Number System - Study Mode
[#241] There are 154 beads in a rosary and all are coloured, either RED or BLUE or GREEN. The number of blue ones is three less than red and five more than green. The number of Red beads are:
Correct Answer
(A) 55
Explanation
Solution: Let the number of red beads = x
Hence, Blue beads = (x - 3)
and Green beads = (x - 8)
According to the sum,
x + x - 3 + x - 8 = 154
or, 3x - 11 = 154
or, x = 55
[#242] Recently, a small village, in Tamilnadu where only male shepherd reside with four sheep each, was devastated by Tsunami waves. Therefore 8 persons and 47 sheep were found to be dead and the person who luckily survived, left the village with one sheep each since 21 sheep were too injured to move so have left on their on luck, in the village. The number of sheep which were earlier in the village was :
Correct Answer
(C) 80 sheep
Explanation
Solution: Let there be x people in the village so, then 4x sheep must be there.
No, number of person leaving the village, = (x - 8) [as 8 person died in Tsunami] And the number of sheep to be carried with the survived people, 4x - (47 + 21) = x - 8. [Here we are equating No of alive sheep and no. of alive person. As 1 person has 4 sheep means 1 person = 4 sheep.] Or, 3x = 60 Or, x = 20 Or, 4x = 80 Hence, 80 sheep
[#243] A boy appeared in CAT for four consecutive year years, but coincidentally each time his net score was 75. He told me that there was $$frac{1}{3}$$rd negative marking for every wrong answer and 1 mark was allotted for every correct answer. He has attempted all the questions every year, but certainly some answers have been wrong due conceptual problem. Which is not the total number of questions asked for CAT in any year, in that period?
Correct Answer
(C) 150
Explanation
Solution: Option method: The best way to go through options. You will find that when you consider 150 questions you cannot get 75 marks anyhow. Alternatively: Since 75 is an integer, he must have to do (75 + 4x) problems, where x is a whole number. Now we put the value of x (0, 1, 2, 3, 4, 5 .........) to get the correct answer. As he gets the net marks in integer it means when he does 3n question wrong, he losses actually 4n marks.
[#244] The highest power of 17 which can divide exactly the following: (18 2 - 1) (18 4 - 1) (18 6 - 1) (18 8 - 1) . . . . (18 16 - 1) (18 18 - 1) is :
Correct Answer
(C) 9
Explanation
Solution: Total number of terms in expression = 9 (18 2 - 1) = (18 - 1) × (18 + 1) (18 4 - 1) = (18 2 + 1) × (18 2 - 1) = (18 2 + 1) × (18 - 1) × (18 + 1) (18 6 - 1) = [(18 3 ) 2 -1] = (18 3 + 1) (18 3 - 1) = 17 × k and so on. Hence, there will be 9 times 17 in the whole expression as each term of expression gives one 17. Therefore for maximum power of 17 will be 9.
[#245] If a = 7, b = 5, c = 3, then the value of a 2 + b 2 + c 2 - ab - bc - ca is :
Correct Answer
(D) 12
Explanation
Solution: = (a 2 + b 2 + c 2 - ab - bc - ca) = (a + b + c) 2 - 3 (ab + bc +ca) = (7 + 5 + 3) 2 - 3 (35 + 15 + 21) = (15) 2 - 3 × 71 = (225 - 213) = 12