Pattern 6
1. Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?a) 114 b) 135 c) 21 d) 71
Solution: I do not know perfectly but I got some solutions from internet I do not know correctly whether it is true or not,((3*9*5))-((3-2)*(9-2)*(5-2)) so answer is 114.
2. A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?
a) 2000 b) 5000 c) 3000 d) 7000
3. Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape?
a) 98 b) 104 c) 100 d) 61
4. Leena cut small cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm, width 50 cm and depth 50 cm. How many more cubes does she need to make a perfect cube?
a)500 b)250 c)750 d)650
5. Leena cut small cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm and depth 3 cm. How many more cubes does she need to make a perfect cube?
a) 910 b) 250 c) 750 d) 650
6. A lady builds 9cm length, 10cm width,3cm height box using 1 cubic cm cubes. What is the minimum number of cubes required to build the box?
a) 730 b) 270 c) 720 d) 310
Pattern 7:
1. (40*40*40 – 31*31*31)/(40*40+40*31+31*31)=?
a)8 b)9 c )71 d)51
Solution: a3 -b3 =(a-b)*(a2+a*b+b2)
so from this formula we will find (a-b) value
2. (98*98*98 – 73*73*73)/( 98*98*98 – 73*73*73)=?
a).171 b).4 c).420 d).415
3. (209*144)^2 + (209*209)+(209*144)+(144*144) = ?
a)905863729 b)905368729 c)905729368 d)65
Pattern 8:
1. ((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16 d)15
Solution: substitute x=4y in above we can find solution
2. x/2y = 2a,then 2x/x-2ay=?
a)4 b)8 c)16 d)2
3. 3X/5Y = 5Y/3X…..Find the value of X/Y
a)3/5 b)5/3 c)2/5 d)5/2
4. What is the value of (3X+8Y)/(X-2Y), if X/2Y=2
a)8 b)none c)10 d)13
5. (4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2 a)48/5 b)46/5 c)47/5 d)49/5 6. ((4x+2y)/(4x-2y)= ? as (x/2y) = 2
a)8/7 b)9/7 c)11/7 d)6/7
Pattern 9:
1. A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?
a)16 b)56 c)112 d)28
Solution: 8c2
2. A pizza shop made pizzas with many flavors. There are 10 different flavors, in that 7 flavors are taken to make pizza. In how many ways they can arrange?
a)240 b)120 c)65 d)210
3. A pizza shop made pizzas with many flavors. There are 9 different flavors, in that 2 flavors are taken to make pizza. In how many ways they can arrange?
a)16 b)26 c)36 d)46
Pattern 10:
1. 3, 22, 7, 45, 15,? , 31
a)91 b)151 c)90 d)5
2. 8 6 17 14 35 31 75 _ 143?
3. Inspired by Fibonacci series Sangeet decided to create his own series which is 1, 2, 3, 7, 7, 22, 15, 67, 31, _, 63?
a)202 b)31 c)76 d)49
4. 3, 12, 7, 26, 15, ?
a)54 b)27 c)108 d)31
5. 1! + 2! + ……. + 50!=?
a)3.1035*10^64 b)2.1021*10^65 c)3.1035*10^63 d)3.1035*10^62
6. 1, 2, 3, 6, 7, 14, _, 32?
7. 5, 9, 12, 18, 26, 36, 47, 72, _?
a)75 b)135 c)100 d)55
8. 3, 15, x, 51, 53,159,161
a)17 b)34 c)54 d)112
1. Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?a) 114 b) 135 c) 21 d) 71
Solution: I do not know perfectly but I got some solutions from internet I do not know correctly whether it is true or not,((3*9*5))-((3-2)*(9-2)*(5-2)) so answer is 114.
2. A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?
a) 2000 b) 5000 c) 3000 d) 7000
3. Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape?
a) 98 b) 104 c) 100 d) 61
4. Leena cut small cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm, width 50 cm and depth 50 cm. How many more cubes does she need to make a perfect cube?
a)500 b)250 c)750 d)650
5. Leena cut small cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm and depth 3 cm. How many more cubes does she need to make a perfect cube?
a) 910 b) 250 c) 750 d) 650
6. A lady builds 9cm length, 10cm width,3cm height box using 1 cubic cm cubes. What is the minimum number of cubes required to build the box?
a) 730 b) 270 c) 720 d) 310
Pattern 7:
1. (40*40*40 – 31*31*31)/(40*40+40*31+31*31)=?
a)8 b)9 c )71 d)51
Solution: a3 -b3 =(a-b)*(a2+a*b+b2)
so from this formula we will find (a-b) value
2. (98*98*98 – 73*73*73)/( 98*98*98 – 73*73*73)=?
a).171 b).4 c).420 d).415
3. (209*144)^2 + (209*209)+(209*144)+(144*144) = ?
a)905863729 b)905368729 c)905729368 d)65
Pattern 8:
1. ((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16 d)15
Solution: substitute x=4y in above we can find solution
2. x/2y = 2a,then 2x/x-2ay=?
a)4 b)8 c)16 d)2
3. 3X/5Y = 5Y/3X…..Find the value of X/Y
a)3/5 b)5/3 c)2/5 d)5/2
4. What is the value of (3X+8Y)/(X-2Y), if X/2Y=2
a)8 b)none c)10 d)13
5. (4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2 a)48/5 b)46/5 c)47/5 d)49/5 6. ((4x+2y)/(4x-2y)= ? as (x/2y) = 2
a)8/7 b)9/7 c)11/7 d)6/7
Pattern 9:
1. A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?
a)16 b)56 c)112 d)28
Solution: 8c2
2. A pizza shop made pizzas with many flavors. There are 10 different flavors, in that 7 flavors are taken to make pizza. In how many ways they can arrange?
a)240 b)120 c)65 d)210
3. A pizza shop made pizzas with many flavors. There are 9 different flavors, in that 2 flavors are taken to make pizza. In how many ways they can arrange?
a)16 b)26 c)36 d)46
Pattern 10:
1. 3, 22, 7, 45, 15,? , 31
a)91 b)151 c)90 d)5
2. 8 6 17 14 35 31 75 _ 143?
3. Inspired by Fibonacci series Sangeet decided to create his own series which is 1, 2, 3, 7, 7, 22, 15, 67, 31, _, 63?
a)202 b)31 c)76 d)49
4. 3, 12, 7, 26, 15, ?
a)54 b)27 c)108 d)31
5. 1! + 2! + ……. + 50!=?
a)3.1035*10^64 b)2.1021*10^65 c)3.1035*10^63 d)3.1035*10^62
6. 1, 2, 3, 6, 7, 14, _, 32?
7. 5, 9, 12, 18, 26, 36, 47, 72, _?
a)75 b)135 c)100 d)55
8. 3, 15, x, 51, 53,159,161
a)17 b)34 c)54 d)112
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