GMAT Maths Practice Paper

  GMAT PAPER- I 1. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross? (a) 19th (b) 28th (c) 30th (d) 37th (e) 32nd (c) Suppose their paths cross after x minutes. 1 Now, 11 + 57x = 51 – 63x ⇒ 120x = 40 ⇒ x = 3 ⎛1 ⎞ ⎜ 3 × 57 ⎟ ⎝ ⎠ = 19. Number of floors covered by David in (1/3) min. = Solution. So their paths will cross at (11 + 19)th i.e. 30th floor. 2. A machine P can print one lakh books in 8 hours; machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished? (a) 11:30 a.m. (b) 12 noon (c) 12:30 p.m. (d) 1 p.m. (e) 1:30 p.m. ⎛1 1 1 ⎞ ⎜ + + ⎟ (d) (P + Q + R)’s 1 hour’s work = ⎝ 8 10 12 ⎠ = ⎛ 37 ⎞ ⎜ 120 × 2 ⎟ ⎝ ⎠ Solution. 37 120 37 Work done by P, Q and R in 2 hours = ⎛ 37 ⎞ 23 ⎜1 − 60 ⎟ ⎝ ⎠ = 60 . Remaining work = ⎛ 1 1 ⎞ ⎜ 10 + 12 ⎟ ⎝ ⎠ = 60 . (Q + R)’s 1 hour’s work = 11 11 = 60 Now, 60 work is done by Q and R in 1 hour. ⎛ 60 23 ⎞ 23 23 ⎜ × ⎟ So, 60 work will be done by Q and R in ⎝ 11 60 ⎠ = 11 hours 2 hours So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m. 3. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Which direction is Shashidhar facing? (1) In the early morning Shashidhar was standing in front of a puppet and the shadow of the puppet was falling to the right of Shashidhar. (2) In the early morning Shashidhar was standing on the ground. His shadow was falling behind him when he turned to his left. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) (c) (d) (e) Solution. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (d) (1) ⇒ The sun is to the left of Shashidhar and since it is morning, the left of Shashidhar is East. Hence, he is facing South. (2) ⇒ Since it is morning, he is facing South. ∴ Each statement alone is sufficient to answer the question. 4. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. ABCD is a square. What is the value of circumference of the inner circle? A B D C (1) (2) (a) (b) (c) (d) (e) Solution. The radius of the outer circle is 10 cm. The difference between the radii of the two circles is 2.929 cm. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (a) A B E O F D C (1) ⇒ OC = 10 cm Diagonal of square = 20 cm 20 ⇒ Side of square = = 10 2 cm 2 = 5 2 cm. Hence circumference of inner circle can be determined. Therefore, statement (1) alone is sufficient to answer the question. (2) ⇒ It is not sufficient to answer the question. 5. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. 10 2 radius of the inner circle OE = 2 Is (x2 – y2) an odd number ? (1) x and y are integers. (2) is an odd number. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (b) Statement (2) ⇒ x + y is odd ⇒ x is even and y is odd or vice versa. ⇒ x − y is odd ⇒ (x 2 − y 2 ) is odd 6. A man walked diagonally across a square plot. Approximately, what was the percent saved by not walking along the edges? (a) 20 (b) 24 (c) 30 (d) 33 (e) 25 (c) Let the side of the square be x metres and the person goes from A to C diagonally. Then, AB + BC = 2x metres. C B Solution. D A AC = = (1.41x) m. Saving on 2x metres = (0.59x) m ⎛ 0.59x ⎞ ⎜ 2x × 100 ⎟ % = 30 % ⎠ Saving % = ⎝ (approx.) 2x 7. Which of the following numbers is exactly divisible by 24? (a) 35718 (b) 63810 (c) 537804 (e) None of these (d)A number is divisible by 24 if it is divisible by 3 and 8, both. 718 is not divisible by 8. 810 is not divisible by 8. 804 is not divisible by 8. For 3125736, Sum of digits = 27, which is divisible by 3. And, 736 is divisible by 8. So, given number is divisible by 3 and 8. (d) 3125736 Solution. 8. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A person bought 2 kg of rice from a shop. But when he entered the next shop he found that the price was less. He calculated that if he bought 6 kg from that shop his average price would be Rs. 20. Then what is the price in the first shop? (1) The price in the second shop was Rs 18 per kg. (2) The difference in the prices was Rs 8 per kg. (a) (b) (c) (d) (e) Solution. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (d) Let the price in first shop = Rs x per kg ⇒ 18 × 6 + x × 2 = 20 8 ⇒ x can be determined. 6x + 2( x + 8) = 20 8 ⇒ x can be determined. (1) ⇒ (2) ∴ Each statement alone is sufficient for answering the question. 9. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. How many boys are there in the class? (1) The number of boys is 120% of the number of girls in the class. 5 (2) (a) (b) (c) (d) (e) Solution. The number of girls is 11 th of the total number of students. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (e) Let the total number of students = N (2) ⇒ Number of Girls = 5 11 N 5 (1) ⇒ Number of Boys = 120% of 11 N Q We haven’t the value of N. ∴ Both statements are not sufficient to answer the question. 10. The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is: (a) 13.6 cm3 (b) 89.8 cm3 (c) 121 cm3 (d) 147.68 cm3 3 (e) 144 cm (b) Volume of the largest cone = Volume of a cone with the diameter of the base = 7 cm and the height = 7 cm. ⎛ 1 22 ⎞ 3 ⎛ 269.5 ⎞ ⎜ 3 × 7 × 3.5 × 3.5 × 7 ⎟ cm = ⎜ 3 ⎟ ⎠ ⎝ ⎠ cm3 = 89.8 cm3. =⎝ Solution. 11. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs 2.40 per hour for regular work and Rs 3.20 per hours for over-time. If he earns Rs 432 in 4 weeks, then how many hours does he work for? (a) 160 (b) 175 (c) 180 (d) 195 (e) 200 (b) Suppose the man works over-time for x hours Now, working hours in 4 weeks = (5 × 8 × 4) = 160. ∴ 160 × 2.40 + x × 3.20 = 432 ⇒ 3.20x = 432 – 384 = 48 ⇒ x = 15. Hence, total hours of work = (160 + 15) = 175. Solution. 12. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. Is a quadrilateral ABCD a square? (1) A pair of adjacent sides are equal. (2) The angle enclosed by these equal adjacent sides is 90° (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (e) Inspite of using both statements (1) and (2), we have no idea about the all sides and their corresponding angles of quadrilateral ABCD. Hence, both statements together are not sufficient to answer the question. 13. A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have? (a) 1000 (b) 1074 (c) 1075 (d) 1080 (e) 1024 (b) No. of digits in 1-digit page nos. = 1 × 9 = 9. No. of digits in 2-digit page nos. = 2 × 90 = 180. No. of digits in 3-digit page nos. = 3 × 900 = 2700. No. of digits in 4-digit page nos. = 3189 – (9 + 180 + 2700) = 3189 – 2889 = 300 ⎛ 300 ⎞ ⎜ ⎟ No. of pages with 4-digit page nos. = ⎝ 4 ⎠ = 75. Solution. Hence, total number of pages = (999 + 75) = 1074. 14. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24mile round trip, the downstream 12 miles would then taken only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour? 1 (a) (e) Solution. 1 3 1 4 1 (b) 2 3 2 (c) 1 3 2 (d) 2 3 2 (d) Let the speed of rowing in still water be x mph and the speed of the current be y mph. Therefore, Speed upstream = (x – y) and Speed downstream = (x + y) Now, 12 12 − =6 (x − y) (x + y) 2 2 2 2 2 2 or 6 (x − y ) = 24y or x − y = 4y or x = (4y + y ) . . . . (i) or Also, From (i) and (ii), we have: 4y + y2 = 12 12 − =1 (2x − y) (2x + y) 4x 2 − y 2 = 24y or x2 = 24y + y2 4 . . . . (ii) 24y + y2 or 16y + 4y2 = 24y + y 2 4 8 or 3y2 = 8y or y = 3 8 speed of current = 3 mph = 15. 2 2 mph 3 DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the speed of train ‘X’ in km/h? (1) Length of train ‘X’ is twice that of train ‘Y’ and speed of Y is 100 m/s. (2) Train ‘X’ passes train ‘Y’ in 10 seconds when they are running in same direction. Length of train ‘X’ is 100 metres. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (c) (1) ⇒ Lx = 2Ly and Sy = 100 m/s (2) ⇒ Lx = 100 m ⇒ Ly = 50 m Now, their relative speed = Sx – Sy, where Sx is the speed of train X. Also, (2) ⇒ ‘X’ passes ‘Y’ in 10 sec. ⇒ Sx – Sy = Lx + L y 10 Hence, we can find Sx in km/h. 16. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A fly crawls around the outside of a circle once. A second fly crawls around the outside of a square once. Which fly travels farther? (1) The diagonal of the square is equal to the diameter of the circle. (2) The fly crawling around the circle takes more time to complete his journey than the fly crawling around the square. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (a) Let the diameter of circle = d and side of square = a Then First fly covers the distance = πd and Second fly covers the distance = 4a (1) ⇒ a 2 = d Hence, conclusion can be drawn. (2) ⇒ We have no idea about their speeds. So statement (2) alone is not sufficient. 17. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the cost of flooring a room? (1) The length and breadth of the room is 9 m and 6 m respectively. (2) The cost of the tiles is Rs. 6 per cm2. (a) (b) (c) (d) (e) Solution. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (c) Cost = Area of room × Rate per square area and Area = length × breadth ∴ Both statements together are necessary to answer the question. 18. The price of wheat falls by 16%. By what percentage a person can increase the consumption of wheat so that his overall budget does not change? (a) 16% (b) 18% (c) 18.5% (d) 19% (e) 20% ⎡ ⎤ R ⎛ 16 ⎞ 400 × 100⎥ % ⎢ % ⎜ × 100 ⎟ % (100 − R) ⎠ = 21 ⎣ ⎦ = ⎝ 84 (d) Increase in consumption = = 19.04% 19%. Solution. 19. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A worker is hired for 6 days. He is paid Rs. 5 more for each day of work than he was paid for the preceding day. How much was he paid for the first day of the work? (1) His total wages for 6 days were Rs. 900. (2) He was paid less than Rs 100 on the first day. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (a) Suppose he was paid Rs x for the first day. (1) ⇒ x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) = 900 Hence x can be calculated. Therefore statement (1) alone is sufficient to answer the question. (2) ⇒ x < 100. ∴ Statement (2) is not sufficient to answer the question. 20. Which of the following statements is not correct? (b) log (2 + 3) = log (2 × 3) (a) log10 10 = 1 (c) log10 1 = 0 (d) log (1 + 2 + 3) = log 1 + log 2 + log 3 (e) All of them are incorrect (b) (a) Since loga a = 1, So log10 10 = 1. (b) log ( 2 + 3) = 5 and log (2 × 3) = log 6 = log 2 + log 3 log (2 + 3) log (2 × 3). (c) Since loga 1 = 0, so log10 1 = 0 (d) log (1 + 2 + 3) = log 6 = log (1 × 2 × 3) = log 1 + log 2 + log 3 So, only (b) is incorrect. Solution. 21. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. In the given figure P, Q and R are centres of three equal circles. What is the area of the shaded portion in the figure shown below? P Xx° Xx° Q Xx° R (1) (2) (a) (b) (c) (d) (e) Solution. QR is known. The triangle is an equilateral triangle. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (a) Since, all three circles are equal. ∴ PQ = QR = PR ⇒ ΔPQR is an equilateral triangle. And area of shaded portion = Area of Δ – 3 (area of each sector), 60° where area of sector = 360° Δ= 3 (side ) 2 4 . × π × (radius ) 2 and area of (1) ⇒ QR is known. ⇒ side of triangle and radius is known. Hence, statement (1) alone is sufficient to answer the question. Now, since all three circles are equal, therefore, statement (2) is restatement of the information given in question. 22. When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number? (a) 339 (b) 349 (c) 369 (d) Data inadequate (e) None of these (b) Given number = 13p + 11. Also, the given number = 17q + 9 13p + 11 = 17q + 9 ⇒ 17q – 13p = 2. By hit and trial, we find that p = 26 and q = 20. Required number = (13 × 26 + 11) = 349. Solution. 23. If A = x% of y and B = y% of x, then which of the following is true? (a) A is smaller than B. (b) A is greater than B. (c) Relationship between A and B cannot be determined. (d) If x is smaller than y, then A is greater than B. (e) None of these ⎛ x ⎞ ⎛ y ⎞ ×x⎟ ⎜ 100 × y ⎟ ⎜ ⎝ ⎠ = ⎝ 100 ⎠ = y% of x ⇒ A = B. (e) x% of y = Solution. 24. DIRECTIONS : Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the distance between D1 and D2? It is given that a man who can row x km/hr in still waters, takes z hrs to row from D1 to D2 and back to D1, in a stream which flows at y km/hr. (1) (2) (a) (b) (c) (d) (e) Value of (x − y ) is known. (x ÷ z) is known. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. 2 2 Solution. (c) Here, Man’s speed upstream = (x – y) km/hr. Man’s speed down stream = (x + y) km/hr Let the required distance be D km then ( x − y) ( x + y) ⇒ 2Dx x 2 − y2 =z D + D = z ⇒ D[x + y + x − y] = z (x − y)(x + y) z(x 2 − y 2 ) x 2 − y 2 = x 2x 2. z ⇒D= x z ∴ To find D, question. 25. x2 – y2 and should be known. Hence, both the statements together are necessary to answer the A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed amongst 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone. (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm (e) 4.5 cm (b) Let h be the height of the conical portion OA and r be the radius of the cone. Then, h = 4r A r B h Solution. O Now, 2 ⎛1 ⎞ π × 6 2 × 15 = 10⎜ π.r 2 .OA + π.r 3 ⎟ 3 ⎝3 ⎠ ⇒ ⇒ π 540π = 10 r 2 (h + 2r ) 3 10 = r 2 ( 4r + 2r ) 540 3 1 = r 2 .6r 54 3 54 r3 = ⇒ 2 ⇒ r = 3 cm. 26. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. ∠BPD > 1 (∠ABP − ∠APB) 2 Is in the figure shown below? (AP is tangent) P C D B A (1) (2) (a) (b) (c) (d) (e) Solution. Length of AC is known. PD is the bisector of ∠BPC . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (b) Since ∠APB and ∠BCP are angles in alternate segments of chord PB. ∴∠APB = ∠BCP (2) ⇒ In , side CB has been produced to A, forming exterior angle ∠ABP ∴∠ABP = ∠BCP + ∠CPB ⇒ ∠ABP = ∠APB + 2∠BPD ⇒ 2∠BPD = ∠ABP − ∠APB 1 ⇒ ∠BPD = (∠ABP − ∠APB) 2 Hence, we can be determined the answer. 27. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is: (a) 40% (b) 42% (c) 44% (d) 46% (e) 54% (c) Let the original length = x metres and the original breadth = y metres. ⇒ original area = (xy) m2. ⎛ 120 ⎞ ⎛6 ⎞ ⎜ 100 x ⎟ m = ⎜ 5 x ⎟ m; ⎠ ⎝ ⎠ New length = ⎝ ⎛ 120 ⎞ ⎛6 ⎞ ⎜ 100 y ⎟ m = ⎜ 5 y ⎟ m ⎝ ⎠ ⎝ ⎠ Solution. New breadth = 6 ⎞ 2 ⎛ 36 ⎞ 2 ⎛6 ⎜ 5 x × 5 y ⎟ m = ⎜ 25 xy ⎟ m ⎝ ⎠ ⎝ ⎠ New Area = . ⎛ 11 ⎞ 1 ⎜ xy × × 100 ⎟ % xy ⎝ 25 ⎠ % Increase = = 44%. 28. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the value of x? (1) 2x + 4 =14 (2) x + y = 7 (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (a) We can find the value of x using the statement (1) alone. While statement (2) alone are not sufficient to answer the question. 29. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the height of a right-angled triangle? (1) The area of the right-angled triangle is equal to the area of a rectangle whose breadth is 12 cm. (2) The length of the rectangle is 18 cm. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (e) (1) ⇒ Area of right-angled triangle = 12 × L (2) ⇒ L = 18 cm. Using (1) and (2) we can only calculate the area of right-angled triangle. Since we don’t know the base of triangle, the height cannot be calculated. 30. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. When will the sun rise tomorrow? (1) The sun will set tomorrow at 6.15 pm. (2) Tomorrow’s day will be of 11 hr 50 min. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (c) Sunrise Time – Sunset time = length of day ∴ both statements together are necessary to answer the question. 31. There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is : (a) 20 (b) 80 (c) 100 (d) 200 (e) 180 (c) Let the number of students in rooms A and B be x and y, respectively. Then, ⇒ x – y = 20 x – 10 = y + 10 . . . . (i) and x + 20 = 2(y – 20) ⇒ x – 2y = – 60 . . . . (ii) Solving (i) and (ii), we get : x = 100, y = 80. Solution. 32. Rajeev buys goods worth Rs 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods. (a) Rs 6876.10 (b) Rs 6999.20 (c) Rs 6654 (d) Rs 7000 (e) Rs 6256.25 Solution. Sales tax = 10% of Rs (6650 – 399) = Rs = Rs 625.10. Therefore, the final amount = Rs (6251 + 625.10) = Rs 6876.10 33. DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. A certain garden consists only of apple trees, mango trees and orange trees. Which type of tree is the most numerous? (1) There are 4/5 as many orange trees as there are mango trees. (2) There are 2/3 as many mango trees as there are apple trees. (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient (c) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (d) EACH statement ALONE is sufficient (e) Statements (1) and (2) TOGETHER are NOT sufficient. Solution. (c) (1) ⇒ orange trees < mango trees (2) ⇒ mango trees < apple trees Using (1) & (2), we conclude that the most numerous trees are apple trees. ∴ both statements together are necessary to answer the question. ⎛ 6 ⎞ ⎜ 100 × 6650 ⎟ ⎝ ⎠ = Rs 399. (a) Rebate = 6% of Rs 6650 = Rs ⎛ 10 ⎞ ⎜ 100 × 6251⎟ ⎝ ⎠ 34. A manufacturer undertakes to supply 2000 pieces of a particular component at Rs 25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer ? (a) Rs 12,000 (b) Rs 13,000 (c) Rs 14,000 (d) Rs 15,000 (e) Rs 18,000 ⎡ 100 ⎤ ⎛ 100 ⎞ × 25 × 1900 ⎟ ⎜ ⎢ 125 × 25 × (95% of 2000) ⎥ ⎣ ⎦ = Rs ⎝ 125 ⎠ = Rs 38000. (b) Total cost incurred = Rs Solution. Loss to manufacturer = 38000 – (25 × 1000) = Rs 13000 35. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? (a) 9 (b) 10 (c) 11 (d) 12 (e) 18 (d) Let the required number of working hours per day be x. More pumps, less working hours per day. (Indirect Proportion) Less days, more working hours per day. (Indirect Proportion) Pumps 4 : 3⎫ ⎬: :8 : x Days 1: 2 ⎭ Solution. 4×1×x=3×2×8 ⇒ x= 36. 3× 2 × 8 4 ⇒ x = 12 hours DIRECTIONS: Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer. What is the perimeter of rectangle ABCD? A B C D (1) (2) (a) (b) (c) (d) (e) Solution. Area of the circle is 78.5 sq cm. AB = 10 cm. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient. (c) (1) ⇒ πr2 = 78.5 Hence, r can be determined and then breadth of rectangle = 2r (2) ⇒ Length of rectangle Hence, using statements (1) & (2), perimeter of rectangle can be determined. 37. An amount of Rs 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is , then the amount invested in each share was : (a) Rs 52,500; Rs 47,500 (b) Rs 62,500; Rs 37,500 (c) Rs 72,500; Rs 27,500 (d) Rs 82,500; Rs 17,500 (e) None of these 3 9 % 4 Solution. (b) Let the sum invested at 9% be Rs x and that invested at 11% be Rs (100000 – x). ⎛ x × 9 × 1 ⎞ ⎡ (100000 − x) × 11× 1 ⎤ ⎜ ⎟ ⎢ ⎥ 100 ⎦ = Then, ⎝ 100 ⎠ + ⎣ 9x + 1100000 − 11x 39000 100 ⇒ = 4 = 9750 39 1 ⎞ ⎛ ⎜100000 × 4 × 100 ⎟ ⎝ ⎠ ⇒ 2x = (1100000 – 975000) = 125000 ⇒ x = 62500 Therefore, the sum invested at 9% = Rs 62500 and the sum invested at 11% = Rs (100000 – 62500) = Rs 37500.