GMAT Hard Math Questions | PS

GMAT Problem Solving | 700 800 Level Questions

  1. GMAT 700 Level Sample Question in Algebra / Inequalities

    If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, how many values can x take?

    1. 47
    2. 23
    3. 46
    4. 21
    5. 22
    Choice B
    x can take 23 integer values.

  2. 700 800 Level GMAT Sample Question | Probability

    If two distinct integers a and b are picked from {1,2,3,4....100} and multiplied, what is the probability that the resulting number has EXACTLY 3 factors?

    1. \\frac{4}{25 \times 99})
    2. \\frac{2}{25 \times 99})
    3. \\frac{8}{25 \times 99})
    4. \\frac{16}{25 \times 99})
    5. \\frac{32}{25 \times 99})
    Choice B
    2/(25 × 99)

  3. 700 800 Level GMAT Word Problem | Rates Problem Solving Question

    Working alone, A can complete a task in 'a' days and B in 'b' days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

    1. \\frac{46}{9})
    2. \\frac{50}{9})
    3. \\frac{50}{11})
    4. \\frac{36}{7})
    5. \\frac{210}{41})
    Choice D
    They will take 36/7 days.


  4. GMAT 700 800 Level Question | Geometry | Area of Circles

    In the figure given below, ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region?

    semicircle

    1. 4π - 1
    2. 3π - 1
    3. 2π - 4
    4. ½(3π - 1)
    5. 2π - 2
    Choice C
    The area of the shaded region is
    (2π - 4) sq units.

  5. GMAT Hard Math Questions | Algebra | Absolute Values Sample Question

    If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S?
    \\ S = 1+\frac { \left| a \right| }{ a } +\frac {2 \left| b \right| }{ b } +\frac {3 \left| ab \right| }{ ab } -\frac {4 \left| c \right| }{ c } \\)

    1. 12
    2. 14
    3. 22
    4. 20
    5. 18
    Choice E
    The difference is 18.

  6. GMAT 700 Level Sample Question in Statistics

    Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?
    I. The maximum possible range of the set is greater than 33.
    II. The median can never be an even number.
    III. If y = 37, the average of the set will be greater than the median.

    1. I only
    2. I and II only
    3. I and III only
    4. III only
    5. I, II and III
    Choice E
    All three statements are correct.

  7. GMAT Hard Math Algebra - Absolute Values | GMAT Problem Solving

    If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

    1. -12
    2. -18
    3. -24
    4. -36
    5. -48
    Choice D
    The minimum possible value for xy is -36.

  8. GMAT Challenging Question | Statistics Problem Solving

    Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?

    1. 23
    2. 21
    3. 25
    4. 26
    5. 24
    Choice C
    Least possible value for c is 25.


  9. GMAT Hard Math | Arithmetic | Permutation Combination Sample Question

    How many four-digit positive integers exist that contain the block 25 and are divisible by 75. (2250 and 2025 are two such numbers)?

    1. 90
    2. 63
    3. 34
    4. 87
    5. 62
    Choice C
    34 such four-digit numbers exist.

  10. 700 800 Level GMAT Word Problem | Number Properties & Equations Problem Solving Question

    A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.

    1. 14
    2. 11
    3. 2
    4. 8
    5. 5
    Choice E
    The movie hall sold 5 $7 tickets.

  11. GMAT 700 800 Level Question | Coordinate Geometry & Permutation Combination

    Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality 11 < x < 29 and 5 ≤ y ≤ 13?

    1. 153
    2. 153C4
    3. 4896
    4. 2448
    5. 5508
    Choice C
    4896 rectangles can be constructed.

  12. GMAT Hard Math Question | Algebra | Difficult Equations Question

    Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?

    1. 5
    2. 2
    3. 9
    4. 3
    5. 7
    Choice D
    3 gift hampers did not have $5 certificates.

  13. GMAT 700 Level Sample Question in Counting Methods

    149 is a 3-digit positive integer, product of whose digits is 1 × 4 × 9 = 36. How many 3-digit positive integers exist, product of whose digits is 36?

    1. 21
    2. 27
    3. 9
    4. 45
    5. 12
    Choice A
    21 numbers exist.

  14. GMAT Hard Math Arithmetic | Permutation Combination - Selections | GMAT Problem Solving

    A student is required to solve 6 out of the 10 questions in a test. The questions are divided into two sections of 5 questions each. In how many ways can the student select the questions to solve if not more than 4 questions can be chosen from either section?

    1. 100
    2. 210
    3. 150
    4. 200
    5. 105
    Choice D
    In 200 ways.

  15. GMAT 700 800 Level Question | Arithmetic | Counting Methods Problem Solving

    How many 6-digit numbers can be formed using the digits {1, 2, 3, ... 9} such that any digit that appears in such a number appears at least twice?

    1. 1809
    2. 7569
    3. 9369
    4. 8649
    5. 8289
    Choice C
    9369 such numbers.


  16. GMAT Hard Math | Arithmetic | Number Properties Sample Question

    If y is the highest power of a number 'x' that can divide 101! without leaving a remainder, then for which among the following values of x will y be the highest?

    1. 111
    2. 462
    3. 74
    4. 33
    5. 210
    Choice E
    When x = 210.

  17. GMAT 650 Level Algebra Question | Polynomials

    If a, b, .. , j are real numbers such that (a - 1)2 + (b - 2)4 + (c - 3)6 + ... + (j - 10)20 = 0, what is the value of b × d × f × h × j?

    1. 120
    2. 36,28,800
    3. 3840
    4. 240
    5. 1536
    Choice C
    3840

  18. GMAT Hard Math Arithmetic - Counting Methods | GMAT Problem Solving

    What is the sum of all 3-digit positive integers such that all the digits of each of the number is even?

    1. 55,500
    2. 1300
    3. 44,400
    4. 247,275
    5. 54,400
    Choice E
    54,400

  19. GMAT Challenging Math Question | Arithmetic | Number Properties - Remainders

    What is the least number that when divided by 44 leaves a remainder 31, when divided by 56 leaves a remainder 43, and when divided by 32 leaves a remainder 19?

    1. 2464
    2. 2477
    3. 2451
    4. 616
    5. 603
    Choice C
    2451

  20. GMAT Number Properties Practice | 650 Level Question | Factors Problem Solving

    What is the product of all the factors of the cube of a positive integer 'n' if the product of all the factors of square of n is n3?

    1. n4
    2. n6
    3. n9
    4. n5
    5. Cannot be determined
    Choice B
    n6

  21. GMAT Arithmetic Question | Numbers Counting Methods Problem Solving

    How many even 3-digit positive integers with distinct digits are there?

    1. 400
    2. 320
    3. 328
    4. 356
    5. 408
    Choice C
    328 integers.

  22. GMAT Algebra Practice Question | Equations & Numbers PS

    If x and y are non-negative integers such that 4x + 7y = 68, how many values are possible for (x + y)?

    1. 11
    2. 3
    3. 5
    4. 17
    5. 14
    Choice B
    3 Values.



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