CAT 2020 Quant x maro G Strategy

If log4 5 = (log4 y) (log6 √5), then y equals

The number of real-valued solutions of the equation 2^x + 2^−x = 2 − (x − 2)² is

If x = (4096)⁷+4√3, then which of the following equals 64?

The number of distinct real roots of the equation (x + 1/x)² − 3(x + 1/x) + 2 = 0 equals

Among 100 students, x1 have birthdays in January, x2 have birthdays in February, and so on. If x0 = max(x1, x2, ..., x12), then the smallest possible value of x0 is

How many distinct positive integer-valued solutions exist to the equation (x² − 7x + 11)(x² − 13x + 42) = 1?

The area of the region satisfying the inequalities |x| − y ≤ 1, y ≥ 0, and y ≤ 1 is.

If y is a negative number such that 2y2log35 = 5log23, then y equals

The number of pairs of integers(x,y) satisfying x ≥ y ≥ −20 and 2x + 5y = 99 is

The value of loga^a/b + logb^b/a, for 1 < a ≤ b cannot be equal to

If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals

Let f(x) = x² + ax + b and g(x) = f(x + 1) − f(x − 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

The number of integers that satisfy the equality (x2 − 5x + 7)x + 1 = 1 is

In how many ways can a pair of integers (x , a) be chosen such that x² − 2 | x | + | a − 2 | = 0 ?

If x¹ = −1 and x^m = x^m + 1 + (m + 1) for every positive integer m, then x¹⁰⁰ equals

Let N, x and y be positive integers such that N = x + y, 2 25, then how many distinct values are possible for N?

Let loga30 = A, loga5/3= −B and log2a = 1/3, then log3a equals

The area, in sq. units, enclosed by the lines x = 2, y = |x − 2| + 4, the X-axis and the Y-axis is equal to

If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) − f(−10) is equal to

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

Let m and n be positive integers, If x² + mx + 2n = 0 and x² + 2nx + m = 0 have real roots, then the smallest possible value of m + n is

The points (2 , 1) and (−3 , −4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is