List of top Quantitative Aptitude Questions on Algebra asked in NPAT

If \( x \), \( y \), and \( z \) are positive integers and \( p = \left( \left( (x - 1)^2 / |x| \right) + 2 \right) + \left( \left( (y - 1)^2 / |y| \right) + 2 \right) + \left( \left( (z - 1)^2 / |z| \right) + 2 \right), \) then \( p<6 \).
If \( 3x^2 - 5x + 1 = 0 \), then the value of \( x^2 + \frac{1}{9x^2} \) will be:
If \( a \), \( b \), and \( c \) are three fractions such that \( a<b<c \), and if the smallest fraction is divided by the middle fraction, the result is \( \frac{15}{16} \), which exceeds the largest fraction by \( \frac{3}{16} \). If \( a + b + c = \frac{49}{24} \), then what is the difference between \( c \) and \( b \)?
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z^2} \), where \( x, y, z \) are positive integers, then the value of \( 2x + 3y - 4z \) is:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y + \frac{1}{z}} \), where \( x, y, z \) are positive integers, then the value of \( (2x + 3y - 4z) \) is:
If \(a^2 + c^2 + 17 = 2(a - 2b^2 - 8b)\), then the value of \((a + b + c) \left( [(a - b)^2 + (b - c)^2 + (c - a)^2] \right)\) is:
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z^2} \), where \( x, y, z \) are positive integers, then the value of \( 2x + 3y - 4z \) is:
If \(a^2 + c^2 + 17 = 2(a - 2b^2 - 8b)\), then the value of \((a + b + c) \left( [(a - b)^2 + (b - c)^2 + (c - a)^2] \right)\) is: