CAT Question Bank (Quant) - Gaurav Sharma - Set 1
Q38) The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is
Q39) A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. what fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?
E. None of the above
Q40) Amit’s office is 12 km from his house. In the evenings he picks up his wife from her office, which is 6 km from his office and then travels 4 km to his gym. If he is then x km from his house, what is the range of values for x?
(a) 4 ≤ x ≤ 12
(b) 2 ≤ x ≤ 18
(c) 4 ≤ x ≤ 22
(d) 2 ≤ x ≤ 22
Q41) p,q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is
A. ≥ 40 and < 50
B. ≥ 50 and < 60
C. ≥ 60 and < 70
D. ≥ 70 and < 80
E. ≥ 80 and < 90
Q42) Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that at least two of Sara’s friends are connected with each other. On her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?
A. ≥ 105
B. ≤ 123
C. < 125
D. ≥ 100 and ≤ 125
E. ≥ 105 and ≤ 123
Q43) Prof. Mandal walks to the market and comes back in an auto. It takes him 90 minutes to make the round trip. If he take an auto both ways it takes him 30 minutes. On a Sunday, he decides to walk both ways. How long would it take him?
A. 100 minutes
B. 120 minutes
C. 140 minutes
D. 150 minutes
E. None of the above
Q44) In base 8, the greatest four digit perfect square is
Q45) Ramesh bought a total of 6 fruits (apples and oranges) from the market. He found that he required one orange less to extract the same quantity of juice as extracted from apples. If Ramesh had used the same number of apples and oranges to make the blend, then which of the following correctly represents the percentage of apple juice in the blend?
A. 25 %
E. None of the above
Q46) In a square PQRS, A and B are two points on PS and SR such that PA = 2AS, and RB = 2BS If PQ = 6, the area of the triangle ABQ is (is it a repeat)
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Q47) Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram’s car at the rate of 25 kmph, while Shyam walked at 5 kmph. After sometime, Hari got off and started walking at the rate of 5 kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was:
Q48) How many whole numbers between 100 and 800 contain the digit 2?
Q49) Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs 21 lakhs each when they reach the age of 21. He is looking for plans that will give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should be
A. 5% and 7.5% respectively
B. 8% and 12% respectively
C. 10% and 15% respectively
D. 15% and 22.5% respectively
E. 20% and 30% respectively
Q50) The lengths of the three edges of a cuboid are increased by a%, b% and c%. The volume increases by V%, where V is an integer. How many values can V take if a, b, c are real numbers and 10 ≤ a, b, c ≤ 20?
(d) Cannot be determined
Q51) 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?
Q52) A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?
a) a must be 2
b) c must be 2
c) b must be 0
Q53) If number of students a class is firstly increased by a% then decreased by b% then there is no change in number of students then |b-a| = ?
a. a * b
b. b – a
c. a * b/100
Q54) 4n has twice the number of factors as n. Which of the following could be the remainder when n is divided by 8?
Q55) A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?
d. None of these
Q56) What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
a) 1 or 7
b) 2 or 14
c) 3 or 21
d) 4 or 28
Q57) A natural number when increased by 50% has its number of factors unchanged. However when the value of number is reduced by 75% the number of factors is reduced by 66.66%..One such number could be