GMAT Hard Math Questions | Algebra

Must solve GMAT practice questions in algebra. The following topics are covered in the GMAT quant section from algebra:

1. Quadratic Equations
2. Exponents
3. Inequalities
4. Absolute Value
5. Functions

1. 700 Level GMAT Sample Question in Inequalities & Polynomials

   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

   Correct AnswerChoice B
   x can take 23 integer values.

   Solution Video Solution

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2. GMAT Hard Math Data Sufficiency Question

   Is x³ > x²?

   Statement 1: x > 0
   Statement 2: x < 1

   Correct AnswerChoice B
   Statement (2) alone is sufficient

   Solution Video Solution

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3. GMAT Data Sufficiency Question | Inequalities & Exponents

   If m and n are non-zero integers, is mⁿ > nⁿ?

   Statement 1: |m| = n
   Statement 2: m < n

   Correct AnswerChoice A
   Statement (1) alone is sufficient

   Solution Video Solution

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4. 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})

   Correct AnswerChoice D
   They will take 36/7 days

   Solution Video Solution

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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

   Correct AnswerChoice E
   The difference is 18.

   Solution Video Solution

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6. 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

   Correct AnswerChoice D
   The minimum possible value for xy is -36.

   Solution Video Solution

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7. 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

   Correct AnswerChoice E
   The movie hall sold 5 $7 tickets.

   Solution Video Solution

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8. 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

   Correct AnswerChoice D
   3 gift hampers did not have $5 certificates.

   Solution Video Solution

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9. 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

   Correct AnswerChoice C
   3840

   Solution Video Solution

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10. GMAT Challenging Question | Geometry DS | Coordinate Geometry & Quadratic Equations

    If y = (x - p)(x - q), is the sum of integers p and q positive?

    Statement 1: The curve cuts the y-axis at -20
    Statement 2: Minimum value of y is -36

    Correct AnswerChoice E
    Data Insufficient

    Solution Video Solution

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11. GMAT Data Sufficiency | Number Properties

    What is the value of (m + n) if m and n are positive integers?

    Statement 1: m² – n² = 105
    Statement 2: Neither m nor n is divisible by 8.

    Correct AnswerChoice E
    Data Insufficient.

    Solution Video Solution

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12. 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

    Correct AnswerChoice B
    3 Values.

    Solution Video Solution