1 The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

A. 240 B. 270 C. 295 D. 360

Answer: Option B Explanation: Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270.
2. If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

A. 0.172 B. 1.72 C. 17.2 D. 172

Answer: Option C Explanation: [latex]\frac{29.94}{1.45}[/latex] = [latex]\frac{299.4}{14.5}[/latex] ([latex]\frac{2994}{14.5}[/latex] * [latex]\frac{1}{10}[/latex])[ Here, Substitute 172 in the place of [latex]\frac{2994}{14.5}[/latex] ] =[latex]\frac{172}{10}[/latex] =17.2
3. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

A. 2700 B. 2900 C. 3000 D. 3100

Answer: Option A Explanation: Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000 =([latex]\frac{45}{100}[/latex] * 6000) = 2700.
4. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 3 B. 4 C. 5 D. 6

Answer: Option C Explanation: C.P. of 6 toffees = Re. 1 S.P. of 6 toffees = 120% of Re. 1 = Rs.[latex]\frac{6}{5}[/latex] For Rs.[latex]\frac{6}{5}[/latex], toffees sold = 6. For Re. 1, toffees sold =(6*[latex]\frac{5}{6}[/latex])= 5.

6. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

A. Rs. 500 B. Rs. 1500 C. Rs. 2000 D. None of these

Answer: Option C Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000 x = 1000. B's share = Rs. 2x = Rs. (2 * 1000) = Rs. 2000.
7. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000 B. 9400 C. 9600 D. 9800

Answer: Option A Explanation: Greatest number of 4-digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600.
8. The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

A. 9, 10 B. 10, 11 C. 11, 12 D. 12, 13

Answer: Option A Explanation: Let the two consecutive positive integers be x and x + 1 [latex]x^{2}[/latex]+ (x + 1)2 - x(x + 1) = 91 [latex]x^{2}[/latex]+ x - 90 = 0 (x + 10)(x - 9) = 0 => x = -10 or 9. As x is positive x = 9 Hence the two consecutive positive integers are 9 and 10.
9. What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

A. 814 B. 820 C. 840 D. 844

Answer: Option B Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) [latex] cm^{2}[/latex] Required number of tiles =[latex]\frac{1517 x 902}{41 x 41}[/latex] =814.
10. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

A. 5600 B. 6000 C. 6400 D. 7200

Answer: Option C Explanation: Number of bricks =[latex]\frac{Volume of the wall}{Volume of 1 brick}[/latex] = [latex]\frac{800 * 600 * 22.5}{25 * 11.25 * 6}[/latex] = 6400.

11. In how many of the given years was the production of fertilizers more than the average production of the given years?

A. 1 B. 2 C. 3 D. 4

Answer: Option D Explanation: Average production (in 10000 tonnes) over the given years =[latex]\frac{1}{8}[/latex](25 + 40 + 60 + 45 + 65 + 50 + 75 + 80) = 55 The productions during the years 1997, 1999, 2001 and 2002 are more than the average production.
12. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A. 2.91 m B. 3 m C. 5.82 m D. None of these

Answer: Option B Explanation: Area of the park = (60 x 40)[latex] m^{2}[/latex] = 2400 [latex] m^{2}[/latex] Area of the lawn = 2109 [latex] m^{2}[/latex] . Area of the crossroads = (2400 - 2109) [latex] m^{2}[/latex] = 291 [latex] m^{2}[/latex] . Let the width of the road be x metres. Then, 60x + 40x - [latex] x^{2}[/latex] = 291 [latex] x^{2}[/latex] - 100x + 291 = 0 (x - 97)(x - 3) = 0 x= 3.
13. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in [latex]m^{3}[/latex]) is:

A. 4830 B. 5120 C. 6420 D. 8960

Answer: Option B Explanation: Clearly, l = (48 - 16)m = 32 m, b = (36 -16)m = 20 m, h = 8 m. Volume of the box = (32 x 20 x 8) [latex]m^{3}[/latex]= 5120 [latex]m^{3}[/latex].
14 . Considering Cosine Rule of any triangle ABC, possible measures of angle A includes

A. angle A is acute B. angle A is obtuse C. angle A is right-angle D. all of above

Answer: Option D Explanation: all of above
15. What is the overall percentage of Tarun?

A. 52.5% B. 55% C. 60% D. 63%

Answer: Option C Explanation: Aggregate marks obtained by Tarun = [ (65% of 150) + (35% of 130) + (50% of 120) + ((77% of 100) + (80% of 60) + (80% of 40) ] = [ 97.5 + 45.5 + 60 + 77 + 48 + 32 ] = 360. The maximum marks (of all the six subjects) = (150 + 130 + 120 + 100 + 60 + 40) = 600. Therefore Overall percentage of Tarun =([latex]\frac{360}{600}[/latex] * 100)% = 60%.

16. The sum and the product of the roots of the quadratic equation [latex]x^{2}[/latex]+ 20x + 3 = 0 are?

A. 10, 3 B. -10, 3 C. 20, -3 D. None of these

Answer: Option D Explanation: Sum of the roots and the product of the roots are -20 and 3 respectively
17. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

A. 4 B. 5 C. 6 D. 8

Answer: Option C Explanation: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
18. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A. 20 B. 30 C. 48 D. 58

Answer: Option B Explanation: Let the three parts be A, B, C. Then, A : B = 2 : 3 and B : C = 5 : 8 = (5 *[latex]\frac{3}{5}[/latex]) : (8 * [latex]\frac{3}{5}[/latex]) = 3 : [latex]\frac{24}{5}[/latex] A : B : C = 2 : 3 :[latex]\frac{24}{5}[/latex] = 10 : 15 : 24 B = 98 * [latex]\frac{15}{49}[/latex] = 30
19. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30% B. 70% C. 100% D. 250%

Answer: Option B Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 125% of Rs. 100 = Rs. 125 New S.P. = Rs. 420. Profit = Rs. (420 - 125) = Rs. 295. Required percentage =([latex]\frac{295}{420}[/latex] * 100)% = 70%
20. What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

A. 1 B. 14 C. 20 D. 21

Answer: Option C Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such numbers =14 Required percentage = ([latex]\frac{14}{70}[/latex] * 100)% = 20%

21. 3889 + 12.952 - ? = 3854.002

A. 47.095 B. 47.752 C. 47.932 D. 47.95

Answer: Option D Explanation: Let 3889 + 12.952 - x = 3854.002. Then x = (3889 + 12.952) - 3854.002 = 3901.952 - 3854.002 = 47.95.
22. 5358 * 51 = ?

A. 273258 B. 273268 C. 273348 D. 273358

Answer: Option A Explanation: 5358 * 51= 5358 x (50 + 1) = 5358 * 50 + 5358 * 1 = 267900 + 5358 = 273258.
23. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

A. 57% B. 60% C. 65% D. 90%

Answer: Option A Explanation:Total number of votes polled = (1136 + 7636 + 11628) = 20400. Required percentage = [[latex]\frac{11628}{20400}[/latex]x 100] % = 57%.