Below is a set of 10 GMAT-style Data Sufficiency questions. Each question follows the official GMAT format and is accompanied by detailed step-by-step solutions.
Each problem consists of a question and two statements, labeled (1) and (2).
Find the length of the rectangle.
(1) The perimeter of the rectangle is \(120\).
(2) The width of the rectangle is \(20\).
Given:
\[ x = 2t - z + 5w, \quad y = 2t - 1, \quad z = 2w + 1 \]Find the value of \(x\).
(1) \(y = 3\)
(2) \(z = -5\)
Find the area of an isosceles right triangle.
(1) The length of one leg is \(10\) cm.
(2) The length of the hypotenuse is \(10\sqrt{2}\).
Is \(x = y\)?
(1) \(|x| = |y|\)
(2) \(xy > 0\)
In a library, there are three types of books: Mathematics, Biology, and Geography. There are \(150\) more Geography books than Mathematics books. How many books are in the library?
(1) The ratio of Mathematics to Biology books is \(5:7\).
(2) The ratio of Biology to Geography books is \(7:8\).
What is the value of \(x^2 + y^2\)?
(1) \(x + y = 4\)
(2) \(x = \dfrac{2}{y}\)
What is the value of \(x\)?
(1) \(2x + 0.5y = 7\)
(2) \(0.4x + 0.2y = 1.4\)
What is the perimeter of the quadrilateral?
(1) The area of the quadrilateral is \(600\).
(2) One side of the quadrilateral is \(30\).
Let \(m\) and \(n\) be positive numbers with \(m < n\). What is the value of \(m^2 - n^2\)?
(1) \(|m + n| = 14\)
(2) \(|m - n| = 2\)
What is the volume of the sphere?
(1) The surface area of the sphere is \(400\pi\).
(2) The radius of the sphere is \(10\).