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    Default TestFunda Answers - Algebra

    This thread contains questions, answers and solutions in Algebra from TestFunda Answers.

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    Post TestFunda Answers - Algebra

    Say, he is selling 100 gms of product.
    So, according to data, he actually provided only 80 gms to customer.
    Now, in 80 gms, he added 20% impurities. So in 96 gms, 16 gms is impure.
    Effectively, we have 80 gms of pure product in 96 gms; so we have (80*80/96) pure product. That's 66.67 gms of pure product.

    So, he has sold 66.67 gms of pure product as 100 gms of pure product. Profit margin=50% 


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    Post TestFunda Answers - Algebra

    option 1.
    One value is 8. Because (8-7)^n is always 1.
    For x=6 does not provide solution.

    Another value is whatever makes (x-7)^0.
    So, if x^2-29x+154=0, then we get required answer. For this, two values of x are possible.

    Total 3 values. 
    Last edited by ajay_h; 13-Oct-10 at 9:15 PM.

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    Post TestFunda Answers - Algebra

    Option 2.
    42 product A, and 12 product B, we can utilize resources properly.

    Actually, Option 1,3 and 4 can easily be eliminated. Because, if you produce only product B, then you get answer as Rs.280 and Option 3 and 4 are way too high.

    If you take any random numbers where production of A is higher than B, you can easily see that, you can approach towards Rs.294. I don't have exact method, but intelligent guessing serves well for this type of questions.


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    Post TestFunda Answers - Algebra

    On the last day of college, students exchanged autographs with each other. A total of 870 autographs were exchanged. How many students were there?
    Options
    1) 
    30
    2) 
    32
    3) 
    40
    4) 
    42
    Additional Notes: please give the solution with reason...i thought the answer should come by n(n+1)/2 with options...but didn't get any....

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    Post TestFunda Answers - Algebra

    as there are in all 870 autographs... tht means tat every student has got an autograph fromall the students...
    there fore 30 students * 29 autographs received by each student=870 

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    Post TestFunda Answers - Algebra

    The problem is that they have not defined an exchange, I remamber in a previous question they had defined exchange between two person, in this case it is exchange of an autograph , just take the example of 3 students exchange will occur always in pair of 2 ,so we have 3C2 pairs and in each exchange, number of autographs will be two so total (3C2 *2) , generalising this we get if n students are there then auto graphs exchanged will be (NC2 *2)=870 , solve or go by options to get 30 students

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    Post TestFunda Answers - Algebra

    Let the number of units produced for A be a and that for B be b. Then profit P is given by,

    P = 5a + 7b

    We have to maximize P keeping in mind 2 constraints on grinding and polishing hours as follows.

    Total Number of Griding Hours required for a and b ≤ 120
    → 2a + 3b ≤ 120   ------- (1)

    Similarly condition for polishing hours is
    3a + 2b ≤ 150 ---------(2)

    If we substitute the value of a from equation (1) into the expression for P we get
    P ≤ 300 - b/2  ------- (3)
    Similarly, from equation (2) we get,
    P ≤ 250 + 11b/3   ------- (4)

    When we equate the expressions (3) and (4) for P we get b = 12. Any value of b, higher or lower than this will give a lesser value of P. 

    Hence, maximum value of P occurs when b = 12 i.e. P = 294
    Hence, option 2. 

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    Post TestFunda Answers - Algebra

    In a remote village, the villagers have a strange process of calculating their average incomes and expenditures. According to an old custom of their village, the average monthly income had to be calculated on the basis of 14 months in a calendar year. Mr.X comes back from abroad and convinces 273 families of his fellow villagers to start calculating the average national income on the basis of 12 months per calendar year. Now if it is known that according to the old system, the average estimated income in his community is 87 rupees per month, then what will be the change in the average estimated savings for the village while other factors remain the same.
    Options
    1) 
    Rs.251.60
    2) 
    282.75
    3) 
    312.75
    4) 
    Cannot be determined

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    Post TestFunda Answers - Algebra


    Option 4 is answer.

    We do not know anything about savings or expenditure in old system as well as new system. i.e. we do not know whether expenditure was Rs. 40 (saving Rs. 47), Rs. 50 (saving Rs. 37), Rs. 80 (saving Rs. 7). So, we cannot determine anything here.

    Option 4 is answer.
    We do not know anything about savings or expenditure in old system as well as new system. i.e. we do not know whether expenditure was Rs. 40 (saving Rs. 47), Rs. 50 (saving Rs. 37), Rs. 80 (saving Rs. 7). So, we cannot determine anything here.

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    Post TestFunda Answers - Algebra









    Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5% and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30% of the hours of what was actually allotted to do the three jobs individually. Find what percentage of the total time allotted is the time wasted by Munish.




    Options
    1) 
    38.33%
    2) 

    39.4


    3) 
    49.09%
    4) 
    58.33%

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    Post TestFunda Answers - Algebra

    what is the number of solutions for a+b+c+d<11?
    what is the number of solutions for a+b+c+d<=11?
    given that a,b,c,d is a natural number.

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    Post TestFunda Answers - Algebra

    There are 27 spl primes less than 1000.

    Consider 1 digit spl primes. They are 2, 3, 5, and 7.

    Consider 2 digit spl primes. To get these we can start appending numbers on the right of the 1 digit prime numbers. In that case the 2 digit prime numbers are 23, 29, 31, 37, 53, 59, 71, 73, 79.

    Consider 3 digit prime numbers. To get these we can start appending numbers on the right of the 2 digit prime numbers. In that case the 3 digit prime numbers are 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797.

    So in all there are 27 spl primes less than 1000.

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    Post TestFunda Answers - Algebra

    From the given relation, a1, a2 ≤ (1+2)= 3
    ∴ a1, a2 ≤ 3
    Similarly, a1, a3 ≤ 4
    a1, a4 ≤ 5
    a1, a5 ≤ 6
    ....
    a1, a2010 ≤ 2011.

    So we get, a1 ≤ 3, a2 ≤ 3, a3 ≤ 4, a4 ≤ 5, .........., a2010 ≤ 2011.
    Applying AM ≥ GM we get,

    (a1+a2+a3+......+a2010)/2010 ≥ (a1*a2*a3*......*a2010)1/2010
    ∴ (a1*a2*a3*......*a2010)1/2010 ≤ (3+3+4+5+6+....+2011) / 2010 = [((2+2011)*2010/2 + 1)/2010] = 2013/2 + 1/2010
    ∴ a1*a2*a3*......*a2010 = (2013/2 + 1/2010)2010

    Hence, required product is (2013/2 + 1/2010)2010

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    Post TestFunda Answers - Algebra

    Oops.. Quite a difficult question.

    For 2x2 matrix, smallest sum is 6 = 2x2 + 2
    For 3x3 matrix, smallest sum is 11 = 3x3 + 2
    For 4x4 matrix, smallest sum is 19 = 4x4 + 3
    For 5x5 matrix, smallest sum is 28 = 5x5 + 3

    So for a nxn matrix, smallest sum is nxn + [n/2] + 1
    For 10x10 matrix, smallest sum is 10x10 + 6 = 106.

    Hence, the required value of the smallest sum is 106. 

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    Post TestFunda Answers - Algebra

    ok...Since a,b,c,d are natural nos they have to be at least 1,1,1,1 i.e a+b+c+d=4 at least
    Now acc. to first question we have to find a+b+c+d<11 . Assigning the min value to a,b,c,d we ultimately have to find a+b+c+d<7 or a+b+c+d=6,5,4,3,2,1,0, hence the answer would be 9C3+8C3+7C3+....+3C3.
    Now  the second question says a+b+c+d<=11. Again assigning the min value to a,b,c,d we get a+b+c+d<=7
    therefore we have to find a+b+c+d=7,6,5,4,3,2,1,0..hence answer is 10C3+9C3+.....3C3
    Hope u followed it.. 

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