# ข้อสอบ GMAT Math วิชาคณิตศาสตร์ เตรียมต่อ ป.โท มีเฉลยให้ด้วย

## GMAT Math

1. Set T is a finite set of positive consecutive multiples of 14. How many of these integers are also multiples of 21?

(1)Set T consists of 30 integers.

(2)The smallest integer in Set T is a multiple of 21.

(1)Set T consists of 30 integers.

(2)The smallest integer in Set T is a multiple of 21.

2. IF yz ≠ 0 , is \displaystyle \frac{x-y+z}{2z}< \frac{x}{2z}-\frac{y}{2z}-\frac{x}{y}?

(1)\displaystyle \frac{x}{y}< -\frac{1}{2}

(2)\displaystyle xy< 0

(1)\displaystyle \frac{x}{y}< -\frac{1}{2}

(2)\displaystyle xy< 0

3. Is \displaystyle x>9?

(1)\displaystyle x^2+3x=28

(2)\displaystyle 9x=5x-28

(1)\displaystyle x^2+3x=28

(2)\displaystyle 9x=5x-28

4. A beer company spent $100,000 last year on hops, yeast, and malt. How much of the total expenditure was for hops?

(1)The expenditure for yeast was 20% greater than the expenditure for malt.

(2)The total expenditure for yeast and malt was equal to the expenditure for hops.

(1)The expenditure for yeast was 20% greater than the expenditure for malt.

(2)The total expenditure for yeast and malt was equal to the expenditure for hops.

5. What is the value of j+k?

(1) mj + mk = 2m

(2) 5j + 5k = 10

(1) mj + mk = 2m

(2) 5j + 5k = 10

6. x is a positive integer less than 20. What is the value of x?

(1) x is the sum of two consecutive integers.

(2) x is the sum of five consecutive integers.

(1) x is the sum of two consecutive integers.

(2) x is the sum of five consecutive integers.

7.If arc XYZ above is a semicircle, what is its length?

(1) q = 2

(2) r = 8

(1) q = 2

(2) r = 8

8.What is the value of x?

(1)(x)(x + 1) = (2013)(2014)

(2)x is odd

(1)(x)(x + 1) = (2013)(2014)

(2)x is odd

9.If Alyssa is twice as old as Brandon, by how many years is Brandon older than Clara?

(1)Four years ago, Alyssa was twice as old as Clara is now.

(2)Alyssa is 8 years older than Clara.

(1)Four years ago, Alyssa was twice as old as Clara is now.

(2)Alyssa is 8 years older than Clara.

10.In the first hour of a bake sale, students sold either chocolate chip cookies, which sold for $1.30, or brownies, which sold for $1.50. What was the ratio of chocolate chip cookies sold to brownies sold during that hour?

(1)The average price for the items sold during that hour was $1.42

(2)The total price for all items sold during that hour was $14.20

(1)The average price for the items sold during that hour was $1.42

(2)The total price for all items sold during that hour was $14.20

11. If a, b, and c are distinct positive integers where a<b<c and \displaystyle \sqrt{abc}=c what is the value of a?

(1) c=8

(2) The average of a,b, and c is \displaystyle \frac{14}{3}

(1) c=8

(2) The average of a,b, and c is \displaystyle \frac{14}{3}

12. Line M is tangent to a circle, which is centered on point (3, 4). Does Line M run through point (6, 6)?

(1) Line M runs through point (-8, 6)

(2) Line M is tangent to the circle at point (3, 6)

(1) Line M runs through point (-8, 6)

(2) Line M is tangent to the circle at point (3, 6)

13. For nonnegative integers x and y, what is the remainder when x is divided by y?

(1) \frac{x}{y} =13.8

(2) The numbers x and y have a combined total of less than 5 digits.

(1) \frac{x}{y} =13.8

(2) The numbers x and y have a combined total of less than 5 digits.

14. If x and y are positive integers, is xy an integer?

(1) Every factor of y is also a factor of x

(2) Every factor of x is also a factor of y

(1) Every factor of y is also a factor of x

(2) Every factor of x is also a factor of y

15. What is the average of the terms in set J?

(1) The sum of any three terms in Set J is 21

(2) Set J consists of 12 total terms.

(1) The sum of any three terms in Set J is 21

(2) Set J consists of 12 total terms.

16. Is xy > 24?

(1) y - 2 < x

(2) 2y > x + 8

(1) y - 2 < x

(2) 2y > x + 8

17. If xy≠0, is \displaystyle \frac{1}{x}+\frac{1}{y}=16?

(1) \displaystyle x+y=16xy

(2) \displaystyle x=y

(1) \displaystyle x+y=16xy

(2) \displaystyle x=y

18. What is the value of x+2y?

(1) \displaystyle 3^x9^y=27^12

(2) \displaystyle x=2y

(1) \displaystyle 3^x9^y=27^12

(2) \displaystyle x=2y

19. Is \displaystyle a^2>3a-b^4?

(1) \displaystyle 3a-b^4=-5

(2) \displaystyle a>5 and \displaystyle b>0

(1) \displaystyle 3a-b^4=-5

(2) \displaystyle a>5 and \displaystyle b>0

20. If \displaystyle xy\neq 0, is \displaystyle a>\frac{y}{x}?

21. What is the value of two-digit integer x?

(1) The product of the two digits is 14.

(2) x is divisible by 9.

(1) The product of the two digits is 14.

(2) x is divisible by 9.

22. In a retail store, the average (arithmetic mean) sale for month M was d dollars. Was the average (arithmetic mean) sale for month J at least 20 percent higher than that for month M?

(1) For month M, total revenue from sales was $3,500.

(2) For month J, total revenue from sales was $6,000.

(1) For month M, total revenue from sales was $3,500.

(2) For month J, total revenue from sales was $6,000.

23. (NOTE: not drawn to scale) Is a > 85?

(1) b > 75

(2) c > 95

(1) b > 75

(2) c > 95

24. Is a>b−c?

(1) c>b−a

(2) b<c+a

(1) c>b−a

(2) b<c+a

25. Is \displaystyle x>6?

(1) \displaystyle x^2=49

(2) \displaystyle 7x=x^2

(1) \displaystyle x^2=49

(2) \displaystyle 7x=x^2

26. 3,8,a,17,b If b=3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a>2

(2) a

(1) a>2

(2) a

^{2}<9
27. Is \displaystyle p^3< p?

(1) p<1

(2) p is an integer

(1) p<1

(2) p is an integer

28. Is the area of circular region X greater than the area of circular region Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.

(2) The radius of circle X is greater than the radius of circle Y.

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.

(2) The radius of circle X is greater than the radius of circle Y.

29. An artist's portfolio consisting of 1,000 photos is divided into 20 subjects. After an extensive photo shoot, two more subjects are then added to the portfolio. Is the average (arithmetic mean) number of photos in each subject greater than 55?

(1) Each of the new subjects has fewer than 117 photos.

(2) Each of the new subjects has more than 71 photos.

(1) Each of the new subjects has fewer than 117 photos.

(2) Each of the new subjects has more than 71 photos.

30. Jeff’s average (arithmetic mean) monthly utility bill for the months of June, July, and August was $75. During which month did he receive the highest bill?

(1) The lowest bill was received in July.

(2) The total of his bills for July and August was $160.

(1) The lowest bill was received in July.

(2) The total of his bills for July and August was $160.

31. A certain company paid bonuses of $125 to each of its executive employees and $75 to each of its non-executive employees. If 100 of the employees were non-executives, how many of the employees were executives?

(1) The company has a total of 120 employees.

(2) The total amount that the company paid in bonuses to its employees was $10,000.

(1) The company has a total of 120 employees.

(2) The total amount that the company paid in bonuses to its employees was $10,000.

32. A certain jewelry store sells gold necklaces in 18-inch and 28-inch lengths, and all necklaces of the same length sell for the same price per necklace regardless of the number of necklaces purchased. What is the price of a 28-inch necklace at this jewelry store?

(1) The total price of an 18-inch and a 28-inch gold necklace is $68.

(2) The total price of two 18-inch necklaces and one 28-inch necklace is $96.

(1) The total price of an 18-inch and a 28-inch gold necklace is $68.

(2) The total price of two 18-inch necklaces and one 28-inch necklace is $96.

33. For integers \displaystyle a,b, and c, \displaystyle \frac{a}{(b-c)}=1 .What is the value of \displaystyle \frac{(b-c)}{c}?

(1) \displaystyle \frac{a}{b}=\frac{3}{5}

(2) \displaystyle a and \displaystyle b have no common factors greater than 1.

(1) \displaystyle \frac{a}{b}=\frac{3}{5}

(2) \displaystyle a and \displaystyle b have no common factors greater than 1.

34. By how many years is Jason older than Allison?

(1) Jason is 6 years older than twice David’s age.

(2) In 8 years, Allison will be twice as old as David is now.

(1) Jason is 6 years older than twice David’s age.

(2) In 8 years, Allison will be twice as old as David is now.

35. Exactly how many show dogs does Sheila have?

(1) Of Sheila’s show dogs, exactly 3 have won prizes of at least $500.

(2) Of Sheila’s show dogs, exactly 40% have not won a prize of $500 or more.

(1) Of Sheila’s show dogs, exactly 3 have won prizes of at least $500.

(2) Of Sheila’s show dogs, exactly 40% have not won a prize of $500 or more.

36. Julie runs a small art museum. How many paintings does her museum have?

(1) Her next acquisition of 4 Monet paintings will increase the number of paintings in the museum’s collection by 10%

(2) The museum currently exhibits 3 impressionist paintings for every 2 non-impressionist paintings.

(1) Her next acquisition of 4 Monet paintings will increase the number of paintings in the museum’s collection by 10%

(2) The museum currently exhibits 3 impressionist paintings for every 2 non-impressionist paintings.

37. A bake sale sells only individual cupcakes and boxes of cookies. If cupcakes sell for $2 each, and a box of cookies sells for $15, how many boxes of cookies did Kevin buy?

(1) Kevin spent $27

(2) Kevin bought 6 cupcakes

(1) Kevin spent $27

(2) Kevin bought 6 cupcakes

GMAT Math

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