Breakup G Strategy: Numbers + Maximum/Minimum | Hard
Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose values lies between 150 and 500.If p is less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is: _____
Solution & Explanation
Correct Answer: 397
Give p + q + r = 900 , 0.3q ≤ p ≤ 0.7q
r lies between 150 to 500 and is a perfect square
So r = 169 , 196 , 225 , 256 , 289 , 324 , 361 , 400 , 441 , 484
For maximum p (0.7q) , r should be minimum, r = 169
0.7q + 1q + 169 = 900 , q = 430 so p = 0.7 × 430 = 301
For minimum p (0.3q) , r should be maximum r = 484
0.3q + 1q + 484 = 900 , q = 320 , so p = 0.3 × 320 = 96
Pmax + P min = 301 + 96 = 397
Answer 397
Concepts of Number system + Maximum/Minimum | Hard
For a 4 digit number greater than 1000 , sum of the digits in thousands , hundreds and tens places is 15.And the sum of digits in hundreds , tens and units place is 16.Also the digits in tens place is 6 more than the digit in the unit place. The difference between the largest possible and smallest possible value of the number is :
1.735
2.3289
3.4078
4.811
Solution & Explanation
Given conditions for a 4-digit number:
a + b + c = 15 —– I
b + c + d = 16 —– II
c = d + 6 ——- III
Solving the equations:
b = 10 – 2d
a = d – 1
Now using values for d:
If d = 3:
a = 2, b = 4, c = 9, number = 2493
If d = 2:
a = 1, b = 6, c = 8, number = 1682
Largest number = 2493, Smallest number = 1682
Difference = 2493 – 1682 = 811
Answer 811
