| Coverage : The GRE Practice Test - Math - Algebra has been developed to test the basic concepts and skills related to Algebra. This test covers the concepts of linear algebra, equation solving, finding roots for the equation and applying formulae to solve equations. |
| 1. | If 6x²=24, then
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| a. | | The quantity in column A is greater |
| b. | | The quantity in column B is greater |
| c. | | The two quantities are equal |
| d. | | The relationship cannot be determined from the information given.
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| 2. | Solve:2x+3y=21 and -3x-6y=42. |
| a. | | x=5, y=18 |
| b. | | x=-5, y=18 |
| c. | | x=84, y=-49 |
| d. | | x=-18, y=-5
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| 3. | Which one is greater?
A = 9x² + 9y² or B = (3x+3y)² |
| a. | | A |
| b. | | B |
| c. | | Both are equal |
| d. | | Cannot be determined
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| 4. | Solve:[(1/3)+(1/2)-(1/12)] |
| a. | | 4/3 |
| b. | | -11/12 |
| c. | | -3/4 |
| d. | | 9/12
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| 5. | Solve for x :
6x² + 10x - 4 = 0 |
| a. | | 2,-2 |
| b. | | 1,1/3 |
| c. | | -2,1/3 |
| d. | | -1/3,1
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| 6. | Solve the equation :
3x - y = 10
x + 2y = 15 |
| a. | | x=y= 5 |
| b. | | x=y= -5 |
| c. | | x=5,y=-5 |
| d. | | x=-5,y=5
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| 7. | If x = 10y, then 30y = 3z, then x = ? |
| a. | | 2z |
| b. | | 3z |
| c. | | z |
| d. | | 5z
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| 8. | If 2x + 13 x + 9x + 4x = 112, then 2x+3 = ? |
| a. | | 8 |
| b. | | 9 |
| c. | | 10 |
| d. | | 11
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| 9. | If z = 2, then z^4 (z^4 - z² ) =? |
| a. | | 110 |
| b. | | 192 |
| c. | | 162 |
| d. | | 182
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| 10. | If x=2, then [((3 - 1)/(3-x))(( 3 - 1)/(4-x))(( 3 - 1)/(5-x))] |
| a. | | 1/3 |
| b. | | 50/3 |
| c. | | 20/3 |
| d. | | 4/3
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| 11. | If x+1/x = 8, then x² + 1/x² = ? |
| a. | | 52 |
| b. | | 53 |
| c. | | 54 |
| d. | | 62
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| 12. | Given x² + 1/ x² = 51, find value for x-1/x. |
| a. | | 7 |
| b. | | -7 |
| c. | | 5 |
| d. | | ±7
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| 13. | Find the value for x³+y³, given xy=200, (x+y) = 30. |
| a. | | 9000 |
| b. | | 6000 |
| c. | | 7000 |
| d. | | 6500
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| 14. | Find the value of following expression :
[{ 5.79 × 5.79 × 5.79 + 4.21 × 4.21 × 4.21} ÷ { 5.79 × 5.79 - 5.79 × 4.21 + 4.21 × 4.21}] |
| a. | | 21.790 |
| b. | | 10.00 |
| c. | | 15.19 |
| d. | | 11.111
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| 15. | If one root of the quadratic equation 8x² - 28x + y = 0 is six times the other.Find the value of y. |
| a. | | 10 |
| b. | | 2 |
| c. | | 8 |
| d. | | 9
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| 16. | If 16x² + 24x + r = 0 have equal roots, find the value of r. |
| a. | | 8 |
| b. | | 12 |
| c. | | 9 |
| d. | | 10
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| 17. | Solve the inequality 4x-2 > 8 for x. |
| a. | | 1/2 |
| b. | | -3/2 |
| c. | | 5/2 |
| d. | | 3/4
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| 18. | Solve the inequality [( 3x -2)/-2] < 4. |
| a. | | -3 |
| b. | | 1 |
| c. | | 2 |
| d. | | -2
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| 19. | Solve for x and y :
(x - 2) / 6 = (y - 2) / 7 = (x - y) / 3 |
| a. | | x = 2, y = -2 |
| b. | | x = 2, y = 2 |
| c. | | x = -2, y = -2 |
| d. | | x = -2, y = 2
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| 20. | A two digit number is four times the sum of its digits. The number obtained by
interchanging the digits is less by 12 than twice the original number. |
| a. | | 84 |
| b. | | 36 |
| c. | | 72 |
| d. | | 48
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| 21. | If 1 is added to the numerator of a certain fraction its value becomes 3/4 and if 1 is added to its denominator it becomes 2/3. Find the original fraction. |
| a. | | 5/10 |
| b. | | 2/5 |
| c. | | 7/10 |
| d. | | 3/7
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| 22. | (2x+4)²= 256. Find the values of x. |
| a. | | -5, 2 |
| b. | | -10, 6 |
| c. | | 7, 6 |
| d. | | 16, -6
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| 23. | A natural number is greater than another natural number by 2. The sum of their squares is 100. Find the numbers. |
| a. | | 3, 5 |
| b. | | 8, 10 |
| c. | | 6, 8 |
| d. | | 5, 7
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| 24. | The digit in the ten's place of a two digit number is equal to the square of the digit in the unit's place. If 18 is subtracted from that number, its digits are interchanged. Find that number. |
| a. | | 42 |
| b. | | 93 |
| c. | | 11 |
| d. | | 83
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| 25. | The length of a rectangle is less than twice its breadth by 1 cm. If its length is reduced by 5 cm and breadth is increased by 5 cm, then its area is increased by 35 sq.cm. Find the length and breadth of the rectangle. |
| a. | | 25 cm, 13 cm |
| b. | | 16 cm, 7 cm |
| c. | | 21 cm, 11 cm |
| d. | | 15 cm, 12 cm
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| 26. | The average of 5 quantities is 30. The average of three of them is 20. What is the average of remaining two numbers? |
| a. | | 54 |
| b. | | 45 |
| c. | | 40 |
| d. | | 60
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| 27. | The average of 11 results is 75. The average of first six is 60 and that of last six is 70. What is the seventh result? |
| a. | | 54 |
| b. | | 82 |
| c. | | 62 |
| d. | | 45
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| 28. | If a factory 'A' makes x bags in an hour and another factory 'B' makes y bags in two hours. How many bags will both factories make in 6 hours? |
| a. | | 2x+ y |
| b. | | 6x+ 3y |
| c. | | 4x+ 4y |
| d. | | 2x+ 3y
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| 29. | If 6.4 ÷ 64 T 10 = 4.25 - 3.25, which of the following signs should replace the T? |
| a. | | + |
| b. | | - |
| c. | | × |
| d. | | ÷
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| 30. | Twenty five years ago, my age was 1/2 of what it is now. What is my present age? |
| a. | | 25 |
| b. | | 52 |
| c. | | 54 |
| d. | | 50
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| 31. | How many 1/6s are there in 36+1/3. |
| a. | | 218 |
| b. | | 300 |
| c. | | 250 |
| d. | | Data insufficient
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| 32. | If 5 points are marked at an equal distance between two poles, which are 20 m apart, what is the distance between any two of the points? |
| a. | | 4m |
| b. | | 5m |
| c. | | 2m |
| d. | | 3m
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| 33. | Harry reads 2/5 of a book on the first day and 5/6 of the remainder on the second day. If the number of pages still unread are 50, how many pages did the book contain? |
| a. | | 420 |
| b. | | 500 |
| c. | | 380 |
| d. | | 492
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| 34. | After covering 5/6th of journey, Veronica found she has traveled 80 km. How much of her journey is left? |
| a. | | 92 km |
| b. | | 96 km |
| c. | | 106 km |
| d. | | 82 km
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| 35. | In a test, a student was asked to find 5/12 of a certain number. By mistake, the student found 5/2 of it. His answer was 250 more than the correct answer. Find the original number. |
| a. | | 120 |
| b. | | 180 |
| c. | | 282 |
| d. | | 200
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| 36. | Given ab = 54,
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| a. | | The quantity in column A is greater. |
| b. | | The quantity in column B is greater. |
| c. | | The two quantities are equal. |
| d. | | The relationship cannot be determined.
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| 37. | If z = 1/xy then 3/z is equal to. |
| a. | | 3xy |
| b. | | 3/xy |
| c. | | 3/(x+y) |
| d. | | 3/x + 3/y
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| 38. | Find two numbers whose sum is 164 and their difference is 6. |
| a. | | 83, 89 |
| b. | | 79, 85 |
| c. | | 92, 86 |
| d. | | 84, 70
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| 39. | Which statement is true:
| Column A | Column B |
| a³ × a² | 5a² ×a² |
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| a. | | The quantity in column A is greater. |
| b. | | The quantity in column B is greater. |
| c. | | The two quantities are greater. |
| d. | | The relationship cannot be determined.
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| 40. | How many 8 cent balloons can be purchased for 'z' cents? |
| a. | | 8z |
| b. | | z/8 |
| c. | | 8/z |
| d. | | 8+z
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| 41. | If f(x) = x³ - x, what is f(f(3)) = ? |
| a. | | 12800 |
| b. | | 24240 |
| c. | | 13800 |
| d. | | 12840
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| 42. | Solve for a : 3ª - 2×3ª + 3 = 0 |
| a. | | -1 |
| b. | | 1 |
| c. | | 0 |
| d. | | -2
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| 43. | The value of (-2 - (-8)) is how much bigger than the value of (-8 - (-2))? |
| a. | | 6 |
| b. | | 12 |
| c. | | 0 |
| d. | | 8
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| 44. | Evaluate : 100 - 6[3³ + 27/3 + 4(10-14)] |
| a. | | 120 |
| b. | | -20 |
| c. | | -120 |
| d. | | 10
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| 45. | Sum of two numbers is 85 and their LCM is 102. Find them. |
| a. | | 7, 78 |
| b. | | 6, 17 |
| c. | | 34, 3 |
| d. | | 34, 51
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| 46. | A car travels 'x' miles in ' y' hours. How long will it take to cover 'z' miles, at same speed ? |
| a. | | xyz |
| b. | | y/z |
| c. | | yz/x |
| d. | | xy/z
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| 47. | Which statement is true:
| Column A | Column B |
| (1/2 - 1/16) / (1/8) | 3 |
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| a. | | The quantity in column A is greater |
| b. | | The quantity in column B is greater |
| c. | | The two quantities are equal |
| d. | | The relationship cannot be determined.
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| 48. | Which statement is true:
| Column A | Column B |
| [(1/a)/a] / [a³ ×(1/a²)] | (1/a) × (1/a) ×(1/a) |
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| a. | | The quantity in column A is greater |
| b. | | The quantity in column B is greater |
| c. | | The two quantities are equal |
| d. | | The relationship cannot be determined
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| 49. | Evaluate: 8/x/2/x |
| a. | | 4 |
| b. | | x²/16 |
| c. | | 16/x² |
| d. | | 4x
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| 50. | Given aTbTc = a² + b² + c² - abc, then find the value of 2T(3T4T2)T3. |
| a. | | 18 |
| b. | | 8 |
| c. | | 44 |
| d. | | 14
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