Csat---math Questions
#1
A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively. [ U.P.S.C ( 2011 ) Pre. ]
#2
Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ? [ U.P.S.C ( 2011 ) Pre. ]
#3
A contract on construction job specifies a penalty for delay in completion of the work beyond a certain date is as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc. The penalty for each succeeding day being 50 more than that of the preceding day. How much penalty should the contractor pay if he delays the work by 10 days ? [ U.P.S.C ( 2011 ) Pre. ]
#4
A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose? [ U.P.S.C ( 2013 ) Pre. ]
#5
Five persons fire bullets at a target at an interval of 6,7,8,9 and 12 seconds respectively . The number of times they would fire the bullets together at the target in an hour is [ U.P.S.C ( 2014 ) Pre. ]
#6
For a charity show, the total tickets sold were 420. Half of these tickets were sold at the rate of Rs. 5 each, one-third at the rate of Rs. 3 each and the rest for Rs. 2 each. What was the total amount received ? [ U.P.S.C ( 2014 ) Pre. ]
#7
In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is [ U.P.S.C ( 2015 ) Pre. ]
#8
A cow costs more than 4 goats but less than 5 goats. If a goat costs between Rs. 600 and Rs. 800, which of the following is a most valid conclusion ? [ U.P.S.C ( 2015 ) Pre. ]
#9
There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed? [ U.P.S.C ( 2016 ) Pre. ]
#10
In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs. 2 by one student only, the total collection is Rs. 443. Then how many students are there in the class ? [ U.P.S.C ( 2016 ) Pre. ]
#11
In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ? [ U.P.S.C ( 2016 ) Pre. ]
#12
A daily train is to be introduced between station A and station B starting from each at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the shuttle service ? [ U.P.S.C ( 2016 ) Pre. ]
#13
In a question paper there are five questions to be attempted and answer to each question has two choices – True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is : [ U.P.S.C ( 2016 ) Pre. ]
#14
If R and S are different integers both divisible by 5, then which of the following is not necessarily true ? [ U.P.S.C ( 2016 ) Pre. ]
#15
How many numbers are there between 100 and 300 which either begin with or end with 2 ? [ U.P.S.C ( 2016 ) Pre. ]
#16
In a race, a competitor has to collect 6 apples which are kept in a straight line On a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart ? [ U.P.S.C ( 2016 ) Pre. ]
#17
A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target? [ U.P.S.C ( 2016 ) Pre. ]
#18
If there is a policy that 1/3rd of a population of a community has migrated every year from one place to some other place , what is the leftover population of that community after the sixth year , if there is no further growth in the population during this period ? [ U.P.S.C ( 2017 ) Pre. ]
#19
There are three pillars X,Y, and Z of different heights. Three spiders A,B and C start to climb on these pillars simultaneously. In one chance A climbs on X 6 cm but slips down 1 cm . B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm . If each of them requires 40 chances to reach the top of the pillars , what is the height of the shortest pillar ? [ U.P.S.C ( 2017 ) Pre. ]
#20
Certain 3-digit numbers have the following characteristics : 1. All the three digits are different. 2. The number is divisible by 7. 3. The number on reversing the digits is also divisible by 7. How many such 3-digit numbers are there ? [ U.P.S.C ( 2017 ) Pre. ]
#21
How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place? [ U.P.S.C ( 2017 ) Pre. ]
#22
A 2 – digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder ? [ U.P.S.C ( 2017 ) Pre. ]
#23
There are certain 2 – digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2- digit numbers are there ? [ U.P.S.C ( 2017 ) Pre. ]
#24
What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150 ? [ U.P.S.C ( 2017 ) Pre. ]
#25
If X is between -3 and -1, and Y is between -1 and 1, then X2 – Y2 is in between which of the following ? [ U.P.S.C ( 2018 ) Pre. ]
#26
X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number ? [ U.P.S.C ( 2018 ) Pre. ]
#27
A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, the difference between the first and last digits is [ U.P.S.C ( 2018 ) Pre. ]
#28
While writing all the numbers from 700 to 1000, how many numbers occur in which the digit at hundred’s place is greater than the digit at ten’s place, and the digit at ten’s place is greater than the digit at unit’s place? [ U.P.S.C ( 2018 ) Pre. ]
#29
A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults? [ U.P.S.C ( 2018 ) Pre. ]
#30
If x – y = 8, then which of the following must be true? [ U.P.S.C ( 2018 ) Pre. ] 1. Both x and y must be positive for any value of x and y. 2. If x is positive, y must be negative for any value of x and y. 3. If x is negative, y must be positive for any value of x and y. Select the correct answer using the code given below. [UPSC (2018)PRE]
#31
The number of times the digit 5 will appear while writing the integers from 1 to 1000 is [ U.P.S.C ( 2019 ) Pre. ]
#32
In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football ? [ U.P.S.C ( 2019 ) Pre. ]
#33
If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct ? [ U.P.S.C ( 2019 ) Pre. ]
#34
Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is [ U.P.S.C ( 2019 ) Pre. ]
#35
How many triplets (x, y, z) satisfy the equation x + y + z = 6, where x, y and z are natural numbers ? [ U.P.S.C ( 2019 ) Pre. ]
#36
An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible ? [ U.P.S.C ( 2019 ) Pre. ]
#37
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is [ U.P.S.C ( 2019 ) Pre. ]
#38
A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have ? [ U.P.S.C ( 2019 ) Pre. ]
#39
Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is [ U.P.S.C ( 2019 ) Pre. ]
#40
How many zeroes are there at the end of the following product ? 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60 [ U.P.S.C ( 2020 ) Pre. ]
#41
Let XYZ be a three-digit number, where (X+ Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [ U.P.S.C ( 2020 ) Pre. ]
#42
Let p, q, r and s be natural numbers such that p - 2016 = q + 2017 = r - 2018 = s + 2019. Which one of the following is the largest natural number ? [ U.P.S.C ( 2020 ) Pre. ]
#43
If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure ? [ U.P.S.C ( 2020 ) Pre. ]
#44
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195 . The torn page contains which of the following numbers ? [ U.P.S.C ( 2020 ) Pre. ]
#45
Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. The sum of the numbers is 15902 , then what is the difference between the values of A and D ? [ U.P.S.C ( 2020 ) Pre. ]
#46
How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4 ? [ U.P.S.C ( 2020 ) Pre. ]
#47
What is the largest number among the following ? [ U.P.S.C ( 2020 ) Pre. ]
#48
What is the greatest length x such that 3 1/2 m and 8 3/4 m are integral multiples of x? [ U.P.S.C ( 2020 ) Pre. ]
#49
The recurring decimal representation 1.272727 ..... is equivalent to [ U.P.S.C ( 2020 ) Pre. ]
#50
What is the least four – digit number when divided by 3,4,5 and 6 leaves a remainder 2 in each case ? [ U.P.S.C ( 2020 ) Pre. ]
#51
In adult Population or a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers ? [ U.P.S.C ( 2020 ) Pre. ]
#52
What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100 ? [ U.P.S.C ( 2020 ) Pre. ]
#53
A sum of Rs. 2500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6 . What is the difference between the maximum share and the minimum share? [ U.P.S.C ( 2020 ) Pre. ]
#54
For what value of n , the sum of digits in the number ( 10 ^ n + 1 ) is 2 ? [ U.P.S.C ( 2020 ) Pre. ]
#55
How many pairs of natural numbers are there such that the difference of whose squares is 63 ? [ U.P.S.C ( 2020 ) Pre. ]
#56
Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3 , 3/4 , 4/5 and 5/6 ? [ U.P.S.C ( 2020 ) Pre. ]
#57
A digit n > 3 is divisible by 3 but not divisible by 6 . Which one of the following is divisible by 4 ? [ U.P.S.C ( 2020 ) Pre. ]
#58
If 1 litre of water weighs 1 kg, then how many cubic millimetres of water will weigh 0.1 gm ? [ U.P.S.C ( 2020 ) Pre. ]
#59
A frog tries to come out of a dried well 4.5 m deep with slippery walls . Every time the frog jumps 30 cm , slides down 15 cm .What is the number of jumps required for the frog to come out of the well ? [ U.P.S.C ( 2020 ) Pre. ]
#60
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English, The number of Indians who can speak English is [U.P.S.C ( 2021 ) Pre.]
#61
Consider all 3 – digit numbers ( without repetition of digits ) obtained using three non – zero digits which are multiples of 3 . Let S be their sum . Which of the following is/are correct ? 1. S is always divisible by 74 . 2. S is always divisible by 9 . Select the correct answer using the code given below : [ U.P.S.C ( 2021 ) Pre. ]
#62
Integers are listed from 700 to 1000 . In how many integers is the sum of the digits 10 ? [ U.P.S.C ( 2021 ) Pre. ]
#63
A boy plays with a ball and he drops it from a height of 1.5 m . Every time the ball hits the ground , it bounces back to attain a height 4/5th of the previous height . The ball does not bounce further if the previous height is less than 50 cm . What is the number of times the ball hits the ground before the ball stops bouncing ? [ U.P.S.C ( 2021 ) Pre. ]
#64
If 3 2019 is divided by 10, then what is the remainder? [ U.P.S.C ( 2021 ) Pre. ]
#65
The number 3798125P369 is divisible by 7 . What is the value of the digit P ? [ U.P.S.C ( 2021 ) Pre. ]
#66
From January 1, 2021, the price of petrol (in Rupees per litre) on m' day of the year is 80 + 0.1m, where m = 1, 2, 3, …., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0-15n for any n. On which date in the year 2021 are the prices of these two fuels equal ? [ U.P.S.C ( 2021 ) Pre. ]
#67
A biology class at high school predictor that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population ? [ U.P.S.C ( 2021 ) Pre. ]
#68
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ? [ U.P.S.C ( 2021 ) Pre. ]
#69
The difference between a 2 - digit number and the number obtained by interchanging the positions of the digits is 54 . Consider the following statements : 1. The sum of the two digits of the number can be determined only if the product of the two digits is known . 2. The difference between the two digits of the number can be determined . Which of the above statements is/are correct ? [ U.P.S.C ( 2021 ) Pre. ]
#70
When a certain number is multiplied by 7, the product comprises ones only ( 1111...) . What is the smallest such number ? [ U.P.S.C ( 2021 ) Pre. ]
#71
Using 2,2,3,3,3 as digits , how many distinct numbers greater than 30000 can be formed ? [ U.P.S.C ( 2021 ) Pre. ]
#72
Consider the following statements : 1. The sum of 5 consecutive integers can be 100 . 2. The product of three consecutive natural numbers can be equal to their sum . Which of the above statements is/are correct ? [ U.P.S.C ( 2021 ) Pre. ]
#73
Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store .If Jay bought 3 pens and 5 pencils , and Vijay bought 2 pens and 7 pencils , then which one of the following is correct ? [ U.P.S.C ( 2021 ) Pre. ]
#74
A person P asks one of his three friends X as to how much money he had .X replied , “If Y gives me ₹ 40 then Y will have half of as much as Z , but if Z gives me ₹ 40 ,then three of us will have equal amount ” . What is the total amount of money that X,Y and Z have ? [ U.P.S.C ( 2021 ) Pre. ]
#75
In an objective type test of 90 questions , 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer . After attempting all the 90 questions, a student got a total of 387 marks . What is the number of incorrect responses ? [ U.P.S.C ( 2021 ) Pre. ]
#76
Consider the following addition problem : 3 P + 4P + PP + PP = RQ2 ; where P, Q and R are different digits . What is the arithmetic mean of all such possible sums ? [ U.P.S.C ( 2021 ) Pre. ]
#77
Consider the following multiplication problem : ( PQ ) × 3 = RQQ , where P , Q and R are different digits and R ≠ 0 . What is the value of ( P + R ) ÷ Q ? [ U.P.S.C ( 2021 ) Pre. ]
#78
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only) . The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number? [ U.P.S.C ( 2022 ) Pre. ]
#79
A bill for ₹ 1,840 is paid in the denominations of 50, 20 and 10 notes. 50 notes in all are used. Consider the following statements : 1. 25 notes of 50 are used and the remaining are in the denominations of 20 and 10. 2. 35 notes of 20 are used and the remaining are in the denominations of 50 and 10. 3. 20 notes of 10 are used and the remaining are in the denominations of 50 and 20. Which of the above statements are not correct? [ U.P.S.C ( 2022 ) Pre. ]
#80
Which number amongst 2 40 , 3 21 , 4 18 and 8 12 is the smallest ? [ U.P.S.C ( 2022 ) Pre. ]
#81
On one side of a 1.01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants? [ U.P.S.C ( 2022 ) Pre. ]
#82
A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two-digit number. How many coins does A have in the beginning ? [ U.P.S.C ( 2022 ) Pre. ]
#83
Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements : 1. The 4-digit least value of x is 1332. 2. The 3-digit greatest value of x is 888 . Which of the above statements is/are correct ? [ U.P.S.C ( 2022 ) Pre. ]
#84
What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261? [ U.P.S.C ( 2022 ) Pre.]
#85
15 × 14 × 13 × ... × 3 × 2 × 1 = 3 m × n Where m and n are positive integers, then what is the maximum value of m? [ U.P.S.C ( 2022 ) Pre.]
#86
What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits? [ U.P.S.C ( 2022 ) Pre.]
#87
Five friends P. O, X, Y and Z purchased some notebooks. The relevant information is given below : [ U.P.S.C ( 2022 ) Pre.] 1. Z purchased 8 notebooks more than X did. 2. P and together purchased 21 notebooks. 3. O purchased 5 notebooks less than P did. 4. X and Y together purchased 28 notebooks. 5. P purchased 5 notebooks more than X did. If each notebook is priced 40, then what is the total cost of all the notebooks?
#88
A person X wants to distribute some pens among six children A B C D E and F. Suppose A gets twice the number of pens received by three times that of four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number ? [ U.P.S.C ( 2022 ) Pre.]
#89
What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3 ? [ U.P.S.C ( 2022 ) Pre.]
#90
Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q ? [ U.P.S.C ( 2022 ) Pre.]
#91
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number : [ U.P.S.C ( 2022 ) Pre.] 1. p x q can be an odd number. 2. q / p can be a prime number. 3. p + q can be a prime number. Which of the above statements are correct ?
#92
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible? [ U.P.S.C ( 2023 ) Pre.]
#93
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of ( p + q ) ( r + s ) ? [ U.P.S.C ( 2023 ) Pre.]
#94
A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13 ? [ U.P.S.C ( 2023 ) Pre.]
#95
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number? [ U.P.S.C ( 2023 ) Pre.]
#96
What is the sum of all digits which appear in all the integers from 10 to 100 ? [ U.P.S.C ( 2023 ) Pre.]
#97
Three of the five positive integers p, q, r, s, t are even and two of them are odd ( not necessarily in order ). Consider the following : 1. p + q + r – s - t is definitely even . 2. 2p + q + 2r - 2s + t is definitely odd . Which of the above statements is/are correct ? [ U.P.S.C ( 2023 ) Pre.]
#98
Consider the following in respect of prime number p and composite number c. 1. 𝑝+𝑐 / 𝑝−𝑐 can be even. [ U.P.S.C ( 2023 ) Pre.] 2. 2p+c can be odd. 3. pc can be odd. Which of the statements given above are correct ?
#99
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+C ? [ U.P.S.C ( 2023 ) Pre.]
#100
For any choices of values of X, Y and Z, the 6 digit number of the form XYZXYZ is divisible by : [ U.P.S.C ( 2023 ) Pre.]
#101
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions ? [ U.P.S.C ( 2023 ) Pre.]
#102
What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100 ? [ U.P.S.C ( 2023 ) Pre.]
#103
What is the unit digit in the expansion of (57242) 9×7×5×3×1 ? [ U.P.S.C ( 2023 ) Pre.]
#104
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E, and F are distinct non - zero digits such that ABC+ DEF= 1111, then what is the value of A+B+C+D+E+F ? [ U.P.S.C ( 2023 ) Pre.]
#105
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D ? [ U.P.S.C ( 2023 ) Pre.]
#106
What is the remainder if 2 192 is divided by 6 ? [ U.P.S.C ( 2023 ) Pre.]
#107
AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D. E, F, G, H, I are distinct digits. If E= 0, F=8, then what is A+B+C equal to ? [ U.P.S.C ( 2023 ) Pre.]
#108
There are large number of silver coins weighing 2gm, 5gm, 10gm, 25gm, 50gm each. Consider the following statements : 1. To buy 78 gm of coins one must buy at least 7 coins. 2. To weigh 78 gm using these coins one can use less than 7 coins. Which of the statements given above is/are correct? [ U.P.S.C ( 2023 ) Pre.]
#109
How many natural numbers are there which given a remainder of 31 when 1186 is divided by these natural numbers? [ U.P.S.C ( 2023 ) Pre.]
#110
Let pp, qq and rr be 2 digit numbers where p < q < r. If pp + qq + rr =tt0, where tt0 is a 3 digit number ending with zero, consider the following statements : 1. The number of possible values of p is 5. 2. The number of possible values of q is 6 Which of the above statements is/are correct? [ U.P.S.C ( 2023 ) Pre.]
#111