MISCELLANEOUS MCQS

Q.1 There is a pie to be divided among 20 people. A man eats 3 pizza, a women eats two pieces and a child eats half a piece of pie. Find the number of men, women and children so that they are 20 people in total and everyone gets some pie. There are 20 pieces of pie in all. A) 7 women, 1 men and 12 children B) 5 women, 1 men and 14 children C) 6 women, 2 men and 12 children D) 4women, 2 men and 14 children Ans. B Suppose for men x, women y & children z, 3x+2y+0.5z=20x=1,y=5,z=14 On looking into options,1.90-11*2 = 68,2.90-12*2=66,3.90-14*2=62,4.90-10*2=70, from this only 68 is divisible by 4 ,hence Ans. is 11 Q.2 Raman was given some money by his father on his birthday. Raman spent all of it in five stores. In each store he spent one rupee more than half of what he had when he came in. How much did he get from his father ?A) Rs. 30B) Rs. 25C) Rs. 46D) Rs. 62Ans. DJust take the options & follow acc to the question as follows :Stores Exp. Remaining amount1) Rs.62 62/2+1=32 Rs.302) Rs.30 30/2+1=16 Rs.143) Rs. 14 14/2+1=8 Rs.64) Rs.6 6/2+1=4 Rs.25) Rs.2 2/2+1=2 Rs.0 Q.3 A parcel weighing 12 kg is to be sent from New Delhi to Mumbai a distance of 1450 km.The Parcel Postage Rates are shown in the following table: Distance Category Rate upto to 2 kg INR For every additional kg over 2 kg INRLocal 35 5Upto 500 km 50 8501 to 1000 km 60 1210001 to 2000 km 70 25More than 2000 km 90 35 How much will it cost to send the parcel ? A) 85 INR B) 95 INR C) 320 INR D) 840 INR Ans. C Weight of the parcel sentfrom New Delhi to Mumbai = 12 kgDistance between New Delhi and Mumbai = 1450 km Q.4 This distance lies in the distance category 1001-2000 km. So, the cost to send 12 kg parcel would be the cost of sending a 2 kg parcel at Rs 70 plus the cost for every additional kg over 2 kg i.e. atRs 25 /kg.Thus, cost of sending the parcel = Rs 70 + (12–2) kg × Rs 25/kg = Rs 70 + Rs 10 × 25 = Rs 320 PASSAGE: There are 128 cubes with me which are coloured according to two schemes viz.64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up. Q.5 How many cubes have at least two coloured red faces each ?A) 0B) 32C) 64D) 128Ans. D64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each.Therefore, total number of the required cubes is 128 Q.6 What is the total number of red faces ?A) 0B) 320C) 128D) 64Ans. BNo. of red faces among first 64 cubes = 128No. of red faces among second 64 cubes = 192Therefore, total number of red faces = 128 + 192 = 320 Q.7 How many cubes have two adjacent blue faces each ?A) 0B) 64C) 32D) 128Ans. BSecond 64 cubes are such each of whose two faces are blue. Q.8 How many cubes have only one red face each ?A) 128 B) 32C) 64D) None of the aboveAns. DOut of 128 cubes no cube have only one face is red Q.9 Which two colours have the same number of faces ?A) Red and YellowB) Blue and GreenC) Red and GreenD) Red and BlueAns. BFirst 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue.

Q.1 In a row of children Rohan is seventh from the left & Bali is fourth from the right. When Rohan & Bali exchange their position, Rohan will be fifteenth from the left. Bali’s position from the right will be ? A) 4th B) 12th C) 11th D) 8th Ans. BIst case: 1  2  3  4  5  6  7             8  9                          Rohan10  11  12  13  14  15  16  17  18                             Bali2nd case:         1  2  3  4  5  6  7          8   9                                 Bali                         Rohan  12      11  10 10  11  12  13 14   15       16   17  189     8     7    6   5     4        3      2    1 Q.2 Mr. Vajpayee M.D. of X,Y,Z company asked five persons -Asit,Varun,Chandra,Danny & Eshita about their interest in a new project. He got following replies: Asit: None of us is interested Varun : One of us is interested Chandra : Two of us are interested Danny : Three of us are interested Eshita : Four of us are interested From his experience Mr. Vajpayee knows that those who are interested only tells the truth & others lie.How many of them are interested in the new project ?A) 3 B) 4 C) 2 D) 1 Ans. D Q.3 There are four roads, I have come from the South & want to go to the temple. The road to the right leads me away from the coffee house while straight road leads to a college. In which direction is the temple ? A) North B) South C) East D) west Ans. C Q.4 A cube has 6 faces each of different colour. Red face is opposite to the black. The green face is in between red & black. Blue face is adjacent to the white & brown face is adjacent to the blue. Four colours adjacent to green are : A) Red,Black,Brown & White B) Red,Brown,Blue & White C) Red,Black,Blue & White D) Red, Black , Brown & Blue Ans. A         6 (Front surface)1- Green, 2- Brown,3-Blue,4-White5- Black6-red Therefore, Green surface is following four colours- Red, Black,Brown & White Q.5 If 378 Coins consists of one rupee, 50 paise & 25 paise whose values are proportional to 13:11:7, Number of 50 paise coins will be : A) 133 B) 132 C) 128 D) 136 Ans. B 13*x+11*2x+7*4x = 378 13x+22x+28x = 378 63x = 378 X = 378/63 = 6 Therefore, Required number of 50 paise coins = 22x =22 * 6 =132

  Q.1 In a row of children Rohan is seventh from the left & Bali is fourth from the right. When Rohan & Bali exchange their position, Rohan will be fifteenth from the left. Bali’s position from the right will be ? A) 4th B) 12th C) 11th D) 8th Ans. BIst case: 1  2  3  4  5  6  7             8  9                          Rohan10  11  12  13  14  15  16  17  18                             Bali2nd case:         1  2  3  4  5  6  7          8   9                                 Bali                         Rohan  12      11  10 10  11  12  13 14   15       16   17  189     8     7    6   5     4        3      2    1 Q.2 Mr. Vajpayee M.D. of X,Y,Z company asked five persons -Asit,Varun,Chandra,Danny & Eshita about their interest in a new project. He got following replies: Asit: None of us is interested Varun : One of us is interested Chandra : Two of us are interested Danny : Three of us are interested Eshita : Four of us are interested From his experience Mr. Vajpayee knows that those who are interested only tells the truth & others lie.How many of them are interested in the new project ?A) 3 B) 4 C) 2 D) 1 Ans. D Q.3 There are four roads, I have come from the South & want to go to the temple. The road to the right leads me away from the coffee house while straight road leads to a college. In which direction is the temple ? A) North B) South C) East D) west Ans. C Q.4 A cube has 6 faces each of different colour. Red face is opposite to the black. The green face is in between red & black. Blue face is adjacent to the white & brown face is adjacent to the blue. Four colours adjacent to green are : A) Red,Black,Brown & White B) Red,Brown,Blue & White C) Red,Black,Blue & White D) Red, Black , Brown & Blue Ans. A         6 (Front surface)1- Green, 2- Brown,3-Blue,4-White5- Black6-red Therefore, Green surface is following four colours- Red, Black,Brown & White Q.5 If 378 Coins consists of one rupee, 50 paise & 25 paise whose values are proportional to 13:11:7, Number of 50 paise coins will be : A) 133 B) 132 C) 128 D) 136 Ans. B13*x+11*2x+7*4x = 378 13x+22x+28x = 378 63x = 378 X = 378/63 = 6 Therefore, Required number of 50 paise coins = 22x =22 * 6 =132

Q.1 A certain type of board is sold only in length of multiples of 2ft. The shortest board sold is 6ft & the largest is 24 ft. A builder needs a large quantity of this type of board in 5 ½ ft length. For minimum wastage the lengths to be ordered should be : A) 24 ft B) 26 ft C) 12 ft D) 22 ft Ans. D Just see Options, & according to the options just put values & then find the wastage: Each 6ft board yields one 5 ½ board with ½ waste Each 12 ft board yields two 5 ½ board with 1 ft waste (2*5 ½ =11, 12-11 = 1 ft waste) Each 24 ft board yields four 5 ½ boards with 2ft waste (4*5 ½ =22, 24-22 = 2 ft waste) Each 22ft board may be divided into four 5 ½ ft boards with no waste (4*5 ½ = 22) Q.2 A gardener plants 17,956 trees in such a way that there are many rows as are trees in a row. The number of trees in a row is : A) 144 B) 154 C) 134 D) 136 Ans. C v 17,956 = 134 Q.3 A men went to shop & was shown some shirts costing Rs. 100 each & some trousers costing Rs. 150 each. If he had Rs.1200 with him, what was the maximum number of trousers that he could have purchased , if he had also wanted to purchase some shirts ? A) 5 B) 8 C) 2 D) 6 Ans. D We have to find greatest multiple of 150 contained in 1200, such that there is a remainder which is a multiple of 100 (i.e. Just divide 1200/150 in such a way that it leaves a remainder which is divisible by 100) Therefore, 1200 = 150*6+3*100 Therefore he can buy 6 trousers along with the 3 shirts Q.4 Karan ranked thirteen from the top & twenty six from the bottom among those who have passed in the annual examination in a class. If six students have failed in the annual examination, how many students appeared ? A) 45 B 38 C) 44 D) 50 Ans. C No. of students who pass= (12+25) + 1= 38 Total number of students= 38 + 6=44 Q.5 John ranked 21st in a class of fifty Students. What is his rank from the end ? A) 30th B) 32nd C) 20th D) 31st Ans. A 50-21=29 29+1=30

Q.1 Diameters of two circular coins are in the ratio of 1:3. The smaller coin is to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times smaller coin rolled around the bigger coin ? A) 6 B) 9 C) 3 D) 4 Ans. C Since, Diameter of small coin/Diameter of big coin = 1/3 Radius of small coin/Radius of big coin = 1/3 Therefore, circumference of small coin = 2pk Circumference of big coins = 2p (3 k) = 6pk = 3 (2pk) Q.2 A ray of light is incident towards a plane mirror at an angle of 60O with the mirror surface. What will be the value of angle of reflection ? 600 Mirror A) 300 B) 00 C) 600 D) 900 Ans. A Since, Normal to the surface of mirror is 900, Therefore angle of incidence will be 90 – 60 = 300 As angle of reflection must be equal to the angle of incidence according to the laws of reflection. Q.3 A man is facing west turns through 450 clockwise, again 1800 clockwise and then turns through 2700 anti clockwise. Which direction is he facing now? A) North–East B) North-West C) South–East D) South–West Ans. D Clearly, the man initially faces in the  west direction. On moving 45o clockwise, he faces in the direction North. On further moving 180o clockwise, he faces in the direction South.  Finally, on moving 270o anti–clockwise, he faces in the direction, which is South–west. Q.4  I am facing east. I turn 1000 in the clockwise direction and then 1450 in the anticlockwise direction. Which direction am I facing now? A) East B) Northeast C) North D) South-west Ans. B Q.5 A bus starts from city A. The no. of women in the bus is half of the no. of men. In city B, 10 men left bus & 5 women entered. Now no. of men & women is equal. In the beginning how many passengers entered the bus? A) 15 B) 30 C) 36 D) 45 Ans. D Suppose in city A the no of men is 2x Then the no. of women is =x In city B: 2x-10 = x+5 X=15 So, A= 30 Thus , the no. of passengers in the beginning =30+15 =45

Q.1 Doctors have advised sheetal, a chocolate freak, not to take more than 20 chocolates in one day. When she went to the market to buy her daily quota, she found that if she buys chocolates from a market complex she would have 3 Rs more for the same no. of chocolates than she would have spent. Had she bought them from her uncle scrooge’s shop , getting two sweets less per rupee. she finally decided to get them from uncle scrooge shop paying only in one rupee coins. how many chocolates did she buy? A) 12 B) 9 C) 18 D) 15 Ans. A Let n be the number of chocolates she bought. Price at market = 1/(x-2) Price at Scrooge’s shop = 1/(x) n/(x-2) = n/(x) + 3 2n = 3x(x-2) n = 3x(x-2)/2 Now, through hit &trial method, (Just put value of X starting from 1,,,then 2,,,then 3 as so on…& you will find after putting x=4 it will calculate & comes as 12) n=12 Q.2 How much would she have spent at the market complex? A) 6 B) 9 C) 12 D) 5 Ans. A At the market complex n/(x-2) = 12/2 = 6 Q.3 Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers? A) 12 & 8 Apples per tree B) 11 & 9 Apples per tree C) 10 & 14 Apples per tree D) 17 & 21 Apples per tree Ans. B Explanation: Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that a + 1 = b + 3 = c – 1 = d + 3 = e – 6 But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3. Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively. Therefore 11 x – 1 = 13 y + 3 By trial and error method, we get the value for x and y as 11 and 9 Q.4 If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour? A) 451 times B) 651 times C) 751 times D) 851 times Ans. A Explanation: There are 60 minutes in an hour. In ¾ of an hour there are (60 * ¾) minutes = 45 minutes. In ¾ of an hour there are (60 * 45) seconds = 2700 seconds. Light flashed for every 6 seconds. In 2700 seconds 2700/6 = 450 times. The count start after the first flash, the light will flashes 451 times in ¾ of an hour Q.5 There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had ? A) Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars. B) Sudhir had 40 cars, Arvind had 30 cars & Gauri had 10 cars C) Sudhir had 41 cars, Arvind had 40 cars & Gauri had 8 cars D) Sudhir had 42 cars, Arvind had 50 cars & Gauri had 6 cars Ans. A Explanation: Sudhir Arvind Gauri Finally 24 24 24 Before Gauri’s transaction 12 12 48 Before Arvind’s transaction 6 42 24 Before Sudhir’ s transaction 39 21 12

Q.1 There are 31 kgs of rice. With a 1 kg weight,Find out the minimum number of weighings required to weigh 31 kgs. A) 5 weighings B) 6 weighings C) 7 weighings D) 8 weighings Ans. A 5 weighings ie., 1-1, 2-2, 4-4, 8-8, 16-16. Q.2 A green grocer was selling apple at a penny each, chikoos at 2 for a penny, peanuts at 3 for a penny. A father spent 7 pennies and got same amount of each type of fruit for each of his three children. What did each children get? Options: A) 1 apple, 2 chikoos, 2 peanuts B) 1 apple, 2 chikoos, 1 peanut C) 1 apple, 3chikoos, 2 peanuts D) 1 apple, 1 chikoos, 1 peanut Ans. B Apple=Rs.1, 2 Chikoos are of 1 penny or 1 chikoo= ½ =0.5 In same way, 3 peanuts for 1 penny ,or 1 peanut = 1/3 =0.33 Now see options & determine where 7 pennies are consuming: A) 1 apple i.e. 1*3 (since 3 students are there) 2 chikoos,i.e. 2*3=6 Or 6*0.5 = 3 2 peanuts,i.e. 0.33*6 Now,3+6*0.5+0.33*6 =12 Q.3 After gathering 770 chestnuts, three girls divided them up so that amounts were in the same proportion as their ages. As often as Mary took four chestnuts, Nelli took three, and for every six that Mary received, Susie took seven. How many chestnuts did each girl get? A) Mary-264,Nelli-198,Susie-298 B) Mary-198, Nelli-264,Susie-298 C) Mary-200,Nelli-275,Susie-300 D) Mary-255,Nelli-280,Susie-310 Ans. A Let mary take m , nellie take n and susie take s chestnuts … then , m : n =4:3 = 12:9 and , s : m = 7:6 = 14:12 therefore, s : m : n = 14 : 12 :9 so susie got (14/35) *770 =308 mary got =264 and nellie =198 Q.4 A king gave each of his sons a few gold coins such that no pair of sons has the same number of gold coins as any other pair of sons. If the king has six sons, What is the minimum number of gold coins that the king could have given his sons? A) 21 B) 28 C) 30 D) 32 Ans. D The series is 1,2,3,5,8,13… ( addition of two consecutive numbers gives the next number). no pair of sons will have equal number of gold coins Q.5 Maria buys one clown fish and 3 guppies for $5 and 2 clown fish and 5 guppies for $9. Find the price of 1 guppy. A) $1 B) $2 C) $3 D) $4 Ans. A Let c be price of clown fish and g be that of guppy. c + 3g = 5 …….(i) and 2c + 5g = 9…………(ii) Solving (i) and (ii), we get g = 1, c = 2

Q.1 In an examination, the number of those who passed and the number of those who failed were in the ratio 5 : 2. Had 25 more appeared, and 5 less passed, the ratio of passed to failed would have been 3 : 2. Find the number of candidates who appeared, initially. A) 215 B) 210 C) 200 D) 175 Ans. D Number of those who passed to number of those failed = 5 : 2 Let number of students who passed = 5x and number of students who failed = 2x Total number of students = 5x + 2x = 7x When 25 more students appeared then total students = 7x + 25 When students increased, 5 less passed Now number of students passed = 5x – 5 Number of students who failed = (7x + 25) – (5x – 5) = 7x + 25 – 5x + 5 = 2x + 30 New ratio of passed to failure = 3 : 2 According to question ? 2 (5x – 5) = 3 (2x + 30) 10x – 10 = 6x + 90 ? 10x – 6x = 90 + 10 4x = 100, x = 25 Hence number of students who appeared = 7 × 25 = 175. Q.2 Two friends A and B have a certain amount of money in the ratio 2 : 3. If A gives Rs. 20 to B, the ratio will become 7 : 13. If B gives Rs. 20 to A, what will be the ratio of the money with A and B? A) 4 : 5 B) 3 : 4 C) 9 : 11 D) 2 : 3 Ans. C Assume 2k and 3k to be the money with A and B. If A gives Rs. 20 to B the ratio will become = 2K-20 / 3K+20 = 7/13 If B gives Rs. 20 to A, the ratio will be = 2K+20 / 3K-20 = 9/11 Q.3 In a market in Lucknow, the price of a bag of 8 Oranges was Rs. 180/-. On the same day in Ludhiana a market was selling 5 Oranges for Rs. 100/-. A 3 bag was priced at Rs. 380/- in Chennai that day. In Bangalore Oranges were selling for Rs. 230 a dozen. The Oranges each weighed 150g. Where were the Oranges Cheapest ? A) Chennai B) Ludhiana C) Bangalore D) Lucknow Ans. A weight of 8 Oranges = 1.2kg cost of 1.2 kg = Rs.180 cost of 1 kg Oranges = Rs.150 LUDHIANA weight of 5 Oranges = 0.75kg cost of 0.75 kg = Rs.100 cost of 1 kg = Rs.133.33 CHENNAI cost of 3kg Oranges = Rs.380 cost of 1 kg Oranges = Rs.126.66 BANGALORE weight of 12 Oranges = 1.8 kg cost of 1.8kg Oranges = Rs.230 cost of 1 kg Oranges = Rs.127.77 from the above solution, it is clear that the Oranges were cheapest in Chennai Q.4 In a row of students Sonam is eighth from the right & Rahul is sixteenth from the right. How many boys are there in a row? A) 22 B) 23 C) 24 D) Data inadequate Ans. D Since there are Total no. of students are not present Q.5 A man is facing northwest. He turns 90 degrees in the clockwise direction and then 135degrees in the anti-clockwise direction. Which direction is he facing now? A) East B) West C) North D) South Ans. B Man is facing north-west direction. He turns 90 degree in the clockwise direction and then 135 degrees in the anti-clockwise direction So, net movement = 135-90 = 45 degrees in the anti-clockwise direction 45 degrees in the anti-clockwise direction from north-west = WEST So, the man is facing west

  Q.1 In an examination, the number of those who passed and the number of those who failed were in the ratio 5 : 2. Had 25 more appeared, and 5 less passed, the ratio of passed to failed would have been 3 : 2. Find the number of candidates who appeared, initially.   A) 215   B) 210   C) 200   D) 175   Ans. D Number of those who passed to number of those failed = 5 : 2 Let number of students who passed = 5x and number of students who failed = 2x Total number of students = 5x + 2x = 7x When 25 more students appeared then total students = 7x + 25 When students increased, 5 less passed Now number of students passed = 5x – 5 Number of students who failed = (7x + 25) – (5x – 5) = 7x + 25 – 5x + 5 = 2x + 30 New ratio of passed to failure = 3 : 2 According to question   ? 2 (5x – 5) = 3 (2x + 30) 10x – 10 = 6x + 90 ? 10x – 6x = 90 + 10 4x = 100, x = 25 Hence number of students who appeared = 7 × 25 = 175.   Q.2 Two friends A and B have a certain amount of money in the ratio 2 : 3. If A gives Rs. 20 to B, the ratio will become 7 : 13. If B gives Rs. 20 to A, what will be the ratio of the money with A and B?   A) 4 : 5   B) 3 : 4   C) 9 : 11   D) 2 : 3   Ans. C   Assume 2k and 3k to be the money with A and B.   If A gives Rs. 20 to B the ratio will become   = 2K-20 / 3K+20 = 7/13    If B gives Rs. 20 to A, the ratio will be  = 2K+20 / 3K-20 = 9/11   Q.3 In a market in Lucknow, the price of a bag of 8 Oranges was Rs. 180/-. On the same day in Ludhiana a market was selling 5 Oranges for Rs. 100/-. A 3 bag was priced at Rs. 380/- in Chennai that day. In Bangalore Oranges were selling for Rs. 230 a dozen. The Oranges each weighed 150g. Where were the Oranges Cheapest ?   A) Chennai   B) Ludhiana   C) Bangalore   D) Lucknow   Ans. A weight of 8 Oranges = 1.2kg cost of 1.2 kg = Rs.180 cost of 1 kg Oranges = Rs.150 LUDHIANA weight of 5 Oranges = 0.75kg cost of 0.75 kg = Rs.100 cost of 1 kg = Rs.133.33 CHENNAI cost of 3kg Oranges = Rs.380 cost of 1 kg Oranges = Rs.126.66 BANGALORE weight of 12 Oranges = 1.8 kg cost of 1.8kg Oranges = Rs.230 cost of 1 kg Oranges = Rs.127.77 from the above solution, it is clear that the Oranges were cheapest in Chennai   Q.4 In a row of students Sonam is eighth from the right & Rahul is sixteenth from the right. How many boys are there in a row?   A) 22   B) 23   C) 24   D) Data inadequate   Ans. D   Since there are Total no. of students are not present   Q.5 A man is facing northwest. He turns 90 degrees in the clockwise direction and then 135degrees in the anti-clockwise direction. Which direction is he facing now?   A) East   B) West   C) North   D) South   Ans. B   Man is facing north-west direction. He turns 90 degree in the clockwise direction and then 135 degrees in the anti-clockwise direction So, net movement = 135-90 = 45 degrees in the anti-clockwise direction 45 degrees in the anti-clockwise direction from north-west = WEST So, the man is facing west    

Q.1 A hollow cube of size 5 cm is taken with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If only 2 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted ? A) 485 B) 486 C) 487 D) 488 Ans. D The big cube is completely hollow.. But, the thickness of its side is 1cm & this is made up of smaller cubes.   Just like the walls of a room. The room is hollow, but, its thickness is due to smaller bricks. The 4 walls of this room is painted from the outside. And, you are asked totally how many sides of all the bricks are now unpainted.   First, you need to know how many bricks (small cubes) are there.   Size of big cube = 5cm Total volume of the big cube = 5*5*5 = 125cm^3   Size of the hollow cube inside the big cube = 3cm Volume of the hollow space inside the big cube = 3*3*3 = 27cm^3   Therefore, volume occupied by small cubes (or volume of thickness) = 125 – 27 = 98cm^3   Size of each small cube = 1cm Volume of each small cube = 1*1*1 = 1cm^3 Total number of small cubes in wall = 98 / 1 = 98   In short, 98 small cubes make up the wall of the big cube. Each cube has 6 faces, so 98 cubes have = 98*6 faces = 588   The four sides of the big cube have 100 painted faces. Because each big side has 25 faces of the small cubes.   Therefore, total unpainted faces = 588 – 100 = 488   Q.2 A large cube is painted green on all six faces & then cut into a certain number of smaller but identical cubes. It was found that amongst the smaller cubes, there were 8 cubes which had no face painted at all. What is the maximum number of cubes that were cut from large original cube ?   A) 46 B) 56 C) 64 D) 54 Ans. C When a cube is painted & cut into smaller n pieces along each side then the total number of smaller cubes obtained will be (n*n*n). From these, remove the outer layer of cubes, that is 2 from each face, then there will be [(n-2) * (n-2) * (n-2)] cubes left. Now. Number of cubes that do not have any face painted is (2*2*2) As, (n-2) = 2 i.e. n=4 Therefore, the maximum number of cubes that were cut from original cube are 4*4*4= 64 Cube   Q.3 Pointing towards a boy, Veena said, “He is the son of the only son of my grandfather”. How is that boy related to Veena?   A) Brother B) Nephew C) Father D) None of these Ans. A   EXPLANATION:       Q.4 Pointing to Kapil, Shilpa said, “His mother’s brother is the father of my son Ashish”. How is Kapil related to Shilpa?   A) Sister–in–law B) Nephew C) Niece D) Aunt Ans. B         Kapil is the nephew of Shilpa.   Q.5 A cube is painted green on all the sides. Then it is cut into 512 cubes of equal size. How many of smaller cubes are painted on 1 side ? A) 18 B) 216 C) 12 D) 14 Ans. B Cube root of 512 is 8. Si, cube is 8*8*8. Each side of the cube  has 64 visible small cube faces, 4 of which are corners (3 green sides) & 24 more are edges (2 coloured sides), so  there are only 36 small cubes with one green face on each of the six sides of the large cube. So, 36*6= 216 Shortcut: Learn this: Vertices are: 8 Edges are: 12 Faces are :6 *To Find 1 face painted: (N/n-2)2 *6 = (8/1-2)2 *6 = 36 *6 =216 *Similarly if it asks you to find 2 faces painted, then use this formula, (N/n-2) * 12 *For 3 faces painted, use this formula, just find how many vertices are there & these are 8 which is answer *For finding no. of smaller cubes: (N/n)3   Q.6 Find the number of triangles in the given figure.     A) 22   B) 24   C) 26   D) 28 Ans. D The figure may be labelled as shown.   The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7 in number. The triangles having two components each are GFL, KEL, AMO, NDP, BHN,  CMJ, NEJ and HFM i.e. 8 in number. The triangles having three components each are IOE, IFP, BIF and CEI i.e. 4 in number. The triangles having four components each are ANE and DMF i.e. 2 in number. The triangles having five components each are FCK, BGE and ADL i.e. 3 in Number. The triangles having six components each are BPF, COE, DHF and AJE i.e. 4 in Number Total number of triangles in the figure = 7 + 8 + 4 + 2 + 3 + 4 = 28.