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Subject:Competition

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that  p + q + r  is not equal to 0?

x + 2y – 3z = p
2x + 6y - 11z = q
x- 2y + 7z  = r

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A.) 5p - 2q - r=0
B.) 5p + 2q + r=0
C.) 5p + 2q - r= 0
D.) 5p - 2q + r= 0
Answer is option : A
Subject:Competition

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

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A.) 31
B.) 63
C.) 75
D.) 91
Answer is option : D
Subject:Competition

In a 4,000 meter race around a circular stadium having a circumference of 1,000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

 

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A.) 20 min
B.) 15 min
C.) 10 min
D.) 5 min
Answer is option : C
Subject:Competition

The function f(x) =  x - 2 + 2.5 - x + 3.6 - x, where x is a real number, attains a minimum at

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A.) x=2.3
B.) x=2.5
C.) x=2.7
D.) None of the these
Answer is option : B
Subject:Competition

A leather factory produces two kinds of bags, standard and deluxe. 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 available 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?

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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
Answer is option : A
Subject:Competition

At the end of year 1998, Shepard bought nine 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 Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

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A.) p equal to q
B.) p is less than q
C.) p is greater than q
D.) p is equal to q/2
Answer is option : C
Subject:Competition

When the curves y = log10x and y = x-1 are drawn in the x-y plane, how many times do they intersect for values x is greater than equal to 1?

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A.) Never
B.) Once
C.) Twice
D.) More than twice
Answer is option : B
Subject:Competition

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?

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A.) 1st
B.) 9th
C.) 12th
D.) None of the above
Answer is option : C
Subject:Competition

A test has 50 questions. A student scores 1 mark for a correct answer, -1/3 for a wrong answer, and -1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

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A.) 6
B.) 12
C.) 3
D.) 9
Answer is option : C
Subject:Competition

Let A and B be two solid spheres such that the surface area of B is 300 % higher than the surface area of A. The volume of A is found to be k % lower than the volume of B. The value of k must be

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A.) 85.5
B.) 92.5
C.) 90.5
D.) 87.5
Answer is option : D
Subject:Competition

DIRECTIONS for Questions: Answer the questions on the basis of the information given below.

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

How many members of the group are males?

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A.) 2
B.) 3
C.) 4
D.) Cannot be determined
Answer is option : D
Subject:Competition

DIRECTIONS for Questions: Answer the questions on the basis of the information given below.

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

What is E's profession?

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A.) Engineer
B.) Lawyer
C.) Professor
D.) Accountant
Answer is option : A


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