Quant Boosters  Kamal Lohia  Set 6

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]

kamal_lohia last edited by zabeer
Faculty and Content Developer at Tathagat  Delhi College of Engineering
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]

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)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
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)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
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%)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q22) Five years ago average age of P and Q was 15 years. Average age of P, Q and R today is 21 years. How old R will be after 10 years.
a. 31
b. 32
c. 33
d. 34
e. 35OA : c (33)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q23) Shweta took a loan of Rs.24000 for purchasing a TV. After two years, she paid it off by Rs.27840. Find the rate of simple interest.
a. 12%
b. 8%
c. 10%
d. 15%
e. 6%OA : b (8%)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q24) There are two equal capacity vessels full of milk solution with milk and water in the ratio 1:3 and 3:5 respectively. If both are mixed in the ratio 3:2, what would be the ratio of milk and water in the new mixture?
a. 3 : 10
b. 4 : 7
c. 3 : 7
d. 9 : 19
e. None of theseOA : c (3 : 7)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q25) Ram prepares solutions of alcohol in water according to customers' needs. This morning Ram has prepared 27 liters of a 12% alcohol solution and kept it ready in a 27 liter delivery container to be shipped to the customer. Just before delivery, he finds that the customer had asked for 27 liters of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many liters of 12% solution is replaced? [XAT2012]
a. 5
b. 9
c. 10
d. 12
e. 15OA : b (9)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q26) A man borrows Rs.6000 at 5% interest, on reducing balance, at the start of the year. If he repays Rs.1200 at the end of each year, find the amount of loan outstanding at the beginning of third year. [XAT2012]
a. 3162.75
b. 4145.00
c. 4155.00
d. 5100.00
e. 5355.00OA : c (4155)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q27) After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark his goods? [CAT1997]
a. 28.56%
b. 35%
c. 22.22%
d. None of theseOA : a (28.56%)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q28) A man invests Rs 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8% per annum, so that he can earn a total of 6% per annum? [CAT1995]
a. 1200
b. 1300
c. 1500
d. 2000OA : c (1500)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q29) Last year Mr. Basu bought two scooters. This year he sold both of them for Rs.30,000 each. On one, he earned 20% profit, and on other he made a loss of 20%. What was his net profit or loss? [XAT2005]
a. He gained less than 2000
b. He gained more than 2000
c. He lost less than 2000
d. He lost more than 2000OA : d (He lost more than 2000)

kamal_lohia last edited by kamal_lohia
Faculty and Content Developer at Tathagat  Delhi College of Engineering
Q30) What sum of money lent out at compound interest will amount to Rs.968 in 2 years at 10% p.a. Interest being charged annually.
a. 850
b. 900
c. 800
d. 950
e. 750OA : c (800)

So we write 1, 2, 3, φ, 4, 5..
1  10 : +1
11  20 : +1
21  30 : +1
31  φ0 : +2 (3φ, φ0)
φ1  40 : +10 (φ1, φ2, φ3, φφ, φ4, φ5, φ6, φ7, φ8,φ9)
41  50 : +1
51  60 : +1
61  70 : +1
71  80 : +1
81  90 : +1
91  94 : +1
Total = +21
So Age of alien = 94 + 21 = 115

Here the expression has odd number of factors.
Which means it is a perfect square.Now if N is even expression is odd(e+e+o =o)
And if n is odd expression is still odd(o+o+o=o)
Thus, the square is of an odd positive number.Putting expression equal to 11^2 satisfies it
And n comes out to be 9
As n(n+3)=108But ,how to ensure that there is no other solution besides this for higher squares????
