gmat class 2

7/30/2019 GMAT Class 2

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MaxGMAT

Squares and Cubes

1. What is the minimum number by which I should divide 1250 with so that I get a perfectsquare?(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

2. Find the number whose square is equal to the difference between the squares of 75.15and 60.12.

(A) 45.09 (B) 24.03 (C) 48.09 (D) 54.18 (E) 53.09

3. The least perfect square number divisible by 2, 3, 4, 5, 6, and 8 is:

(A) 900 (B) 1600 (C) 2500 (D) 2700 (E) 3600

4. What is the value of 1014 986?(A) 998,904 (B) 999,804 (C) 998,814 (D) 998,804 (E) 999,904

Class 2Problem Solving 2

Examples


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MaxGMAT

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5. What is the value of ( ) ( )

?278278832832

278832278832 22

+

++

(A) 832 2 + 278 2 (B) 2 (C) 4 (D) 1 (E) 3

6. The least number by which 1250 should be multiplied to make it a perfect square is:

(A) 2 (B) 3 (C) 4 (D) 8 (E) 6

7. What is the value of the express ion ? 19.19 19.19 19.19 17.2617.26 17.2619.19 19.19 19.19 17.26 17.26 26.17

++

(A) 36.45 (B) 3 6.54 (C) 34.56 (D) 35.64 (E) 3 4.45

8. Simplify( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2.542.53.53.5 42.5 3.5 435.3432.5 3.5 4

222

333

++++

.

(A) 10 (B) (10) 2 (C) > 10 (D) < 10 (E) > 12


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MaxGMAT

HCF & LCM / Factors

9. There are 3 vessels containing water. The first has 71 litres of water, the 2nd has 42litres and the 3rd has 262 litres. You are using a bucket to remove water from thesevessel. Only complete or full buckets of water can be removed. The same bucket is usedfor all the vessels. What is the volume of 1 bucket if it was found that after the bucketwas used to remove water, there were 6 litres, 3 litres, 2 litres in the 1 st , 2 nd , 3 rd vesselrespectively? How many bucketfuls of water were removed in all?

(A) 7, 13 (B) 9, 28 (C) 11, 26 (D) 13, 28 (E) 7, 28

10. A man uses a bucket to empty 5 tanks of capacities 42, 69, 96, 124, and 179 litres.He only draws bucketfulls. He find that there were 3, 4, 5, 7, and 10 litres left ove r respectivelyin the tanks. What was the volume of the bucket?

(A) 7 (B) 9 (C) 11 (D) 12 (E) 13

11. Find the largest number which divides 62, 132, and 237 to leave the same remainderin each case.

(A) 21 (B) 27 (C) 35 (D) 45 (E) 42

12. Find the greatest number of 6 digits, which on being divided by 6, 7, 8, 9 and 10 leaves4, 5, 6, 7, 8 as remainders respectively.

(A) 997918 (B) 997693 (C) 383833 (D) 997981 (E) 383726


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13. Take a three digit number (all the digits different). Reverse the digits and subtract thesmaller three digit number from the larger three digit number. The new number obtainedmust be divisible by which number.(A) 2 (B) 5 (C) 7 (D) 9 (E) 6

Indices & Surds

14. Simplifyx

x

x

x

x

x ab b a

b

aac a c

a

cbc c b

c

b222222

++++++

, where x 0.

(A) 0 (B) 1 (C) x abc (D) x (E) x a+b+c

15 . ?x x 1

1x x 1

1x x 1

1c)(ac)(bb)(cb)(a)ac()ab( =++

+++

+++

(A) 1 (B) 0 (C) x a + b + c (D) x abc (E) x

16. If 2 x = 5 y = 10 z , then ++ z1

y1

x1

= ?

(A) 0 (B) 1 (C) 4 (D) 2 (E) 3


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MaxGMAT

17. If p x p 1/x = p 2 , find the value of x 2 + 2x1

.

(A) 4 (B) 2 (C) 3 (D) 8 (E) 6

1 8. Simplify: 82 6 + (Consider positive roots only)

(A) 2 2 + (B) 1 5 + (C) 8 6 + (D) 2 6 + (E) 22 +

19. Simplify 64 11

(A) 5 6 + (B) 5 6 (C) 3 8 (D) 1 12 (E) 38 +


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MaxGMAT

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DIRECTIONS for Data Sufficiency questions: Each of the data sufficiency problems below consists of a question and two statements, labeled (1) and (2), in which certain dataare given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledgeof mathematics and everyday facts (such as the number of days in July or the meaningof counterclockwise), you are to blacken space.

(A) if statement (1) BY ITSELF is sufficient;

(B) if statement (2) BY ITSELF is sufficient;

(C) if statements (1) and (2) TAKEN TOGETHER are sufficient;

(D) if EITHER statement by ITSELF is sufficient;

(E) if (1) and (2) TOGETHER are NOT SUFFICIENT.

Examples

20. Is the number of trees in the garden equal to 177242?

I. The number of trees in the ground is greater than 176400.

II. The trees are planted in rows with each row having as many plants as the total numberof rows.

21. Is y > z2

zy >+ ?

I. y < z

II. y > z


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MaxGMAT

22. Is the number N divisible by 1001?

I. Number N is a six-digit number formed by repeating a three-digit number.

II. Number N is an eight-digit number formed by repeating an four-digit number.

23. What are the two numbers x and y?

I. Sum of x and y is 528 .

II. HCF of x and y is 33.

24. What i s the value of a + b?

I. 2 a + 3 b = 31

II. 2 a+3 + 3 b+1 = 113

25. What is the value of y in terms of x and y if a x = b y = c 2 .

I. b = ac and a, b & c are not 0, 1 or 1.

II. x, y, z 0


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MaxGMAT

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Questions: 15 Time: 15 minutes

DIRECTIONS for Problem Solving questions: Solve each problem, using any available spaceon the page for scratchwork. Then indicate the best of the answer choices given.

Numbers: All numbers used are real numbers.

Figures: Figures that accompany problems in this test are intended to provide informationuseful in solving the problems. They are drawn as accurately as possible EXCEPT whenit is stated in a specific problem that its figure is not drawn to scale. All figures lie ina plane unless otherwise indicated.

DIRECTIONS for Data Sufficiency questions: Each of the data sufficiency problems below consists of a question and two statements, labeled (1) and (2), in which certain dataare given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledgeof mathematics and everyday facts (such as the number of days in July or the meaningof counterclockwise), you are to blacken space.

(A) if statement (1) BY ITSELF is sufficient;

(B) if statement (2) BY ITSELF is sufficient;

(C) if statements (1) and (2) TAKEN TOGETHER are sufficient;

(D) if EITHER statement by ITSELF is sufficient;

(E) if (1) and (2) TOGETHER are NOT SUFFICIENT.

Numbers: All numbers used are real numbers.

Figures: A figure in a data sufficiency problem will conform to the information given inthe question, but will not necessarily conform to the additional information given in

statements (1) and (2).

You may assume that lines shown as straight are straight and that angle measures are greater than zero.

You may assume that the position of points, angles, regions, etc., exist in the order shown.

All figures lie in a plane unless otherwise indicated.

Example:

xo

P

yo

Q Rz

o

In PQR, what is the value of x?(1) PQ = PR(2) y = 40

Explanation:According to statement (1), PQ = PR; therefore, PQRis isosceles and y = z. Since x + y + z = 180,x + 2y = 180. Since statement (1) does not givea value for y, you cannot answer the question usingstatement (1) by itself. According to statement (2),y = 40; therefore, x + z = 140. Since statement(2) does not give a value for z, you cannot answerthe question using statement (2) by itself. Usingboth statements together, you can find y and z;therefore, you can find x, and the answer to theproblem is C.


Class Test


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MaxGMAT

1. If the HCF and LCM of two numbers is the same, then which of the following is true aboutthe numbers?

I. The two numbers are prime.II. The two numbers are relatively prime to each other i.e. they are co-prime.III. The two numbers are equal.(A) I only (B) II only (C) III only (D) II and III (E) None of these

2. The ratio of two numbers is 2 : 5. If their HCF is 25, what is the LCM?

(A) 50 (B) 75 (C) 250(D) 125 (E) Cannot be determined

3. Three planks of lengths 7 feet 1 inch, 12 feet 9 inches and 9 feet 11 inches are to bemeasured using another small plank. What can be the maximum length of the small plank?

(A) 1.7 feet (B) 1 foot 5 inches (C) 1 foot 2 inches(D) 1.5 feet (E) 1 foot 3 inches

4. What is the sum of a whole number and its reciprocal?

I. The sum is a pr ime number.

II. The sum is an even number.

5. What is the value of x 3 + y 3 ?

I. x + y = 12.

II. xy = 35.

6. A number is such that the square of half of it is the same as four times the number.What is the number?

(A) 12 (B) 14 (C) 16 (D) 18 (E) 20

7. What is the difference between the largest and smallest four-digit numbers that can beformed using the digits 0, 2, 3, 7 and 5 without repitition?

(A) 5732 (B) 5495 (C) 7532 (D) 5497 (E) 7497

8. What is the LCM of three numbers which are in the ratio 1 : 2 : 3?

I. The HCF of the numbers is 12.II. One of the numbers is 18.

Tick guessed questions

1. 2. 3. 4. 5. 6. 7. 8.


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MaxGMAT

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9. a > 0, b < 0, c < b. Which of the following is necessarily true?

I. (a 3 b 3 c 3 ) > 0 II. a cb > 0 III. 0ac

bc q.

II. q 1.

j

Tick guessed questions

9. 10. 11. 12. 13. 14. 15.


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MaxGMATClass 2

Problem Solving 2Class Test

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Class Test

Batch Enrolment No.

1. Total number of questions: 15 2. Number of questions attempted:

3. Correct answers: 4. Wrong answers: 5. Guessed answers:

gmat class 2

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