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In a Factory, three machines \(A, B,\) and \(C,\) working at the same time and at their respective constant rate can do

In a Factory, three machines \(A, B,\) and \(C,\) working at the same time and at their respective constant rate can do a job in \(8\) hours, \(A\) and \(B\) working at their constant rate can do the same job in \(12\) hours. How many hours would it take \(C,\) working alone at its constant rate, to...


Triangle \(ABC\) is inscribed in a rectangle \(ABEF\) forming two right triangles: \(AFC\) and \(BEC.\) Is triangle

Triangle \(ABC\) is inscribed in a rectangle \(ABEF\) forming two right triangles: \(AFC\) and \(BEC.\) Is triangle \(ABC\) an equilateral triangle?

(1) \(BE = \dfrac{\sqrt3 AB}2\)

(2) Point \(C\) is the midpoint of \(EF.\)

Answer: C

Source: e-GMAT


Abe, Beth, Carl and Duncan are four siblings, among which Abe and Carl are twins and Beth and Duncan are also twins. Whe

Abe, Beth, Carl, and Duncan are four siblings, among which Abe and Carl are twins and Beth and Duncan are also twins. When the present ages of the four siblings are multiplied, the product is 900. If Beth is older than Abe, what is the age of Duncan? Assume the ages of all siblings to be integers. (...


Calculate the units digit of the following expression:

Calculate the units digit of the following expression.
\(
1!^1+2!^2+3!^3+4!^4+5!^5+\cdots+10!^{10}
\)

A) 1
B) 3
C) 5
D) 7
E) 9

Answer: D

Source: e-GMAT

by Gmat_mission

Sun Jan 17, 2021 11:16 am
Forum: Problem Solving
Topic: Calculate the units digit of the following expression:
Replies: 0
Views: 27

If \(x\) is not equal to \(0\) or \(-1,\) what is the value of \(|x-2|?\)

If \(x\) is not equal to \(0\) or \(-1,\) what is the value of \(|x-2|?\)

(1) \(\dfrac{|x+1|}{-|x|x^3} \gt 0 \)
(2) \(x^4=16\)

Answer: C

Source: e-GMAT


A solution contains water, milk and liquid chocolate in the ratio of \(2:3:5\) by volume.

A solution contains water, milk and liquid chocolate in the ratio of \(2:3:5\) by volume. If y liters of water and milk each are added to this solution, the resultant solution would contain 25 percent of water by volume. If the volume of this resultant solution is 120 liters, what is the value of y ...


\(p\) is a positive integer greater than 100. Is p divisible by 36?

\(p\) is a positive integer greater than 100. Is p divisible by 36?

(1) The sum of all digits of p is of the form \(9k + 3\)
(2) The last three digits of \(p\) are not divisible by 8

Answer: A

Source: e-GMAT


In a plane, there are two parallel lines. One line has 5 points and another line has 4 different points.

In a plane, there are two parallel lines. One line has 5 points and another line has 4 different points. How many different triangles can we form from these 9 points?

A. 62
B. 70
C. 73
D. 86
E. 122

Answer: B

Source: e-GMAT


\(x, y\) are positive integers. Find the number of even factors of \(4x^2.\)

\(x, y\) are positive integers. Find the number of even factors of \(4x^2.\)

I. \(x^3-y^3+3xy\) is odd and \(x\) is a prime.
II. \(x^{x+y}\cdot y^{3x}+x^{3y}\) is odd.

Answer: C

Source: e-GMAT


In the given figure, \(BD\) is the median of triangle \(ABC\) and the lines \(BD\) and \(CE\) intersect ...

Q1.png In the given figure, \(BD\) is the median of triangle \(ABC\) and the lines \(BD\) and \(CE\) intersect at point \(F.\) If the area of triangle \(BFC\) is \(6\,\text{cm}^2\) and area of the quadrilateral \(FEAD\) is \(18\,\text{cm}^2.\) Find the area of triangle \(FDC,\) if the ratio of the ...


A motorcyclist traveling at a constant speed of \(x\) miles per hour covers a total distance of 150 miles.

A motorcyclist traveling at a constant speed of \(x\) miles per hour covers a total distance of 150 miles. What is the value of \(x?\) (1) It takes the motorcyclist 400 minutes to cover the total distance of 150 miles. (2) The motorcyclist covers \((x+45)\) miles in 3 hours. Answer: D Source: e-GMAT


In College X in the United States, there are 200 students in a class, of which 80 are female.

In College X in the United States, there are 200 students in a class, of which 80 are female. If 10% of the class consists of female non-American students and 3/5th of the class are American students, how many of the students in the class are male American students? A. 20 B. 40 C. 60 D. 80 E. 120 An...


Point \(A\) lies on a circle whose center is at point \(C.\) Does point \(B\) lie inside the circle?

Point \(A\) lies on a circle whose center is at point \(C.\) Does point \(B\) lie inside the circle?
1. \(BC^2 = AC^2 + AB^2\)
2. \(\angle CAB\) is greater than \(\angle ABC\)

Answer: D

Source: e-GMAT


Two points A and B are connected to each other via three paths, as shown in the figure.

abc.png Two points A and B are connected to each other via three paths, as shown in the figure. A person needs to make a round trip from A to B and then back to A, using any of the three paths. What is the ratio of the possible total distances covered, if he never uses the same path for both onward...