GMAT
In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ?(1)The area of triangular region ABX is 32.(2)The length of one of the altitudes of triangle ABC is 8.
A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
What is the volume of a certain rectangular solid?(1)Two adjacent faces of the solid have areas 15 and 24, respectively.(2)Each of two opposite faces of the solid has area 40.
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?(1) The number of distinct points in S is 5.(2) No three of the points in S are collinear.
Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y?(1)y > 4(2)The cost of the 10 kilograms of material K is less than $40.
For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that $${2}^{n}$$ is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m ? (1) $$k>{m}$$ (2)$$\frac{K}{M}$$ is an even integer.
If m is a positive integer, then $${M}^{3}$$ has how many digits?(1) M has 3 digits.(2) $${M}^{2}$$ has 5 digits
If $$x^{2} + y^{2} = 29$$, what is the value of $${(x - y)}^{2} ?$$(1) xy = 10(2) x =5
On a company-sponsored cruise, $$\frac2 3$$ of the passengers were company employees and the remaining passengers were their guests. If $$\frac3 4$$ of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT managers?(1)There were 690 passengers on the cruise.(2)There were 230 passengers who were guests of the company employees.
Is xy > 5?(1) $$1 \le x \le 3 and 2 \le y \le 4$$(2) x + y = 5
If $$r > 0$$ and $$s > 0$$, is$$\frac{r}{s}<\frac{s}{r}$$ ?(1)$$\frac{r}{3s}=\frac{1}{4}$$(2)$$s = r + 4$$
If x is an integer, is $$x \mid x \mid < {2}^{X}$$ ?(1)$$x < 0$$(2)$$x = -10$$
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?(1)The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The figure above represents a circle graph of Company H's total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H's total expenses are $5,400,000, what are the expenses for Division R ?(1)x = 94(2)The total expenses for Divisions S and T are twice as much as the expenses for Division R.
A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?(1)Each paragraph of the preface has more than 100 words.(2)Each paragraph of the preface has fewer than 150 words.
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?(1)Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.(2)Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.
The table above shows the results of a survey of 100 voters who each responded "Favorable" or "Unfavorable" or "Not Sure" when asked about their impressions of Candidate M and of Candidate N. What was the number of voters who responded "Favorable" for both candidates?(1)The number of voters who did not respond "Favorable" for either candidate was 40.(2)The number of voters who responded "Unfavorable" for both candidates was 10.
The length of the edging that surrounds circular garden K is $$\frac12$$ the length of the edging that surrounds circular garden G. What is the area of garden K ? (Assume that the edging has negligible width.)(1)The area of G is 25π square meters.(2)The edging around G is l0π meters long.
If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2?(1) w - z >2(2) z is a the least number in S.
In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A ?(1)The area of square region B is 9.(2)The area of square region C is $$\frac{64}{9}$$