  Section III - Quantitative Skills Questions: 20 (Q 31 - 50) ) Time: 20 Minutes
Directions:
For each of the following questions, select the best or correct answer from the answer choices numbered (1), (2), (3), and (4) and then darken the oval corresponding to your answer choice in the answer sheet.
 Numbers : All numbers are real numbers. Figure : Position of points, angles, regions, etc., can be assumed in the order shown; and angle measures can be assumed to be positive. Lines shown as straight can be assumed to be straight. Figures that accompany questions are intended to provide information useful in answering the questions. However, unless it is stated, a specific figure is not drawn to the scale; the diagrams and figures are drawn as accurately as possible. You should solve the problems NOT by estimating sizes by sight or by measurement, but by using your knowledge of mathematics

Directions for Questions 31 - 35: For each of the following questions (Q 31 - 35) select the best of the answer choices number (1), (2), (3), and (4), and the then darken the corresponding oval in the answer sheet.

 31 The area of square is 49 x 2 . What is the length of a diagonal of the square ? (1)14 x (2) 7 x Ö2 (3)7 x 2 (4)7 x
 32 A rectangular sign is cut down by 10% of its Height and 30% of its Width, what percentage of the original remains ? (1)63 (2) 70 (3)37 (4)None
 33 The sum of the radii of two circles is 7cm., and the difference between their circumference is 8; the circumference of the smaller circle is ______. (1)8 (2)44 (3)26 x 2 (4)18 x
 34 Four objects (W,X,Y and Z) are placed in these ways ----- X is toward east of Y at a distance of 10cm., W is at a distance of 10cm. toward east of Z but at a distance of 15cm., toward south of X. If the distance of Z from Y is also 15cm. to which side of Y does it lie ? (1)South-east (2) North (3)South (4)South-west
 35 The coordinates of the vertices of a quadrilateral ABCD are - A (0,0); B (1,3); C (10,3); and D (9,0) respectively. The area of ABCD is ______. (1)27 (2) 27 /2 (3)9Ö10 (4)None

Directions for Questions 36 - 40: In each of the problems, a question is followed by two statements marked (A) and (B), containing certain, data, pertaining, to the problem. You are to determine whether the data provided by the statements are sufficient to answer the questions.
From the four answer choices marked (1), (2), (3) and (4) choose the correct answer for each question based upon the statement's data, then darken the corresponding oval in the answer sheet.

1. Statement (A) itself but not statement (B) is sufficient to answer the question.
2. Statement (B) itself but not statement (A) is sufficient to answer the question.
3. Statements (A) and (B) taken TOGETHER are sufficient to answer the question but neither alone is sufficient.
4. Statements (A) and (B) taken together are NOT sufficient to answer the question.
 36 What is the value of X ? (a) X2 + X = 2 (b) X2 + 2X - 3 = 0
 37 Is A > B ? (a) AX > BX (b) X < O
 38 If the area of a rectangle is 20, what is its perimeter ? (a) The width of the rectangle is 1 unit less than its length (b) The length of the rectangle is a prime number.
 39 Is S greater than T ? (a)S is greater than 2T. (b)The difference S - T is positive.
 40 Is XÖ5 is an integer ? (a) XÖ12345 is an integer. (b) XÖ336 is an integer.

Directions for questions 41 and 42: Choose the correct answer from the answer choices marked (1), (2), (3), and (4) and then darken the corresponding oval in the answer sheet.

 41 If one-half of the female students in a certain college eat in the cafeteria and one-third of male students eat there, what fractional part of the student body eats in the cafeteria ? (1)5/12 (2) 5/16 (3)3/4 (4)Cannot be determined
 42 A man bought a certain number of books for Rs.20.00. Had he obtained one more book for the same sum, the average price of each book would have been a rupee less. The number of books he bought is __. (1)4 (2) 5 (3)3 (4)None

Directions for Questions 43 - 46: In each of the problems, a question is followed by two statements, marked (A) and (B) containing certain data pertaining to the problem. You are to determine whether the data provided by the statements are sufficient to answer the question. From the four answer choices marked (1), (2), (3), and (4), choose the correct answer for each question based upon the statements data and then darken the corresponding oval in the answer sheet.

1. Statement (A) itself but not statement (B) is sufficient to answer the question.
2. Statement (B) itself but not statement (A) is sufficient to answer the question.
3. Statement (A) and (B) taken together are sufficient to answer the question, neither statement alone is sufficient to answer the question.
4. Either statement (A) alone or statement (B) alone is sufficient to answer the question.
 43 What is the value of X ? (a) 3X - Y = 24 (b) X + 2Y = 10
 44 If Y is a member of the set of numbers (8,12,15,16,20), what number is Y ? (a) Y is a multiple of 4 (b)Y is a multiple of 5
45 In the above figure, two semicircles are inscribed in Square KLMN. What is the area of the shaded portion ?
(a) The area of one semicircle is 32p
(b) The area of KLMN is 256p
 46 What is the seventh member in a series ? (a)Each member in the series is 5 more than the proceeding member. (b)The third member in the series is 3.

Directions for Questions 47 - 50: For each of the following problems, choose the correct or best answer from the four answer choices numbered (1), (2), (3) and (4), then darken the corresponding oval in the answer sheet.

 47 The sum of the reciprocals of two numbers is 1/6 and the difference of their reciprocals is 1/12; the smaller number is ____. (1)8 (2) 12 (3)4 (4)6
 48 The diagonal of a cube is 9cm. The lateral area of the cube (to the nearest sq.cm) is ___. (1)27 (2) 486 (3)54 (4)162
 49 A boat goes downstream 60 km is five hours. The return trip takes one hour longer. The rate of the current is __. (1)10 km/h (2) 2 km/h (3)1 � km/h (4)1 km/h
 50 The area of a square is 9 cm2 . The square and an equilateral triangle have equal perimeters. The area of the triangle to the nearest sq.cm is ___. (1)Ö3 (2) 2 Ö3 (3)3Ö3 (4)4Ö3   