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Part Mathematics

Section 1: Data Sufficiency (1-10)

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are 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 knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether:

1. What is the average of A, B and C ?

(1) 5A + 5B = 60 - 5C
(2) -2A = 2B + 2C-24

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

2. How old is Sara now?

(1) Sara is now 3 times as old as Joe.
(2) 5 years ago, Sara was 5 times as old as Joe.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

3. What is the value of integer X ?

(1) X is even number.
(2) X is prime number.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

4. Is the triangle below isosceles?

(1) X = 2Y
(2) Y = Z/2

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

5. Is n³ an odd integer?

(1) n is an odd integer.
(2) n2 is an odd integer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

6. If 2X + 4Y = 6, then Y = ?

(1) 10X + 20Y = 30
(2) X = 3 - 2Y

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

7. The ratio of boys to girls in a classroom is 9:10. How many girls are in the class room?

(1) There are 45 boys in the classroom.
(2) The classroom contains 5 more girls than boys.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

8. In the figure below, line A, B and C intersect in a single point. What is the value of X° + Y°?

(1) X° + Z° = 100
(2) (X° * Z°) / 20 = 3X°

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

9. What is its perimeter?

(1) The area of the figure is 150 cm2.
(2) X = 12 cm.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

10. If the average of p, q and 50 is 100, then what is the value of q?

(1) p is 50 greater than q.
(2) p + q + 50 = 300

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Section 2: Maths (11-20)

11. if \sqrt[3]{\sqrt{x} + 2} = 3 , what is the value of \displaystyle \frac{x}{5} ?

1

5

25

125

625

12. In the figure below, line s₁//s₂. What is the value of A°+B° ?

30°

55°

45°

60°

50°

13. 5²% of \displaystyle \frac{1}{5^4}is what percent of of \displaystyle \frac{1}{5^3} ?

5

100

25

50

1

14. In how many different ways can 3 girls and 2 boys are arranges in a line?

2! + 3!

2! * 3!

5!

³C₂

³P₂

15. If X, Y and Z are real number and X > Y, then which of the following must be true?

X + Z < Y + Z

XZ < XY

X – Z > Y – Z

X²> Y²

\displaystyle \frac{X}{Z} > \displaystyle \frac{Y}{Z}

16. ΔABC is equilateral, AB = 2 cm. If x, y and z are the midpoints of their respective sides, what is the areas of Δxyz ?

\displaystyle \frac{\sqrt{3}}{4}

\displaystyle \frac{1}{3}

\displaystyle \frac{2}{\sqrt{3}}

\displaystyle \frac{\sqrt{3}}{2}

\displaystyle \frac{3}{2}

17. If one leg of a right triangle has length 5, and the length of the hypotenuse is 13, then the other leg has length .

8

12

\displaystyle \sqrt{154}

\displaystyle \sqrt{194}

2\displaystyle \sqrt{7}

18. If 10 typists can type 20 pages in 2 minutes, how many typists will take to type 30 pages in 5 minutes?

5

6

8

15

37.5

19. Which one of these is the smallest number?

\displaystyle \frac{5}{7}

\displaystyle \frac{51}{71}

\displaystyle \frac{511}{711}

\displaystyle \frac{5111}{7111}

\displaystyle \frac{51111}{71111}

20. If the perimeter of an isosceles triangle is 16 feet and its area is 12 feet2, what is the height of triangle, in feet?

3 feet

4 feet

5 feet

6 feet

8 feet

Section 3: Table and Chart (21-30)

Questions 21-23 refer to the following graph.
The following graph shows Annual Profits for XYZ Company from 2004 to 2010