Sample Questions - Quantative

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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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    20 GRE Quantitative Reasoning Sample Questions

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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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    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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    20 GRE Quantitative Reasoning Sample Questions

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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