CAT (1998-2001) AVERAGE, RATIO & PROPORTION Questions

(1998)

1.       I have one rupee coins, fifty paise coins and twenty five paise coins. The numbers of coins are in the ratio 2.5: 3: 4. If the total amount with me is Rs 210. Find the number of one rupee coins.

(a)    90                        (b) 85                          (c) 100                       (d) 105

2.       There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is removed and is mixed well in the second container. Then three cups of this mixture is removed and is mixed in the first container. Let ‘A’ denote the proportion of water in the first container and ‘B’ denote the proportion of alcohol in the second container. Then,

(a)    A > B                   (b) A < B                       (c) A = B                   (d) Cannot be determined

(1999)

1.       Mr. Launcher plans to launch a new TV channel called Dekha Dekhi (DD). He envisages a viewership of 42%. He plans to capture the viewership from CAT TV and MAT TV, which currently hold viewership of 35% and 48%, each having a distinct and separate target audience. In what ratio should he capture the target audience of the two channels

(a)    6 : 7                    (b) 7: 6                          (c) 1: 1                      (d) 8: 9

(2000)

1.       There are seven consecutive natural numbers such that the average of the first five is n. then average of all seven numbers will be?

(a)    N

(b)   N + 1

(c)    Kn + 1/k where k is a positive constant.

(d)   N + 2/7

(2001)

1.       Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took ¼ of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

(a)    38                       (b) 31                            (c) 41                         (d) None of these

2.       Three maths classes: X, Y and Z take an algebra test.

The average score in class X is 83.   

The average score in class Y is 76.      

The average score in class Z is 85.      

The average score of all students in classes X and Y together is 79.      

The average score of all students in classes Y and Z together is 81.

What is the average for all the three classes?

(a)    81                         (b) 81.5                        (c) 82                        (d) 84.5

3.       A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35⁷⁄₁₅. What was the number erased?

(a)    7                           (b) 8                              (c) 9                          (d) None of these

4.       A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs 40. The total number of 5 rupee coins is

(a)    100                      (b) 140                          (c) 60                        (d) 150

5.       At a certain fast food restaurant, Brian can buy burgers, 7 shakes, and one order of fries for Rs 120 exactly. At the same place it would cost Rs 164.5 for 4 burgers, 10 shakes and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

(a)    Rs 31                    (b) Rs 41                      (c) Rs 21                    (d) Cannot be determined

CAT (1994-1997) AVERAGE, RATIO & PROPORTION Questions

Directions for questions 1 to 3: Read the information given below and answer the questions that follow:

Alphonso, on his death bed, keep half his property for his wife and divides the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Daves together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs 1,575,000.

(1994)

1.       What was the worth of the total property?

(a)    Rs 30 lakh                  (b) Rs 8 lakh                  (c) Rs 18 lakh                     (d) Rs 24 lakh

2.       What was Carl’s original share?

(a)    Rs 4 lakh                    (b) Rs 12 lakh                (c) Rs 6 lakh                        (d) Rs 5 lakh

3.       What was the ratio of the property owned by the widows of the three sons, in the end?

(a)    7: 9: 13                      (b) 8: 10: 15                   (c) 5: 7: 9                             (d) 9: 12: 13

4.       A man buys spirit at Rs 60 per litter, adds water to it and then sells it at Rs 75 per litter. What is the ratio of spirit to water if his profit in the deal is 37.5%?

(a)    9: 1                             (b) 10: 1                         (c) 11: 1                                (d) None of these

(1996)

1.       Two liquids A and B are in the ratio 5: 1 in container 1 and in container 2, they are in the ratio 1: 3, what ratio should the contents of the two container be mixed so as to obtain a mixture of A and B in the ratio 1: 1?

(a)    2: 3                             (b) 4: 3                            (c) 3: 2                                 (d) 3: 4

Directions for questions 6 to 8: Read the information given below and answer the questions that follow:

There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.

(1997)

1.       What is the average weight of the students in group D?

(a)    More than the average weight of A

(b)   More than the average weight of C

(c)    Less than the average weight of C

(d)   Cannot be determined

2.       If one student from Group A is shifted to group B, which of the following will be true?

(a)    The average weight of both groups increases  

(b)   The average weight of both groups decreases         

(c)    The average weight of the class remains the same

(d)   Cannot be determined                                 

3.       If all the students of the class have the same weight, then which of the following is false?

(a)    The average weight of all the four groups is the same.

(b)   The total weight of A and C is twice the total weight of B.

(c)    The average weight of D is greater than the average weight of A.

(d)   The average weight of all the groups remains the same even if the numbers of students are shifted are from one group to another.

4.       The average marks of a student in ten papers are 80. If the highest and the lowest scores are not considered, the average is 81.

(a)    55                         (b) 60                        (c) 62                          (d) can’t be determined

5.       The value of each of a set of silver coins varies as the square of its diameter, if its thickness remains constant and it varies as the thickness, if the diameter remains constant. If the diameters of two coins are in the ratio 4: 3, what should the ratio of their thicknesses be if the value of the first us 4 times that of the second?

(a)    16: 9                    (b) 9: 4                       (c) 9: 16                     (d) 4: 9

CAT 2002-2007 Percentage Questions

1.       Davji shop sells Samosas in boxes of different sizes. The samosas are prized at Rs 2 per Samosa up to 200 samosas. For every additional 20 Samosas, the price of the whole lot goes down by 10 paise per Samosa. What would be the maximum size of the box that would maximize the revenue?

(a)    240                              (b) 300                                   (c) 400                                (d) None of these

                                                                                                                                             (2003 C)

1.       At the end of year 1998, Sheppard bought dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q % of the goats at the end of the year where p > 0 and q > 0. If Sheppard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

(a)    P = q                           (b) p < q                                   (c) p > q                            (d) p = q/2

2.       A leather factory produces two kinds of bags, standard and deluxe bag. The profit margin is Rs 20 on a standard bag and Rs 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. the processing times per bag on the two machines are as follows:

	Time required (Hours/ bag)
	Machine A	Machine B
Standard Bag	4	6
Deluxe Bag	5	10

The total time on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit?

(a)    Standard 75 bags, Deluxe 80 bags                      (b) Standard 100 bags, Deluxe 60 bags                                             

(c) Standard 50 bags, Deluxe 100 bags                     (d) Standard 60 bags, Deluxe 90 bags

Directions for questions 1 to2: shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

Option A: invest in a public sector bank. It promises a return of +0.10%.

Option B: invest in mutual funds of ABC Ltd. a rise in the stock market will result in a return of +5%, while a fall will entail a return of -3%.

Option C: invest in mutual funds of CBA Ltd. a rise in the stock market will result in a return of -2.5%, while a fall will entail a return of +2%.

1.       The maximum guaranteed return to Shabnam is                                                                     (2007)

(a)    0.30%              (b) 0.25%                  (c) 0.10%                (d) 0.20%                   (e) 0.15%

2.       What strategy will maximize the guaranteed return to Shabnam?

(a)    30% in option A, 32% in option B and 38% in option C

(b)   100% in option A

(c)    36% in option B and 64% in option C

(d)   64% in option B and 36% in option C

(e)   1/3 in each of the three options