If x/2 + x/3 = 10, what is the value of x?
Find a common denominator for the fractions (6). So, 3x/6 + 2x/6 = 10 implies 5x/6 = 10.
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Solve for x.
A rectangular garden is 15 meters long and 8 meters wide. What is the length of a diagonal of the garden in meters?
Use the Pythagorean theorem: d^2 = l^2 + w^2. So d^2 = 15^2 + 8^2.
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Wrong!
Calculate the length of the diagonal.
If 30% of a number is 45, what is the number?
Let N be the number. Then 0.30 imes N = 45. Solve for N.
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Wrong!
Calculate the original number.
The sum of five consecutive odd integers is 115. What is the middle integer?
Let the integers be x, x+2, x+4, x+6, x+8. Their sum is 5x + 20 = 115. The middle integer is x+4. Alternatively, the average is the middle number for consecutive integers.
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Find the middle integer.
A cyclist travels 45 miles in 3 hours. What is the cyclist's average speed in miles per minute?
First find speed in miles per hour. Then convert hours to minutes (3 hours = 180 minutes). Speed (mph) = 45/3 = 15 mph. Then 15 miles / 60 minutes.
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Calculate the average speed in miles per minute.
If the perimeter of an equilateral triangle is 24 units, what is the length of one side of the triangle?
An equilateral triangle has 3 equal sides. Perimeter = 3 × side.
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Find the side length.
Simplify: (x^3y^2) / (xy^5) where x eq 0 and y eq 0.
Use the rule a^m / a^n = a^{(m-n)}.
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Simplify the algebraic expression using exponent rules.
A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?
Numbers greater than 4 are 5 and 6. There are 2 favorable outcomes out of 6 total possible outcomes.
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Calculate the probability.
If a = 2b and b = 3c, and c=1, what is the value of a?
Substitute c=1 into b=3c to find b. Then substitute b into a=2b to find a.
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Calculate the value of a.
The sum of two numbers is 20 and their difference is 4. What is the product of the two numbers?
Let the numbers be x and y. Then x+y=20 and x-y=4. Solve this system of equations for x and y, then find xy.
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Find the product of the two numbers.
GRE Problem Solving (Single Answer) Practice Quiz 5
Problem Solving Phenom!
You excel at breaking down and solving these math problems!
Mathlete Material!
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Quantitative Puzzler!
Review problem-solving strategies and fundamental concepts.
