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Important Question for CAT 2009 Exam (1) (Question)

catxprt saidTue, 03 Nov 2009 16:14:05 -0000 ( Link )

Hey CAT Aspirants

Here’s a question which might be helpful for CAT preparation and question like this is likely to be in the upcoming exam.

If the integers a and b are chosen at random from integers from integers 1 to 100 with replacement, then the probability that a number of the form  7 ^ a + 7 ^ b  is divisible by 5 equals?

1. 1 / 2

2. 1 / 4

3. 1 / 8

4. 1 / 16

5. None of these

Be on lookout for more such important questions in my future discussions. Post your answers and we will discuss the solution in coming days.

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  1. jstplayin saidWed, 04 Nov 2009 10:06:56 -0000 ( Link )

    my ans is 2) 1/4

    appch : (7a+ 7b) / 5 can be written as (2a+ 2b)/ 5 so remainders can be (1,4) (4,1) (2,3) and (3,2) for the sum to be divisible by 5. now for (1,4) we can have a : 4,8,12..100 =25 values and b: 2, 6, 10..98=25 values similarly for (2,3)— a: 1,5,9.. 25 values and b: 3, 7,11.. 25 values same for other two cases:

    therefore prob = (2525+2525) 2 / 100 100 = 25 502 /100*100 ==1/4

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  2. venkivety saidTue, 10 Nov 2009 13:07:51 -0000 ( Link )

    k.. expert…....... what??? yaaaaaa catxpert…...

    can u post d reply…..

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  3. shaunakc saidWed, 11 Nov 2009 01:24:31 -0000 ( Link )

    #

    the answer is 1/8. There are just four types of nos – 4k+1, 4k+2, 4k+3, 4k. now if a=4k+1 type of no the remainder is 2. similarly for 4k+2 rem is 4; 4k+3 rem is 3 & for 4k rem is 1. If you take a as 4k+1 type then necessarily b has to be 4k+3 type of no. Similar explanation for 4k+2 & 4k type of nos. Now required probability is 2525/(100100)+ 2525/(100100) = 1/16+1/16 = 1/8

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  4. catxprt saidThu, 12 Nov 2009 08:31:43 -0000 ( Link )

    Shaunak that is correct

    The last digit of any power of 7 is 1, 7, 9 or 3 if the power of 7 is of the form 4k, 4k + 1, 4k + 2 or 4k + 3 respectively. So the sum will be divisible by 5 if the last digits in the two cases are either 1 and 9 or 7 and 3. Out of 1 to 100, there are 25 numbers of each type. Hence the number of ways in which we can select two such a and b out of these 25 numbers is: 2 * 25 * 25 = 1250 and the total number of ways in which two numbers can be selected is 100 * 100 = 10000. Hence the required probability is: (2 * 25 * 25) / (100 * 100) = 1 / 8

    For more important questions take this test

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