Number System - Study Mode
[#346] P is a prime number and (P 2 + 3) is also a prime number . The no. of numbers that P can assume is:
Correct Answer
(C) 1
Explanation
Solution: Only, one value P can be assumed, which is at 2 at P = 2
P 2 + 3 = 7 which is also prime
Again at P = 3, 5, 7, 11 .......
P 2 + 3 = an even number which can not be prime
[#347] A naughty boy Amrit watches a Sachin Tendulkar inning and acts according to number of runs he sees Sachin scoring. The details are: 1 run - place one orange in the basket 2 runs - place one mango in basket 3 runs - place a pear in the basket 4 runs - remove a pear and a mango from the basket One fine day, at the start of the match, the basket is empty. The sequence of runs scored by Sachin in that inning are given as 11232411234232341121314. At the end of the above inning, how many more oranges were there compared to mangoes inside the basket ? (The Basket was empty initially).
Correct Answer
(C) 6
Explanation
Solution: Number of oranges in the basket,= Number of 1 run scored = 8 oranges.
Number of mangoes in the basket,= (number of 2 runs scored - number of 4 runs scored) = 6 - 4 = 2 mangoes.
Number of more oranges in basket than mangoes,
= 8 - 2 = 6
[#348] Three mangoes, four guavas, and five watermelons cost Rs. 750. Ten watermelons, six mangoes and 9 guavas Cost Rs. 1580. What is the cost of six mangoes, ten watermelons and 4 guavas?
Correct Answer
(B) 1180
Explanation
Solution: According to the question,
3M + 4G + 5W = 750 ------- (1)
6M + 9G + 10W = 1580 -------- (2)
6M + 4G + 10W = x (let) ------- (3)
On equation (1) × 2 - equation (2), we get
G = 80
On equation (2) - Equation (3), we get
5G = 1580 - x
Putting, G = 80, We get
x = 1180
[#349] A two digit number ab is added to another number ba, which is obtained by reversing the digits then we get three digit number. Thus (a + b) equals to:
Correct Answer
(D) (a + b) ≥ 10
Explanation
Solution: When two two digit numbers are added and the resultant value is a three digit number . It means there must be a carry over (i.e. The sum of unit digits be greater than 9. Similarly, the sum of the tens digit is also greater than 9) Required numbers = 64 + 46 = 110 Option D is correct
[#350] A gardener plants his garden with 5550 trees and arranged them so that there is one plant more per row as there are rows then number of trees in a row is:
Correct Answer
(D) 75
Explanation
Solution: Let there be n rows, then number of trees in each row = (n + 1) Thus, total number of trees, n × (n +1) = 5550 Now, at this moment this problem can be solved in two ways. First by finding the roots of quadratic equation. Second, by using the values from options. 74 × 75 = 5550 i.e. (n + 1) = 75