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7/27/2019 Sample Questions - Quantative
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20 GRE Quantitative Reasoning Sample Questions
1 | P a g e
NOTE:
a. The number of questions under different question types is NOT representative of the actual GRE)b. The number of questions under each area of testing (Arithmetic, Algebra, Geometry, Data Analysis)
is NOT representative of the actual GRE)
_______________________________________________________________________________________
1. If 35 is the median of the data set including 21, 7, 45, 33, 62 and x, then what is the value of x?
A) 3
B) 14
C) 37
D) 33
E) 48
2. a > b > c > d > 1 and the product of a, b, c, d is 210
Quantity A Quantity B
abcd abc + abd + adc + bcd
Select one of the following four choices:
A) Quantity A is greaterB) Quantity B is greaterC)
The two quantities are equalD) The relationship cannot be determined from the information given
3. The difference between the exterior angle of an (n-1) sided regular polygon and the exterior angle of an
(n+2) sided regular polygon is 60. What is the value of n?
[Numeric Entry question]
4. What is true about the graph of function f defined by
y = 4 + | | x | - 3 |
I. Symmetric with respect to y-axis
II. Has no x intercepts
III. Has one y intercept at (0,7)
A) I and II only
B) I and III only
C) I, II and III
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D) II and III only
E) None
5. N = {12, 18, 2, 6}
P = {1, 4, 2, 3}
If n and p are to be selected at random from sets N and P respectively. What is the probability thatp2
nwill
be a member of set p?
[Numeric Entry question]
Express your answer as a fraction.
6. A data set has a standard deviation equal to 1. If each data value in the data set is multiplied by 4, then
the value of the standard deviation of the new data set is equal to
A) 0.25
B) 0.50
C) 1
D) 2E) 4
7. The range of the function f(x) = -|x - 2| - 3 is
A) y 2
B) y -3
C) y -3
D) y -2
E) y -2
8. The perimeter of the parallelogram PQRS is 50. If PQ > PS and the sides are integers, then what can avalue of PQ be?
Select ALL that apply.
A)11B)12C)13D)14E)15F)16G)17
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9. The No-Child-Left-Behind program at a certain middle school had a total enrolment of 150 students. 55
students were enrolled in Math, 37 students were enrolled in Physics and 22 in both. How many students
were enrolled in neither Math nor Physics?
A) 36
B) 58C) 70D) 80
E) 114
10. Ifa > 0 > b > c, and if |a| > |c|, which of the following inequalities holds in all cases?
Select ALL that apply.
A) bca < 0B) ab + c < 0C) acb < 0D) abc < 0E) abc > 0F) abac > 011. In a class of 40 students, 40% received grade A. In another class of 50 students, 40% received grade A.
What percent of the total number of students in both classes received grade A?
A) 30%
B) 36%
C) 40%D) 60%
E) 80%
In the first class number of students with grade A
In the second class, number of students with grade
So, percent of the total number of students receiving grade A
Use the information below to answer the following two questions:
Bread Sauce Cheese
Rye Spicy tomato American
Wheat Sweet onion Swiss
White Mayonnaise Provolone
Mustard Pepper Jack
Hot peppers
1640100
40
2050100
40A
%4010050402016
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JJs Sandwich offers the below varieties of bread, sauce and cheeseA sandwich from JJs consists of one type of bread, one sauce, and one cheese
12 . Quantity A Quantity BNumber of possible
sandwiches JJs makes 60
Select one of the following four choices:
A) Quantity A is greaterB) Quantity B is greaterC) The two quantities are equalD) The relationship cannot be determined from the information given13. Quantity A Quantity B
Number of sandwiches Number of sandwiches that can be made
that can be made on rye bread on wheat bread
Select one of the following four choices:
A) Quantity A is greaterB) Quantity B is greaterC) The two quantities are equalD) The relationship cannot be determined from the information given14. Use the frequency distribution table below to answer the question:
Data Value Frequency0 3
1 6
2 2
3 1
4 2
Quantity A Quantity BMedian of distribution 2
Select one of the following four choices:
A) Quantity A is greaterB) Quantity B is greaterC) The two quantities are equalD) The relationship cannot be determined from the information given15. Peter can ride his bike 16mph faster than Rebecca can walk. Peter rides at 25miles in the same time Rebecca
walks 15 miles. What is Peters speed in mph?Quantity A Quantity B
Peters speed in mph 24
Select one of the following four choices:
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A) Quantity A is greaterB) Quantity B is greaterC) The two quantities are equalD) The relationship cannot be determined from the information given16. In a Math class of 20 students, one-fifth of them are seniors and there are twice as many juniors asseniors.
Quantity A Quantity BNumber of students who are not 10
junior or seniors
Select one of the following four choices:
A) Quantity A is greaterB) Quantity B is greaterC) The two quantities are equalD) The relationship cannot be determined from the information given17. The ratio of gasoline to edible oil in 40 liters of the mixture is 3:1. How many liters of edible oil should
be added in the mixture to make the ratio of gasoline to edible oil 2:1?
A) 1.5B) 5C) 7.5C) 10E) 15
18. Quantity A Quantity B
Area of the region bounded Area of the right-angled triangleby y = 0,x = 6 andx = y with sides 6, 8, 10
Use the information below to answer the following question:
Category Estimated Expenses
Home Rent $500
Car Payment /Gasoline $750
Groceries $300
Entertainment $50
The table above shows the estimates of the only expenses of Mr. X in a certain month. Mr. Xearns $2000
that month.
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20 GRE Quantitative Reasoning Sample Questions
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19. If Mr. X manages to cut down his actual expenses by 10% over what he estimated in each category, then
by what percent have his savings increased?
A) 10%B) 20%
C) 30%D) 40%E) 50%
Use the information below to answer the following question:
y
x
5
4
3
2
1
1990 1991 1992 1993 1994
Exports(in 000)
Year
20. Which year showed the highest percentage increase of exports over the previous year?
A) 1991B) 1992C) 1993D) 1994E) cannot be determined
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KEY
1. C2. B3. 134. C5.
8
3
6. E7. B8. C, D, E, F, G9. D10.B, C11.C12.C13.C14.B15.A16.B17.A18.B19.D20.A
SOLUTIONS
1. Since 35 is the median of the set, median should lie between 33 and x.Arranging the numbers in increasing order : 7, 21, 33, x, 45, 62
Since there are even number of elements, median =33+
2= 35
Or, x = 37
Hence, C
2. abcd = 210or 2 *3* 5* 7 = 210
since a > b > c > d > 1,a = 7, b = 5, c = 3 and d = 2
Quantity A : 210Quantity B : 105 + 70 + 42 + 30 = 247
Hence, B
3.360
1
360
+2= 6
or , n
2
+ n182 = 0or, (n + 14) (n13 ) = 0So, n = 13
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4. I): Determine f(-x) and simplify it
f(-x) = 4 + | | - x | - 3 | = 4 + | | x | - 3 | since |-x| = |x|
Hence f(x) is even and its graph is symmetric with to the y axis.
(II): Find any x intercepts by solving f(x) = 0
4 + | | x | - 3 | = 0
Add -4 to both sides of the above equation to obtain
| | x | - 3 | = - 4
The absolute value of an expression is never negative, hence the above equation has no solutions and
therefore the graph of the given function has no x intercepts.
(III): Find the y intercept by finding f(0)
f(0) = 4 + | | 0 | - 3 | = 7
The graph of f has a y intercept at (0 , 7).
All three statements in (I), (II) and (III) are true.
Hence, C.
5. There are 4 elements in N.
There are 4 elements in P.
Number ofp2
ncombinations = 4 x 4 = 16
Number of cases whenp2
nis in P = 6
(i.e. 312
6;1
32
6;1
12
2
)
So, probability thatp2
nis in p =
8
3
16
6
6. The standard deviation involves the square root of the sum of (xi - m)2 where xi are the data values and
m is the mean. If each data value is multiplied by k then the mean will be k times. Hence the new standarddeviation will involve the square root of the sum of (k xi - k m)
2 and therefore the new standard deviationwill be k times the old standard deviation. In this case k = 4 and the old standard deviation is one. The
standard deviation after multiplication will be equal to 4.Hence, E
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7. The absolute value is either positive or zero. Hence
|x - 2| 0
Multiply both sides of the inequality by -1 and reverse the symbol of inequality to obtain
- |x - 2| 0
Subtract 3 from both sides of the inequality to obtain
- |x - 2| - 3 - 3
The right side of the above inequality is equal to f(x). Hence the inequality gives f(x) - 3
The above inequality states that the range of y = f(x) is given by y -3
Hence, B
8. Since perimeter of PQRS is 50,
PQ + PR = 25. Also, PQ > PR, and PQ, PR are integers.
So, PQ = 13, 14, 15, ... , 24
Hence, C, D, E, F, G
9. The number of students enrolled in either Math or Physics or both is given by
= + ( )
= 55 + 3722 = 70
So, the number of students enrolled in neither Math nor Physics
= 15070 = 80
Hence, D
10. Plug-in random values for a, b, c, d that satisfy the relation and check for the options. Say,
5 > 0 > -2 > -3.
Hence, B, C
11. In the first class number of students with grade A
In the second class, number of students with grade
So, percent of the total number of students receiving grade A
1640100
40
205010040A
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Hence, C
12. JJs offers 3 types of bread, 5 types of sauce, and 4 types of cheese. Therefore, JJs can make any of 3*5 *4 = 60 types of sandwiches.
Hence, C
13. Fixing the type of bread means JJs can use 1 type of bread, any of the 5 sauces and any of the 4 cheeses
on the sandwich.5 *4 = 20 types of sandwiches that can be made on wheat or rye bread.
Hence, C
14. Since there are 14 data items (an even number) in the frequency table, the median will be the average ofthe middle two, namely the seventh and the eighth pieces.The table contains the data in numerical order, so the first three elements are zeros and thenext six are ones. Therefore, the seventh and eighth pieces of data will both be 1 and the median will be 1.
Hence, B
15. If Peters speed is x mph, Rebeccas speed is (x 16) mph. Since
Time taken for Peter to ride 25 miles = time taken by Rebecca to walk 15 miles,
25
= 15 16
or, x = 40
Hence, A
16. Seniors =
Juniors = 2 x seniors = 8
Quantity A: Students who are not juniors or seniors = 20-(4+8) = 8
Hence, B
17. 40 liters of a mixture in 3:1 ratio would mean 30 liters of gasoline and 10 liters of edible oil.
If x liters of edible oil need be mixed to make the ratio 2:1,
30
10 + =
2
1
or, x = 5.
%401005040
2016
420.5
1
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Hence, B
18. Quantity. A:2
1. 6.6 = 18
Quantity B:21 . 6.8 = 24 How do we know 6 and 8 are the base and height or height and base?
O
y
x
(6,6)
x=yx=6
6
6
Hence, B
19. 10% cut down on all the categories.
1440100
10.16001600
Savings initially = 400
Since Savings = EarningsExpenditures
= 2000(500 + 750 + 300 + 50) = $400
Savings now = 560
Percent increase in savings %40100400
400560
Hence, D
20. Percentage increase from 1990 to 1991 = 1001000
10003000
= 200%
No increase from 91 to 92
Decrease from 92 to 93
Percentage increase from 93 to 94 = 150%
So, highest percentage increase was shown in 1991.
Hence, A