Question Bank  Nitin Gupta, Alphanumeric

Number of Questions  100
Topic  Quant Mixed Bag
Answer Key available?  No
Source  Selected questions/solutions from Nitin Gupta Sir (Alphanumeric)

Q1) The total cost of production of n tube lights per day by Glolight is given by the following function.
C(n) = n^2 + 10n + 363
Selling price per unit of n units produced in a day is given by the following function.
S(n) = 2(80 – n)
If the number of units of tube lights sold per day is equal to number of units of tube lights produced per day then how many units should the factory produce per week to maximize its weekly profit?Production is done on all seven days of the week.
a) 70
b) 175
c) 77
d) None of these

Q2) PQR is an acute angled triangle with perimeter 60 cm. S is a point on QR. The circumcircles of triangles PQS and PSR intersect PR and PQ at T and U respectively such that ST = 8 cm and SU = 7 cm. If < TQR = < QRU, then which of the following represents the value of PT/PU?
(a) 16/19
(b) 3/4
(c) 14/17
(d) 5/6
(e) none of the foregoing

Given that < TQR = < URQ = A (suppose)
< TQR = < TQS = < TPS (angles made by same arc of circle) = A, < TPS = < RPS = < RUS (angles made by same arc of circle) = A. Similarly < URQ = < URS = < UPS (angles made by same arc of circle) = A, < UPS = < QPS = < QTS (angles made by same arc of circle) = A
Therefore we get PS is the angle bisector of QPR and Triangle USR and Triangle TSQ are isosceles. So, SR = SU = 7 and SQ = ST = 8. Therefore QR = 7 + 8 = 15.
Now using PQ + PR = 60  QR = 45 and PQ/PR = 8/7 (angle bisector theorem) we get PR = 21 and PQ = 24
Use QU.QP = QS.QR => QU X 24 = 8 X 15 => QU = 5
So, UP = 19, similarly TR X 21 = 7 X 15 => TR = 5. So, TP = 16
Therefore PT/PU = 16/19
Hence, choice (a) is the right answer

Q3) There are martian amoebae of three types (A, B and C) in a test tube. Two amoebae of any two different types can merge into one amoeba of third type. After several such merges only one amoeba remains in the test tube. What is its type, if initially there were 20 amoebae of type A, 21 amoebae of type B, and 22 amoebae of type B?
a) A
b) B
c) C
d) can be exactly two of the foregoing
e) can not be determined

Q4) A graph has p points. The degree of a point in the graph is the number of other points it is connected to by edges. Each point has degree atmost 3. If there is no edge between two points then there is a third point joined to them both. What is the maximum possible value of p?
(1) 12
(2) 7
(3) 10
(4) 9
(5) 8

Q5) Let X be the set of nonnegative integers. Let functions f: X > X such that x f(y) + y f(x) = (x + y) f(x^2 + y^2) for all x, y. Then which among the following is always true?
(1) f(x) >= 0
(2) f(x) = f(1)
(3) f(0) = 0
(4) Atleast 2 of the foregoing
(5) none of these

Q6) For all positive integers n, let nf(n+1) = n^2 + f(n). If f(1) is a positive integer and f(n) is an integer only for 1 < = n < = 6, then the minimum value of f(1) is
(1) 25
(2) 49
(3) 81
(4) 121
(5) none of the above

Q7) ABC is a triangle with AB = 14, BC = 10 and CA = 6. D and E are points on BC and CA respectively such that CD = 3 and CE = 2.5. A line passing through C and the point of intersection of AD and BE cut the side AB at F. Then AF =
(a) 5
(b) 5.25
(c) 6
(d) 6.25
(e) 7.5

Q8) Given a triangle area of area 6 and perimeter 12, let S be the set of all points a distance 5 or less from a point of the triangle. What is the area of S to the nearest integer?
(1) 126
(2) 134
(3) 145
(4) 157
(5) 168

Q9) The cost of 6 mangoes is equal to the cost of 3 apples, 4 oranges and 5 peaches. The cost of a peach is between that of an apple and an orange. After 5 mangoes are bought with the price of 6 mangoes, it is found that with the remaining money two of the fruits (both different) can be bought. Which of the two fruits can be bought?
(1) an apple and an orange
(2) an apple and a peach
(3) an orange and a peach
(4) exactly two of the foregoing
(5) can not be determined

Q10) With the sale of every article A, suppose you get a discount coupon of Rs 30. the discount coupon can be used to buy the article A on their own but can not be exchanged for cash or used partly with cash. Also there is no discount coupon for the article bought with discount coupon. If the minimum amount with which the articles can be bought without any cash or discount coupon being left is Rs 1000, the the number of articles bought is
(1) 13
(2) 32
(3) 57
(4) can not be determined
(5) none of the foregoing

Q11)
a) A sphere is wrapped completely by the minimum amount of single piece of paper. What percent of the paper will go wasted?
b) A hemisphere is wrapped completely by the minimum amount of single piece of paper. What percent of the paper will go wasted?

Q12) The number of integral x < 4 such that 2^x+2  2^(x+1)  1 = 2^(x+1) + 1 are
(1) 2
(2) 3
(3) 4
(4) 6
(5) none of these

Q13) Let x = √2 + √3 + √5 + √6 + √7. When this expression is expressed as an equation of minimum degree in x with integral coefficients, then the degree of the equation is
(1) 5
(2) 6
(3) 16
(4) 32
(5) none of these

Q14) Divya and Raveena can do a work alone exactly in 20 and 25 days respectively. However, when they work together, they do 25% more work than is expected. If they work for a few days alone and for few days together (both being integers only), then the work could not have been completed in exactly
(1) 10 days
(2) 14 days
(3) 16 days
(4) 17 days
(5) either none or atleast 2 of these

Q15) Sara, Kyna, Riddhi can complete the work W1, W2, W3 alone in 6, 9 and 15 days respectively. If (Kyna, Riddhi), (Riddhi, Sara) and (Sara, Kyna) can do the work W1, W2, W3 respectively in n days each, then n lies in
(1) (3, 3.5)
(2) (3.5, 4)
(3) (4, 4.5)
(4) (4.5, 5)
(5) either none or atleast 2 of these

Q16) Salman does pushups in sets each consisting either of 6, 9, or 20 pushups. By doing 2 sets of 6 pushups, he can do 12 pushups. But he cannot do 13 pushups, as one cannot get 13 by using 20, 6 or 9. What is the maximum number of pushups that Salman cannot do?

Q17) A gardener was given a Rs. 100 note by his landlord and asked him to buy exactly 100 flowers from the nursery by spending all the money. A piece of Daffodil costs Rs15. Canterbury Bells cost Re 1, and Marigold are 25 paise each. He was asked to buy at least one flower of each of the three varieties. How many Canterbury Bells did the gardener buy from the nursery?
(1) 39
(2) 43
(3) 45
(4) 57
(5) None of the foregoing

Q18) How many non empty subsets S of {1, 2, 3, ..., 15} have the following properties?
(a) no two consecutive integers belong to the same set
(b) if S contains k elements, then S contains no number less than k(1) 277
(2) 311
(3) 376
(4) 377
(5) 405