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, 27 2017 13 16. Which of the following statement is worng with regard to common fractions? a. In a proper fraction, the numerator and the denominator are equal b. In a proper fraction, the numerator is less than the denominator c. In an improper fraction, the numerator is bigger than the denominator d. A mixed fraction has a whole number plus an improper fraction Ans: d Explanation: A proper fraction is that in which the numerator is less than the denominator. Ex: 1/3, 3/4, 5/9 (The value of a common fraction is always less than one) An improper fraction is that is which the numerator is either greater than or equal to the denominator Ex: 7/3, 9/2, 4/4, 6/5 (The value of an improper fraction is always either greater than or equal to one) A mixed fraction is that which has a whole number and a proper fraction. The total cost of the sweets? Arithmetic 1. Which of the following numbers is prime. a. 119 b. 187 c. 247 d. 367 2. A certain seven digit number has only once in the once period, only threes in the thousands period and only twos in the lakh period. Write this number in the international system? a. Two million, two hundred thirty three thousand, one hundred eleven b. Twenty two million, thirty three thousand, one hundred eleven c. Two lakh, thirty three thousand, one hundred eleven d. Twenty two lakh, thirty three hundred, one hundred eleven 3. On a Republic Day, the school gives each student one chocolate costing one rupee and on peppermint costing 50 paise. All the students stood in one row, in which there was only one girl who was in the twenty second place from the front and 8th place form the back. The total cost of the sweets? a. Rs.46-50 b. Rs. 43-50 c. Rs. 43-60 d. Rs.44 4. Which one of the following statements is correct? The number 7117299235 5340042332 is? a. divisible by 2, but not by 11 b. divisible by 11, but not by 9 c. divisible by 9, but not by 11 d. divisible by 2, 9, 11 5. By correcting 13.2 + 2.76 to the nearest tens' place, we get.... a. 15 b. 16 c. 1 d. 25 6. Match the sentences and the words against them? A. The value of these is less than 1 J. proper fractions B. The numbers which are divisible by 2 K. Whole numbers C.Area L. Factors M. Even numbers N. Length X breadth O. Place occupied by a closed figure a. A-J, B-L, C-N b. A-J, B-M, C-N c. A-J, B-M, C-O d. A-K, B-M, C-N 7. The product of two numbers is 2480 and their HCF is 8, what will be the LCM of the two numbers? a. 310 b. 301 c. 31 d. 1240 8. The LCM of two numbers is 12 times their HCF. The sum of the HCF and LCM is 403. If one of the numbers is 93, Then what is the other number. a. 122 b. 124 c. 126 d. 128 9. A man leaves his estate to his wife and two sons. If the wife receives 2/3 of the estate and each son receives 1/2 of the reminder, find the value of the entire estate in rupees, if each son receives Rs. 40000 as his share. a. 140000 b. 300000 c. 240000 d. 140000 10. Ruthwik spent 3/7 of his money on a shirt and 1/2 of the remainder on a pair of trousers. If he had rupees 23 left, how much did Ruthwik spend altogether? a. Rs.57-50 b. Rs. 54-50 c. Rs. 25 d. Rs. 74-75 11. Anjana bought some salt. She used 3/8 of it and had 625gr. left. How much salt did she buy? a. 100gr. b. 1000kg. c. 1000gr. d. 100gr. 12. An amount of money is to be distributed among A, B and C in the ratio 3:1:5. The difference between B's share and C's share is rupees 3600. What is the total of A's share and B's share? a. Rs. 2700 b. Rs. 3600 c. Rs. 4500 d. Rs. 5400 13. The price of 282 apples is Rs. 1974. What will be the price of 24 dozens of apples? a. Rs. 2016 b. Rs. 2106 c. Rs. 2160 d. Rs.2006 14. Three items are purchased at Rs.450 each. One of them is sold at a loss of 10%. At what price should the other to be sold so as to gain 20% on the whole transaction. What is the gain percent on these two items. a. 25% b. 30% c. 35% d. 40% 15. A train travelled from Secunderabad railway station with a speed of 80km/hr. and reached Tandur station in on the way it stopped at 4hrs. Lingampally station for 5 minutes and at Vikrabad station for 7 minutes. Find the distance between Secundrabad and Tandur. a. 308km b. 305km c. 304km d. 316km Explanations: 1. Ans: d A prime number is number which has only two factors, one and the number itself it is also called 'unbreakable number' or individual number. The prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. The prime numbers between 100 and 200 are 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197 and 199. The prime numbers between 200 and 300 are 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283 and 293. Prime numbers between 300 and 400 are 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397. The prime numbers between 400 and 500 are 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499. As of January 2017 , the largest known prime number is 274,207,281 − 1, a number with 22,338,618 digits. It was found in 2016 by the Great Internet Mersenne Prime Search (GIMPS). Plot of the number of digits in largest known prime by year, since the electronic computer. In the given problem... The largest number is nearly less then 400. and square root of 400 is 20 prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19 119 is divisible by 17; 187 is divisible by 11; 247 is divisible by 13; 367 is divisible by none of them. 367 is a prime number 2. Answer: a Explanation: In the indian system the number can be written as 22,33,111. the number can be re-written in the international system as 2,233,111 the number in words is two million, two hundred thirty three thousand, one For all hundred eleven comeptative 3. Ans: b exams 4. Ans: d Explanation: If a number has 0, 2, 4, 6 or 8 in its unit's place, then, it is completely divided by 2 Since the units digit in the given number is two, it is divisible by 2. If the sum of all the digits in a number is divisible completely by 9, then, the number itself is divisible by 9. Since sum of the digits= 72, is divisible by 9. Hence, the given number is divisible by 9. In a number, if the sum of the digits in alternate places is equal to the sum of the remaining digits, or, if the difference between the two sums is a multiple of 11, then, the number is divisible by 11. Since sum of digits at odd places of a given number = 36 Sum of digits at even places = 36 Difference= 0. Hence, the number is divisible by 11 5. Ans: b Explanation: The principle of correction to the nearest value:- If a number is to be corrected to certain place, we should see the digit immediately to the right of the place. If the digit is 5 or more, '1' should be added to the digit in the place or if the digit is less than 5 nothing needs to be added to the digit in the place. After correction the excess digits to the right should be removed. In whole numbers: Correction to the nearest unit's place: 9.1----> 9, 8.6---> 9, 10.9---> 11 Correction to the nearest ten's place: 33 ---> 30, 135---> 140, Correction to the nearest hundred's place: 93---> 100, 250---> 300 6. Ans: c 7. Ans: a LCM of the two numbers = Product/HCF = 2480/8 = 310 8. Ans: b Explanation: LCM = 12xHCF ------- (1) and HCF + LCM = 403 ------- (2) Sub. Eq (1) in (2) HCF + 12HCF = 403 B.V.Ramana Director AKR Study circle Vikarabad, tandur 9441022571 13 HCF = 403 HCF = 403/13 = 31 LCM = 12x31 = 372, given number = 93 Other number = (LCM x HCF)/ Given number = (372 x 31)/93= 124 9. Ans:c Explanation: Let the value of the entire estate be Rs. 'A'. then, Part of estate received by wife = (2/3)A remaining part = (A-2A/3) = A/3 Each of the two sons receives (1/2)(A/3) = A/6 Given, A/6 = 40000 A = 240000 Rs. 10. Ans: a Explanation: Amount = Rs. A Expenditure, Shirt 3/7, Trousers 1/2 remaining = A x 4/7 x 1/2 = 23 amount A= 80.50 Expenditure = 80.50 - 23 = 57.50 11. Ans: c Explanation: A x 5/8 = 625 A = 1000gr. 12. Ans: b Explanation: Let the shares of A,B and C be 3t, t and 5t respectively. given 5t-t = 3600, 4t= 3600, t = 900 A's share + B's share = 3 x 900 + 900 = 3600 13. Ans: a Explanation: 282 apples cost Rs. 1974 1 apple costs Rs. 1974/282 24 dozens apples cost = 1974/282 x (24x12) = Rs. 2016 14. Ans: c Explanation: C.P of one item = Rs. 450 C.P of three items= 3x450 = 1350 gain on the whole transaction = 20% S.P of the three items= (1350x120)/100 = 1620 C.P of one item= Rs. 450, Loss = 10% S.P of that item= (450x90)/100 = 405 S.P of remaining two items= 1620 - 405 = 1215 C.P of these two remaining items= 2 x 450= 900 gain on these two items = 1215 - 900 = 315 gain percent = (315/900) x 100 = 30% 15. Ans: c Explanation: Distance covered per unit time is called speed. i.e., speed = distance/time or distance = speed x time or time = distance/speed Distance = speed x time = 80 x 4 = 320km 5min + 7min = 12min 1hr = 80km i.e., 60min ----> 80 1min----> 80/60 = 4/3 12min ---> (4/3) x 12 = 16 distance between secunderabad, Tandur = 320-16 = 304km.