CAT Question Bank  Kamal Lohia

kamal_lohia last edited by zabeer
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Number of Questions: 100
Topic: Quant Mixed Bag
Answer key available?: Yes
Source: Quant Masters Forum

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q1) From a set of first 20 consecutive positive integers, 3 are picked randomly and their sum is found as S. How many different values of S are possible?
A. 18
B. 52
C. 57
D. 1140[OA: B]

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q2) TGₐ is a two digit number in basea such that T > 0 and T, G < a. For which value of TG, can TGₐ be a perfect square in some basea?
A. 32
B. 43
C. both of these
D. none of these[OA : D]

Q3) Find the remainder when 484848 is divided by 728.
A. 0
B. 28
C. 48
D. none of these[OA: A]

Q4) How many distinct integers are there in the sequence [1²/100], [2²/100], [3²/100], [4²/100]... [100²/100] where [x] is greatest integer less than or equal to x?
A. 75
B. 76
C. 100
D. 101[OA : B]

Q5) Sum of ten consecutive integers is N. What is the sum of next ten consecutive integers?
A. 2N
B. N + 45
C. N + 55
D. N + 100[OA : D]

Q6) How many 21 digit numbers are there whose first 10 digits are 1 each and last 10 digits are 2 each and also the complete 21 digit number is divisible by 7?
A. 0
B. 1
C. 2
D. 3[OA : C]

Q7) What is the highest possible common factor of two consecutive terms of a sequence whose nth term is given by n² + 10?
A. 1
B. 2
C. 41
D. 59[OA : C]

Q8) On planet LOGIKA, an alien digit φ is being used between 3 and 4 along with all the usual digit we use on earth. What will be the age of a 94 years old inhabitant of LOGIKA on earth?
A. 103
B. 104
C. 114
D. 115[OA : D]

Q9) Nimai wrote all natural numbers, none of whose digits is a prime number, in order. First ten numbers which Nimai wrote are as follows: 1, 4, 6, 8, 9, 10, 11, 14, 16, 18. What is the 123rd number, Nimai might be writing?
A. 646
B. 666
C. 816
D. 840[OA: C]

Q10) What is the highest power of 2 which divides [10²ºººº/(10¹ºº + 2)] completely where [x] is greatest integer less than or equal to x?
A. 99
B. 100
C. 199
D. 200[OA : C]

Q11) Number of factors of 12100 which are less than 110 but not factors of 110 is
A. 6
B. 7
C. 8
D. 9[OA : A]

Q12) For how many positive integers, N there are odd number of factors of N² + 3N + 13?
A. 0
B. 1
C. 2
D. 3[OA : B]

Q13) Find the remainder when 6{(p  4)!} is divided by p where p is a prime number greater than 2013.
A. 0
B. 1
C. p  1
D. none of these[OA: B]

Q14) Number of factors of P is Q. Number of factors of Q is R. Number of factors of R is S and number of factors of S is 3. If P is smallest such number then what is the sum of digits of P?
A. 3
B. 6
C. 9
D. 12[OA : B]

Q 15) In how many ways can 100 be written as sum of two or more consecutive odd integers?
A. 2
B. 3
C. 4
D. 5[OA : D]

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q16) The average age of a group of boys is 18 years, while that of girls is 16 years. The average age of the class is 16.4 years. Find the maximum number of boys in the class given that the strength of class is a two digit number.
a. 99
b. 59
c. 31
d. 19
e. 16OA : d (19)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q17) Out of 12 clerks in an office, one getting a salary of Rs.350 was sacked and a new one was appointed. The average salary was now reduced by 5. Determine the salary paid to new clerk.
a. 370
b. 340
c. 310
d. 290
e. 285OA : d (290)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q18) The batting average for 40 innings of a cricketer is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of player?
a. 176
b. 175
c. 174
d. 173
e. 172OA : c (174)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q19) 40% of the employees of a certain company are men, and 75% of the men earned more than 25000/ per year. If 45% of the company's employees earned more than 25000/ per year, what fraction of the women employed by the company earned 25000/ per year or less? [CAT1999]
a. 1/4
b. 3/4
c. 1/3
d. 2/11
e. 8/11OA : b (3/4)