Quantitative Aptitude - Numbers and Algebra
2. If 6 ≥ x ≥ -2 and 4 ≥ y ≥ - 4, then limits for
where x and y are non zero integers, is
- Option : D
- Explanation :
y 4 3 2 1 -1 -3 -4
x 6 5 4 3 1 -1 -2
Hence, minimum value of
And maximum value of
- Option : D
- Explanation : (a. n)! = product of n consecutive natural numbers starting from 'a' which is atleast divisible by n!. (n)! = product of n consecutive natural numbers. For n = 2 : (a. n)! = a(a + 1) and n! = 2 a(a + 1) is divisible by 2!. For n = 3 : (a n)! = a(a + 1)(a + 2) and n! = 6. One of the factors of a(a + 1)(a + 2) is divisible by 3 and other by 2. Thus, proceeding in this manner, (a. n)! and n! have HCF = n! ∴ H = n!.
4. If a and b are prime numbers, which of the following is true?
I. a2 has three positive integer factors.
II. ab has four positive integer factors.
III. a3 has four positive integer factors.
Codes
- Option : C
- Explanation :
Factors of a2 are 1. a and a2.
Factors of ab are 1, a, b and ab.
Factors of a3 are 1. a. a2 and a3.
5. If x = b + c, y = c a, z = a b, then
x2 + y2 + z2 - 2xy - 2xz + 2yz is equal to
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