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1. Rahul Singh
GREKING

2. What is Quantitative Reasoning Measure?
The Quantitative Reasoning measure of the GRE revised General Test assesses your:
 basic mathematical skills
 understanding of elementary mathematical concepts
 ability to reason quantitatively and to model and solve problems with quantitative
methods
Some of the questions in the measure are posed in real-life settings, while others are posed in
purely mathematical settings. The skills, concepts and abilities are tested in the four content areas
below:
 Arithmetic
 Algebra
 Geometry
 Data analysis
The content in these areas includes high school mathematics and statistics at a level that is
generally no higher than a second course in algebra; it does not include trigonometry, calculus
or other higher-level mathematics..
The mathematical symbols, terminology and conventions used in the Quantitative Reasoning
measure are those that are standard at the high school level. For example, the positive direction
of a number line is to the right, distances are nonnegative and prime numbers are greater than 1.
Whenever nonstandard notation is used in a question, it is explicitly introduced in the question.
In addition to conventions, there are some important assumptions about numbers and figures that
are listed in the Quantitative Reasoning section directions.
 All numbers used are real numbers.
 All figures are assumed to lie in a plane unless otherwise indicated.
 Geometric figures, such as lines, circles, triangles and quadrilaterals, are not necessarily
drawn to scale. That is, you should not assume that quantities such as lengths and angle
measures are as they appear in a figure. You should assume, however, that lines shown as
straight are actually straight, points on a line are in the order shown and, more generally,
all geometric objects are in the relative positions shown. For questions with geometric
figures, you should base your answers on geometric reasoning, not on estimating or
comparing quantities by sight or by measurement.
 Coordinate systems, such as xy-planes and number lines, are drawn to scale; therefore,
you can read, estimate, or compare quantities in such figures by sight or by measurement.
 Graphical data presentations, such as bar graphs, circle graphs, and line graphs, are drawn
to scale; therefore, you can read, estimate or compare data values by sight or by
measurement.

3. GRE Numeric Entry Questions
1) Working together, two water pumps A and B can fill a water tank in 3 hours. Working alone
pump A can fill the tank in 4 hours. How long does it take pump B, working alone, to fill the
same tank?
Solution
Pump A can fill the tank in 4 hours, therefore the quarter of the tank is filled in one hour, hence the rate of
pump A in filling the tank is
1 / 4
If T is the number of hours for pump B to fill the tank, then its rate is
1 / T
When working together for 3 hours both pumps are working at their rates to fill 1 tank. Hence
3(1 / 4) + 3(1 / T) = 1
The term 3(1 / 4) in the above equation is due to pump A working at its rate for 3 hours. The term 3(1 / T)
is due to pump B and the "1" on the right of the equation corresponds to 1 tank. We now solve the above
equation for T
3(1 / T) = 1 - 3 / 4
3(1 / T) = 1 / 4
1 / T = 1 / 12
T = 12 hours

4. 2) The values of x and y are related by the equation y = k / x, where k is a constant. If y = 45
when x = 3, what is the value of x when y = 180?
Solution
"y = 45 when x = 3" is used to find the constant k by substituting y and x by their values
in the equation y = k / x.
45 = k / 3
Solve for k
k = 3 * 45 = 135
We now use the same equation with known value of k to find x when y = 180 as follows
180 = 135 / x
Solve for x
x = 135 / 180 = 3 / 4
3) A rectangle has a length that is one third of its perimeter. The perimeter is 150 meters.
What is the area of the rectangle?
Solution
Let L, W and P be the length, width and perimeter of the rctangle. Hence "a rectangle has
a length that is one third of its perimeter" is translated as follows
L = P / 3 = 150 / 3 = 50
The perimeter P is given by the formula
P = 2L + 2W
Substitute P by 150 and L by 50 and solve for W
150 = 2 * 50 + 2 W
W = 25
The area A of the rectangle is given by :- A = L W = 50 * 25 = 1250

5. 4) The square of the sum of two numbers is 289. The product of the two numbers is 66.
What is the sum of the squares of the two numbers?
Solution
Let x and y be the two numbers. "The square of the sum of two numbers is 289" is
translated as follows
(x + y)2 = 289
Expand the left side of the above equation
x2 + y2 + 2 x y = 289
x y is the product of the two numbers and is given. Hence
x2 + y2 + 2 (66) = 289
Which gives
x2 + y2 = 157
Hence the sum of the square of x and y is 157
5) In a certain country, in one year, 30% of the total money spent on energy was spent on
generating electricity. If 30 billion dollars were spent on energy, how much money, in
billions, was spent on generating electricity?
Solution
30% of the money spent on energy is given by
30% * 30 = 9

6. Questions Without Solutions For Self Practice.
1) The sum of three consecutive odd integers is 249. Find the largest of these numbers.
2) The sum of two numbers is 3.6 and the difference of these numbers is 1.2. Find the largest
of these numbers.
3) 20% of what number is 125?
4) The price of a shirt was first decreased by 10% and then decreased a second time by 15%.
What was the original price of the shirt if the final price is 22 dollars?(round answer to the
nearest cent)
5) The average of 1/2, 1/4, 2/3 and x is equal to 3/4. Find x.

7. SOLUTIONS FOR GIVEN QUESTIONS
1. Let x be the smallest of these numbers. x + 2 and x + 4 will the next two odd
integers. Hence
x + (x + 2) + (x + 4) = 249
Solve for x the above equation.
3x + 2 + 4 = 249
3x = 243
x = 81
The largest of these numbers is x + 4 and its value is
x + 4 = 81 + 4 = 85
2. The sum of two numbers is 3.6 and the difference of these numbers is 1.2. Find the
largest of these numbers.
Solution
Let x and y be the two numbers. Hence
x + y = 3.6 and x - y = 1.2
Solve the above system of equations by adding the left sides and right sides of the
two equations
(x + y) + (x - y) = 3.6 + 1.2
2x = 4.8
x = 2.4
Use equation x + y = 3.6 to finy y
y = 3.6 - 2.4 = 1.2
The largest of these numbers is 2.4

8. 3. 20% of what number is 125?
Solution
Let x the number. Hence
20% x = 125
Solve for x
(20 / 100) x = 125
x = 125 * 100 / 20 = 625
4. The price of a shirt was first decreased by 10% and then decreased a second time
by 15%. What was the original price of the shirt if the final price is 22
dollars?(round answer to the nearest cent)
Solution
Let x be the original price. The price after the first reduction of 10% is given by
x - 10% x = x - (10/100)x = x - 0.1x
The price after the second reduction of 15% is given by
(x - 0.1x) - 15% (x - 0.1x) = x - 0.1x - (15/100)(x - 0.1x)
= x - 0.1x - 0.15(x - 0.1x)
= x - 0.1x - 0.15x + 0.015x
= 0.765x
The final price is 22 dollars. Hence
0.765x = 22
Solve for x
x = 28.7581
Rounded to the nearest cent, the origonal price x is equal to 28.76 dollars

9. 5. The average of 1/2, 1/4, 2/3 and x is equal to 3/4. Find x.
Solution
The average of 1/2, 1/4, 2/3 and x is given by
(1/2 + 1/4 + 2/3 + x) / 4
and is equal to 3/4. Hence
(1/2 + 1/4 + 2/3 + x) / 4 = 3 / 4
Solve for x. First mutliply both sides of the equation by 4 ans simplify
(1/2 + 1/4 + 2/3 + x) = 3 x = 3 - (1/2 + 1/4 + 2/3)
Set all fractions to common denominator
x = 36/12 - (6/12 + 3/12 + 8/12) = 36/12 - 17/12
x = 19/12