Number System - Study Mode
[#236] The number of employees in Examveda and Co. is a prime number and less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:
Correct Answer
101 : 88
Explanation
Solution: Using options,
We find that the sum of numerator and denominator of 97 : 84 is (97 + 84) = 181 which is a prime number.
Hence, it is the appropriate answer
[#237] The remainder , when (2222 5555 + 5555 2222 ) is divided by 7, is
Correct Answer
(C) 0
Explanation
Solution: a n + b n is always divisible by (a + b) when n is odd. So, (2222 5555 + 5555 2222 ) is always divisible by (2222 + 5555) = 7777 And 7777 is multiple of 7, so (2222 5555 + 5555 2222 ) is divisible by 7
[#238] A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8, thumb 9 and then back to the index finger for 10, middle finger for 11 and so on. She counted up 1994. She ended on her
Correct Answer
(C) Middle finger
Explanation
Solution: If the girl counts the way as given in the question, The counting serial for thumb will be 1, 9, 17, 25 . . . . . . Hence, Number 1992 ( as 1992 is divisible by 8, common difference of series formed by counting) will also fall on thumb. Hence, Number 1994 will end on her middle finger.
[#239] How many pairs of natural numbers is there the difference of whose squares are 45.
Correct Answer
(C) 3
Explanation
Solution: (x 2 - y 2 ) = 45
Or, (x - y)(x + y) = 45
Thus, the factors of 45 possibles are 15, 3, 9, 5, 1 and 45
Hence, numbers are 9 and 6 or 7 and 2 or 23 and 22 So, number of such pairs = 3
[#240] The remainder when 10 10 + 10 100 + 10 1000 + . . . . . . + 10 1000000000 is divided by 7 is
Correct Answer
(B) 1
Explanation
Solution: Number of terms in the series = 10. (We can get it easily by pointing the number of zeros in power of terms. In 1 st term number of zero is 1, 2 nd term 2, and 3 rd term 3 and so on.) $$frac{{{{10}^{10}}}}{7},$$ xa0 Written as, $$frac{{{{left( {7 + 3}
ight)}^{left( {4 imes 2 + 2}
ight)}}}}{7}$$ The remainder will depend on $$frac{{{3^2}}}{7}$$ So, remainder will be 2 $$eqalign{
& frac{{{{10}^{1000}}}}{7},,{ ext{remainder}} = 2 cr
& frac{{{{10}^{10000}}}}{7},,{ ext{remainder}} = 1 cr} $$ So, we get alternate 2 and 1 as remainder, five times each. So, required remainder is given by $$eqalign{
& frac{{left( {2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1}
ight)}}{7} cr
& = frac{{15}}{7} cr} $$ Remainder when 15 is divided by 7 = 1