Q1.Three Brothers on a Farm
Three brothers live in a farm. They agreed to buy new seeds: Adam and Ben would go and Charlie stayed to protect fields. Ben bought 75 sacks of wheat in the market whereas Adam bought 45 sacks. At home, they split the sacks equally. Charlie had paid 1400 dollars for the wheat. How much dollars did Ben and Adam get of the sum, considering equal split of the sacks?
Ans: Every farmer's part is 1/3(45+75) = 40 sacks.
Charlie paid $1400 for 40 sacks, then 1 sack costs $1400/40 = $35/sack.
Adam got $35*(45-40)=35*5 = $175.
Ben got $35*(75-40)=35*35 = $1225.
Answer: Ben $1225, Adam $175
Q2.How can you add eight 8's to get the number 1,000? (only use addition)
Ans:888 + 88 + 8 + 8 + 8 = 1,000
Q3.Three Guys at A Hotel Riddle Three guys rent a hotel room for the night. When they get to the hotel they pay the $30 fee, then go up to their room. Soon the bellhop brings up their bags and gives the lawyers back $5 because the hotel was having a special discount that weekend. So the three lawyers decide to each keep one of the $5 dollars and to give the bellhop a $2 tip. However, when they sat down to tally up their expenses for the weekend the could not explain the following details: Each one of them had originally paid $10 (towards the initial $30), then each got back $1 which meant that they each paid $9. Then they gave the bellhop a $2 tip. HOWEVER, 3 • $9 + $2 = $29 The guys couldn't figure out what happened to the other dollar. After all, the three paid out $30 but could only account for $29.
Ans: There are many ways of explaining/thinking about this truly brain bending riddle! It all boils down to the fact that the lawyers's math is incorrect. They did NOT spend $9 • 3 + $2. They spent exactly $27 dollars. $25 for the room and $2 for the tip. Remember they got exactly $3, in total back. Another way to think about the answer to this riddle is to just pretend that the bellhop refunded $3 to the lawyers (rather than giving them $5 and receiving $2 back). If the lawyers get $3 back and each takes $1. They they spent exactly $27 dollars.
Q4.A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Ans:11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes
Q5.You are about to leave for holiday, but you forgot socks! You race back to your room, but all the lights are off, so you can't see the color of the socks. Never mind, because you remember that in your drawer there are ten pairs of white socks, ten pairs of black socks, and eleven pairs of blue socks, but they are all mixed up. How many of your socks do you need to take before you can be sure to have at least one matching pair?
Ans:The answer is four. Although there are many socks in the drawer, there are only three colors, so if you take four socks then you are guaranteed to have at least one matching pair.
Q7.The Insurance Salesman
An insurance salesman walk up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children's ages, you get 36. He says this is not enough information. So she gives a him 2nd hint. If you add up the children's ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she'll give him one last hint which is that her oldest of the 3 plays piano.
Ans: Here is a hint:
1 2 18 = 21
1 3 12 = 16
1 4 9 = 14
6 6 1 = 13
2 2 9 = 13
2 3 6 = 11
3 3 4 = 10
Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her 'oldest' you know it can not be {6,6,1} since she would have two 'older' sons not an 'oldest'.
Ans: Every farmer's part is 1/3(45+75) = 40 sacks.
Charlie paid $1400 for 40 sacks, then 1 sack costs $1400/40 = $35/sack.
Adam got $35*(45-40)=35*5 = $175.
Ben got $35*(75-40)=35*35 = $1225.
Answer: Ben $1225, Adam $175
Q2.How can you add eight 8's to get the number 1,000? (only use addition)
Ans:888 + 88 + 8 + 8 + 8 = 1,000
Q3.Three Guys at A Hotel Riddle Three guys rent a hotel room for the night. When they get to the hotel they pay the $30 fee, then go up to their room. Soon the bellhop brings up their bags and gives the lawyers back $5 because the hotel was having a special discount that weekend. So the three lawyers decide to each keep one of the $5 dollars and to give the bellhop a $2 tip. However, when they sat down to tally up their expenses for the weekend the could not explain the following details: Each one of them had originally paid $10 (towards the initial $30), then each got back $1 which meant that they each paid $9. Then they gave the bellhop a $2 tip. HOWEVER, 3 • $9 + $2 = $29 The guys couldn't figure out what happened to the other dollar. After all, the three paid out $30 but could only account for $29.
Ans: There are many ways of explaining/thinking about this truly brain bending riddle! It all boils down to the fact that the lawyers's math is incorrect. They did NOT spend $9 • 3 + $2. They spent exactly $27 dollars. $25 for the room and $2 for the tip. Remember they got exactly $3, in total back. Another way to think about the answer to this riddle is to just pretend that the bellhop refunded $3 to the lawyers (rather than giving them $5 and receiving $2 back). If the lawyers get $3 back and each takes $1. They they spent exactly $27 dollars.
Q4.A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Ans:11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes
Q5.You are about to leave for holiday, but you forgot socks! You race back to your room, but all the lights are off, so you can't see the color of the socks. Never mind, because you remember that in your drawer there are ten pairs of white socks, ten pairs of black socks, and eleven pairs of blue socks, but they are all mixed up. How many of your socks do you need to take before you can be sure to have at least one matching pair?
Ans:The answer is four. Although there are many socks in the drawer, there are only three colors, so if you take four socks then you are guaranteed to have at least one matching pair.
Q7.The Insurance Salesman
An insurance salesman walk up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children's ages, you get 36. He says this is not enough information. So she gives a him 2nd hint. If you add up the children's ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she'll give him one last hint which is that her oldest of the 3 plays piano.
Ans: Here is a hint:
Why would he need to go back to get the last hint after seeing the number on the house next door? Because the sum of their ages ( the number on the house) is ambiguous and could refer to more than 1 trio of factors.and the solution is: If you list out the trio of factors that multiply to 36 and their sums, you get : 1 1 36 = 38
1 2 18 = 21
1 3 12 = 16
1 4 9 = 14
6 6 1 = 13
2 2 9 = 13
2 3 6 = 11
3 3 4 = 10
Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her 'oldest' you know it can not be {6,6,1} since she would have two 'older' sons not an 'oldest'.
Q7.Taxi Driver A taxi driver states that his cab number is divisible by the no 2,3,4,5,6 with a remainder of 1 and when the number is divided by 11 it does not give any remainder
Ans: No ÷ 2 Remainder = 1
No ÷ 3 Remainder = 1
No ÷ 4 Remainder = 1
No ÷ 5 Remainder = 1
No ÷ 6 Remainder = 1
Least number is = [LCM of 2, 3, 4, 5, 6] + 1
= 60 + 1 = 61
but this is not divisible by 11
try next No. = 60 × 2 + 1 = 121
so required number is 121
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