Quant Boosters  Kamal Lohia  Set 6

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]

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]

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]

Q15) 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]

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)

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)

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)

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)

Q20) Visitors to a show were charged Rs. 15.00 each on the first day, Rs. 7.50 on the second day, Rs. 2.50 on the third day and total attendance on the three days were in the ratio 2:5:13 respectively. The average charge per person for the whole show is
a. Rs 3.00
b. Rs 4.50
c. Rs 5.00
d. Rs 7.50
e. Rs 8.00OA : c (Rs 5.00)

Q21) In a class there are three divisions. The number of students and the average marks in mathematics in the three divisions are 30, 40, 30 and 40%, 30% and 50% respectively. What are the average marks in mathematics of the class?
a. 39%
b. 40%
c. 41%
d. 49%
e. 51%OA : a (39%)