Q94) The sum of the first term and the fifth term of an AP is 26 and the product of the second term by the fourth term is 160. Find the sum of the first seven terms of this AP. Show Answer

Q95) The sum of the third and the ninth term of an AP is 10. Find a possible sum of the first 11 terms of this AP. Show Answer

Q96) The sum of the squares of the fifth and he eleventh term of an AP is 3 and the product of the second and the fourteenth term is equal it P. Find the product of the first and the fifteenth term of the AP. Show Answer

Q97) If the ratio of harmonic mean of two numbers to their geometric mean is 12:13, find the ratio of the numbers. Show Answer

Q98) Find the sum of all possible whole number divisors of 720. Show Answer

Q99) The sum of first 20 and first 50 terms of an AP is 420 and 2550. Find the eleventh term of a GP whose first term is the same as the AP and the common ratio of the GP is equal to the common difference of the AP. Show Answer

Q100) If the first two terms of a HP are 2/5 and 12/13 respectively, which of the following terms is the largest term ? Show Answer

Q101) One side of the stair case is to be closed in by rectangular planks from the floor to each step. The width of each plank is 9 inches and their height are successively 6 inches, 12 inches, 18 inches and so on. There are 24 planks required in total. Find the area in square feet. Show Answer

Q102) The middle points of the sides of a triangle are joined forming a second triangle. Again a third triangle is formed by joining the middle points of this second triangle and this process is repeated infinitely. If the perimeter and area of the outer triangle are P and A respectively, what will be the sum of perimeters of triangles thus formed ? Show Answer

Q103) The middle points of the sides of a triangle are joined forming a second triangle. Again a third triangle is formed by joining the middle points of this second triangle and this process is repeated infinitely. If the perimeter and area of the outer triangle are P and A respectively, find the sum of all the triangles. Show Answer

Q104) A square has a side of 40 cm. Another square is formed by joining the mid-points of the sides of the given square and this process is repeated infinitely. find the perimeter of all the square thus formed. Show Answer

Q105) A square has a side of 40 cm. Another square is formed by joining the mid-points of the sides of the given square and this process is repeated infinitely. find the area of all the square thus formed. Show Answer

Q106) The sum of the first n terms of the arithmetic progression is equal to half the sum of the next n terms of the same progression. Find the ratio of the sum of the first 3n terms of the progression to the sum of its first n terms. Show Answer

Q107) In a certain colony of cancerous cells, each cell break into two new cells every hour. If there is a single productive cell at the start and this process continues for 9 hours, how many cells will the colony have at the end of 9 hours? It is known that the life of an individual cell is 20 hours. Show Answer

Q108) Find the sum of all three-digit whole numbers less than 500 that leave a remainder of 2 when they are divided by 3. Show Answer

Q109) If p, q, r are three consecutive distinct natural numbers then the expression (q + r - p)(p + r - q)(p + q - r) is Show Answer

Q110) If the harmonic mean between two positive numbers is to the inverse of their geometric mean as 12:13; then the numbers could be in the ratio. Show Answer

Q111) Fourth term of an arithmetic progression is 8. What is sum of the first 7 terms of the arithmetic progression ? Show Answer

Q112) Let x 0.50, 0 < y < 1, z > 1. Given a set of numbers, the middle number when they arranged in ascending order is called the median. So the median of the numbers x, y and z would be Show Answer

Q113) Let a, b, c, d, and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer ? Show Answer

Q114) If a, a + 2, and a + 4 are prime numbers, then the number of possible solutions for a is : Show Answer

Q115) Let x and y be positive integers such that x is prime and y is composite. Then, Show Answer

Q116) Let n(>1) be a composite natural number such that the square root of n is not an integer. Consider the following statements:
A: n has a factor which is greater than 1 and less than square root n
B: n has a factor which is greater than square root n but less than n, Then Show Answer

Q117) W1, W2, ......, W7 are 7 positive integral values such that by attaching the coefficients of +1, 0 and -1 to each value available and adding the resultant values, any number from 1 to 1093 (both included) could be formed. If W1, W2, ...., W7 are in ascending order, then what is the value of W3 ? Show Answer