Question
Find the greatest value of (a + b) such that an 8-digit
number 4523a60b is divisible by 15.Solution
Factors of 15 = (3 × 5) and the divisibility rule of 15 says that sum of digits be divided by 3 and the last number will be 5. Possible values of b are 0 and 5 Now, 4 + 5 + 2 + 3 + a + 6 + 0 + 0 = 20 + a Here a can be 1, 4, 7 For greatest we need to take 7 So, a + b = 7 + 0 = 7 which is not present in the option Again, 4 + 5 + 2 + 3 + a + 6 + 0 + 5 = 25 + a Here a can be 2, 5, 8 For greatest we need to take 8 So, a + b = 8 + 5 = 13 which is present in the option ∴ Required answer is 13
If x^2 - 7x + k = 0 has roots that are equal, what is the value of k?
I. 6x2 – 7x - 20 = 0
II. 3y2 - y - 14 = 0
I. 5x² + 17x + 6 = 0
II. 2y² + 11y + 12 = 0
...Solve for x: |2x − 5| + |x + 1| ≤ 10.
I: x2 + 31x + 228 = 0
II: y2 + 3y – 108 = 0
I. 88x² - 13 x – 56 = 0
II. 15 y² + 41 y + 28 = 0
I. 96x² + 52x - 63 = 0
II. 77y² + 155y + 72 = 0
Equation 1: x² - 45x + 500 = 0
Equation 2: y² - 60y + 600 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 2x² - 8x + 6 = 0
Equation 2: y² - 7y + 10 = 0
I. x2 – 10x + 21 = 0
II. y2 + 11y + 28 = 0
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