1. [-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)] is ________________
(A) 3/7
(B) 5/7
(C) 11/7
(D) 19/7
Solution:
[-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)]
= (-9/7) + (-26/7) + (46/7)
= -35/7+ 46/7
=11/7
Answer: (C) 11/7
2. The population of a city in the year 2014 is 1,80,000 and increases at a rate 20% per year.
(A) 2,40,000
(B) 2,59,200
(C) 2,55,000
(D) 2,54,300
Solution:
Principle (P) = 1,80,000
Rate of interest (R) = 20%
Number of years (n) = 2
= P [(1+R)/100]2
=180000 [(1+20)/100]2
=180000 [(120/100 )*(120/100)]
=18(120*120)
=259200
Answer: (B) 2,59,200
3. 3 — 25 here, which of the following number is suitable in —, so that the number will be a perfect square?
(A) 1
(B) 0
(C) 4
(D) 6
Solution:
Note: Question of the this types needs to be solved from the options. When a question directly indicates the options in the question itself, then it is solved by taking each and every options and substituting that option in the question until we can arrive at the solution.
A number among the options at the — will make 3—25 as a perfect square.
Hence, we have 3125, 3025, 3425, 3625 from the options. Among this, we have to find the perfect square.
Now,
√3125 = 55.90 –> Not a perfect Square
√3025 = 55 –> Perfect Square.
√3425 = 58.52 –> Not a perfect Square
√3625 = 60.20 –> Not a perfect Square
Answer: (B) 0
Also note that,
Step 1: option a) is taken and solved, no solution is arrived.
Step 2: option b) is taken and solved, Solution is arrived.
DO NOT STOP WITH THIS, Take all the other options c) & d) and solve it and confirm that, they were not the answers.
4. The average mark of 10 children is 80 then their total mark is
(A) 200
(B) 300
(C) 800
(D) 400
Solution:
Number of children= 10
Average mark of 10 children = 80
Total mark = number of children * Average
Answer: (C) 800
5. A man and woman are engaged in a work. A man can do a piece of work in 4 days and the woman can do in 12 days. Find how many days will they take to finish it together?
(A) 6 days
(B) 5 days
(C) 4 days
(D) 3 days
Solution:
A (Man) do work in = 4 days
B (Woman) do work in = 12
So lets take,
X= 4
Y= 12
Therefore,
xy/x+y
=(12*4)/16
=(3*4)/4
=3
Answer: (D) 3 days
6. Which of the following set of measurements will form a right angle triangle?
(A) 6, 9, 12
(B) 5, 8, 10
(C) 5, 5, 5√2
(D) 3, 4, 4√2
Solution:
Note: This question is also from Option to Question Approach.
For a Right Angled Triangle, consider the three sides, AB, BC & AC
Condition for a Right Angled Triangle is, AB2 + BC2 = AC2
Take option a) 62 + 92 = 117 is not equal to 122
b) 52 + 82 = 89 is not equal to 102
c) 52 + 52 = 50 is Equal to (5√2) 2
(5√2) 2 = 25×2 = 50
d) 3 + 4 = 25 is not equal to (4√2)
Answer: (C) 5, 5, 5√2
7. The value of
(A) 20
(B) 25
(C) 16
(D) 9
Solution:
First Solve the smaller roots within the larger roots so that we can obtain the solution.
√81 = 9
√7+9 = √16 = 4
√60+4 = √64 = 8
√ 248+8 = √256 = 16
√609+16 = √625 = 25
Answer: (B) 25
8. The price of a house is decreased from rupees fifteen lakhs to rupees twelve lakhs. The percentage of decrease is
(A) 10 %
(B) 20 %
(C) 30 %
(D) 40 %
Solution:
Initial price = 15,00,000
Final price = 12,00,000
100% = 150000
? %= 120000
=(100*12)/15
= (100*3)/4
=80%
So 80% is 120000 in 150000
Therefore sub 80 from 100 to get decreased percent
=100-80
=20%
Answer: (B) 20 %
9. If 3 (t – 3) = 5 (2t + 1) then t = ?
(A) -2
(B) 2
(C) -3
(D) 3
Solution:
3(t-3) = 5(2t + 1)
3t – 9 = 10t +5
3t-10t = 5+9
-7t = 14
t=14/7
t=-2
Answer: (A) -2
10. The value of (1.75 * 1.75 + 2 * 1.75 * 0.75 + 0.75 * 0.75) / (1.75 * 1.75 – 0.75 * 0.75)
(A) 3.5
(B) 6.25
(C) 1
(D) 2.5
Solution:
[(a2+2ab+b2)/ (a2+b2)] = a+b
Here,
a = 1.75
b = 0.75
a + b = 1.75+0.75
=2.5
Answer: (D) 2.5
11. The value of 163 + 73 – 233 is
(A) -7728
(B) 7028
(C) 7728
(D) -7718
Solution:
163 = 4096
73 = 343
233 = 12167
=-12167 + 4096 + 343
=-7728
Answer: (A) -7728
12. Find the next term of 4 in the series is 1, 1, 2, 8, 3, 27, 4, …..
(A) 31
(B) 29
(C) 16
(D) 64
Solution:
1, 1, 2, 8, 3, 27, 4, ——
1, 13, 2, 23, 3, 33, 4, 43
1, 1, 2, 8, 3, 27, 4, 64
Answer: (D) 64
13. Three angles of a triangle are x-30°, x – 45°, x + 15°, find the value of x.
(A) 60°
(B) 40°
(C) 80°
(D) 100°
Solution:
Three angles of a triangle are given.
Sum of All the angles of a triangle will be equal to 180°
Therefore, (x-30°) + (x – 45°) + (x + 15°) = 180°
x-30°+x-45°+x+15° = 180°
3x- 60° = 180°
3x = 180° + 60°
3x = 240°
x = 80°
To check the answer, substitute x=80° in the above equation,
(80° – 30°) + (80° – 45°) + (80° + 15°) = 180°
Answer: (C) 80°
14. The difference between simple interest and compound interest for a sum of Rs. 12,000 lent at 10 % per annum in 2 years, is
(A) RS. 80
(B) Rs. 90
(C) Rs. 120
(D) Rs. 100
Solution:
Principle (P) = 12000
Rate of interest (R) = 10%
Number of years (n) = 2
= (PR2)/1002
= [12000* (10*10)/(100*100)]
=120
Answer: (C) Rs. 120
15. The base of a triangle is four times its height and its area is 50m2. The length of the base is
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m
Solution:
b = 4h
½ bh= 50 m2
½ * 4 * h * h = 50
½ * 4 h2 = 50
2 * h2 = 50
h2 = 25
h = 5
b * h = 5 * 4
=20
Answer: (C) 20 m
16. A can do a piece of work in 20 days and B can do it in 25 days. Both of them finished the work and earned Rs. 3600. Then A’s Share is
(A) Rs. 1, 600
(B) Rs. 2,000
(C) Rs. 3,000
(D) Rs. 3,100
Solution:
A can do a work in 20 days
B can do it in 25 days
LCM of 20 and 25 is
5 | 20, 25
5 | 4, 5
2 | 4, 1
2 | 2, 1
| 1, 1
Therefore LCM of 20 and 25 is 5 x 5 x 2 x 2 = 100
Here 100 is the Total Work done.
For A
100 (Total Work)/20(days) = 5
i.e, A is doing 5 part work
For B
100 (Total Work)/25 (days) = 4
i.e, B is doing 4 part work
Per day, Out of 9 parts work, A is doing 5 parts and B is doing 4 parts
Therefore 5/9 is the total work done by A
5/9 x 3600(total share) = 5 x 400 = 2000
Answer: (B) Rs. 2,000
17. If (7/12)-4 * (7/12)3x = (7/12)5
(A) -1
(B) 1
(C) 2
(D) 3
Solution:
-4 + 3x = 5
3x = 9
X= 3
1. [-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)] is ________________
(A) 3/7
(B) 5/7
(C) 11/7
(D) 19/7
Solution:
[-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)]
= (-9/7) + (-26/7) + (46/7)
= -35/7+ 46/7
=11/7
Answer: (C) 11/7
2. The population of a city in the year 2014 is 1,80,000 and increases at a rate 20% per year.
(A) 2,40,000
(B) 2,59,200
(C) 2,55,000
(D) 2,54,300
Solution:
Principle (P) = 1,80,000
Rate of interest (R) = 20%
Number of years (n) = 2
= P [(1+R)/100]2
=180000 [(1+20)/100]2
=180000 [(120/100 )*(120/100)]
=18(120*120)
=259200
Answer: (B) 2,59,200
3. 3 — 25 here, which of the following number is suitable in —, so that the number will be a perfect square?
(A) 1
(B) 0
(C) 4
(D) 6
Solution:
Note: Question of the this types needs to be solved from the options. When a question directly indicates the options in the question itself, then it is solved by taking each and every options and substituting that option in the question until we can arrive at the solution.
A number among the options at the — will make 3—25 as a perfect square.
Hence, we have 3125, 3025, 3425, 3625 from the options. Among this, we have to find the perfect square.
Now,
√3125 = 55.90 –> Not a perfect Square
√3025 = 55 –> Perfect Square.
√3425 = 58.52 –> Not a perfect Square
√3625 = 60.20 –> Not a perfect Square
Answer: (B) 0
Also note that,
Step 1: option a) is taken and solved, no solution is arrived.
Step 2: option b) is taken and solved, Solution is arrived.
DO NOT STOP WITH THIS, Take all the other options c) & d) and solve it and confirm that, they were not the answers.
4. The average mark of 10 children is 80 then their total mark is
(A) 200
(B) 300
(C) 800
(D) 400
Solution:
Number of children= 10
Average mark of 10 children = 80
Total mark = number of children * Average
Answer: (C) 800
5. A man and woman are engaged in a work. A man can do a piece of work in 4 days and the woman can do in 12 days. Find how many days will they take to finish it together?
(A) 6 days
(B) 5 days
(C) 4 days
(D) 3 days
Solution:
A (Man) do work in = 4 days
B (Woman) do work in = 12
So lets take,
X= 4
Y= 12
Therefore,
xy/x+y
=(12*4)/16
=(3*4)/4
=3
Answer: (D) 3 days
6. Which of the following set of measurements will form a right angle triangle?
(A) 6, 9, 12
(B) 5, 8, 10
(C) 5, 5, 5√2
(D) 3, 4, 4√2
Solution:
Note: This question is also from Option to Question Approach.
For a Right Angled Triangle, consider the three sides, AB, BC & AC
Condition for a Right Angled Triangle is, AB2 + BC2 = AC2
Take option a) 62 + 92 = 117 is not equal to 122
b) 52 + 82 = 89 is not equal to 102
c) 52 + 52 = 50 is Equal to (5√2) 2
(5√2) 2 = 25×2 = 50
d) 3 + 4 = 25 is not equal to (4√2)
Answer: (C) 5, 5, 5√2
7. The value of
(A) 20
(B) 25
(C) 16
(D) 9
Solution:
First Solve the smaller roots within the larger roots so that we can obtain the solution.
√81 = 9
√7+9 = √16 = 4
√60+4 = √64 = 8
√ 248+8 = √256 = 16
√609+16 = √625 = 25
Answer: (B) 25
8. The price of a house is decreased from rupees fifteen lakhs to rupees twelve lakhs. The percentage of decrease is
(A) 10 %
(B) 20 %
(C) 30 %
(D) 40 %
Solution:
Initial price = 15,00,000
Final price = 12,00,000
100% = 150000
? %= 120000
=(100*12)/15
= (100*3)/4
=80%
So 80% is 120000 in 150000
Therefore sub 80 from 100 to get decreased percent
=100-80
=20%
Answer: (B) 20 %
9. If 3 (t – 3) = 5 (2t + 1) then t = ?
(A) -2
(B) 2
(C) -3
(D) 3
Solution:
3(t-3) = 5(2t + 1)
3t – 9 = 10t +5
3t-10t = 5+9
-7t = 14
t=14/7
t=-2
Answer: (A) -2
10. The value of (1.75 * 1.75 + 2 * 1.75 * 0.75 + 0.75 * 0.75) / (1.75 * 1.75 – 0.75 * 0.75)
(A) 3.5
(B) 6.25
(C) 1
(D) 2.5
Solution:
[(a2+2ab+b2)/ (a2+b2)] = a+b
Here,
a = 1.75
b = 0.75
a + b = 1.75+0.75
=2.5
Answer: (D) 2.5
11. The value of 163 + 73 – 233 is
(A) -7728
(B) 7028
(C) 7728
(D) -7718
Solution:
163 = 4096
73 = 343
233 = 12167
=-12167 + 4096 + 343
=-7728
Answer: (A) -7728
12. Find the next term of 4 in the series is 1, 1, 2, 8, 3, 27, 4, …..
(A) 31
(B) 29
(C) 16
(D) 64
Solution:
1, 1, 2, 8, 3, 27, 4, ——
1, 13, 2, 23, 3, 33, 4, 43
1, 1, 2, 8, 3, 27, 4, 64
Answer: (D) 64
13. Three angles of a triangle are x-30°, x – 45°, x + 15°, find the value of x.
(A) 60°
(B) 40°
(C) 80°
(D) 100°
Solution:
Three angles of a triangle are given.
Sum of All the angles of a triangle will be equal to 180°
Therefore, (x-30°) + (x – 45°) + (x + 15°) = 180°
x-30°+x-45°+x+15° = 180°
3x- 60° = 180°
3x = 180° + 60°
3x = 240°
x = 80°
To check the answer, substitute x=80° in the above equation,
(80° – 30°) + (80° – 45°) + (80° + 15°) = 180°
Answer: (C) 80°
14. The difference between simple interest and compound interest for a sum of Rs. 12,000 lent at 10 % per annum in 2 years, is
(A) RS. 80
(B) Rs. 90
(C) Rs. 120
(D) Rs. 100
Solution:
Principle (P) = 12000
Rate of interest (R) = 10%
Number of years (n) = 2
= (PR2)/1002
= [12000* (10*10)/(100*100)]
=120
Answer: (C) Rs. 120
15. The base of a triangle is four times its height and its area is 50m2. The length of the base is
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m
Solution:
b = 4h
½ bh= 50 m2
½ * 4 * h * h = 50
½ * 4 h2 = 50
2 * h2 = 50
h2 = 25
h = 5
b * h = 5 * 4
=20
Answer: (C) 20 m
16. A can do a piece of work in 20 days and B can do it in 25 days. Both of them finished the work and earned Rs. 3600. Then A’s Share is
(A) Rs. 1, 600
(B) Rs. 2,000
(C) Rs. 3,000
(D) Rs. 3,100
Solution:
A can do a work in 20 days
B can do it in 25 days
LCM of 20 and 25 is
5 | 20, 25
5 | 4, 5
2 | 4, 1
2 | 2, 1
| 1, 1
Therefore LCM of 20 and 25 is 5 x 5 x 2 x 2 = 100
Here 100 is the Total Work done.
For A
100 (Total Work)/20(days) = 5
i.e, A is doing 5 part work
For B
100 (Total Work)/25 (days) = 4
i.e, B is doing 4 part work
Per day, Out of 9 parts work, A is doing 5 parts and B is doing 4 parts
Therefore 5/9 is the total work done by A
5/9 x 3600(total share) = 5 x 400 = 2000
Answer: (B) Rs. 2,000
17. If (7/12)-4 * (7/12)3x = (7/12)5
(A) -1
(B) 1
(C) 2
(D) 3
Solution:
-4 + 3x = 5
3x = 9
X= 3
Answer: (D) 3
18. If 22 men can build a wall of 110 meters in 10 days. The length of a similar wall built by 30 men in 6 days is
(A) 100 mts
(B) 90 mts
(C) 80 mts
(D) 70 mts
Solution:
m1 = 22
w1 = 110
t1 = 10
m2 = 30
w2 = ?
t2 = 6
w2 = m2 w1 t2 / m1 t1
w2 = (6 * 30 * 110)/(22 * 10)
w2 = 90 mts
Answer: (B) 90 mts
19. If the ratio of length and breadth of a rectangle is 4 : 7. Find the length while its breadth is 77 cm.
(A) 22 cm
(B) 33 cm
(C) 44 cm
(D) 55 cm
Solution:
7x = 77
X= 77
4x = L
4*11= L
L= 44cm
Answer: (C) 44 cm
20. A room is 5 m 40 cm long and 4 m 50 cm broad. Its Area is
(A) 23.4 m2
(B) 24.3 m2
(C) 25 m2
(D) 98.01 m2
Solution:
= l * b
= 25 m2
Answer: (B) 24.3 m2
21. Simplify
5 ¼ + 4 ¾ + 7 5/8 + 6 7/8 ÷ 11 ¾
(A) 98/47
(B) 108/49
(C) 98/45
(D) 96/47
Solution:
22 + (20/8) = 22 + 2(1/2)
= 24(1/2) * 4/47
=98/47
Answer: (A) 98/47
22. Find the rate of interest at which, a sum of money becomes 9/4 times in 2 years.
(A) 69 ½ %
(B) 67 ½ %
(C) 62 ½ %
(D) 61 ½ %
Solution:
n = 9/4
T = 2
= (n-1)/T *100
= (5/4)/2 *100
=5/(4*2)*100
=62 ½ %
Answer: (C) 62 ½ %
23. The breadth, height and volume of a cuboid are 10 cm, 11 cm and 3080 cm3 respectively. Find the length of the cuboid.
(A) 21 cm
(B) 28 cm
(C) 24 cm
(D) 30 cm
Solution:
Volume of a Cuboids is Length X Breath X Height
Therefore, 10 x 11 x length = 3080
110 x length = 3080
Length = 3080/110 = 28
Answer: (B) 28 cm
24. A man bought an old bicycle for Rs. 1, 500. He spends Rs. 500 on its repair and sells it for Rs. 1,800. Find the percentage of his loss.
(A) 10%
(B) 15%
(C) 20%
(D) 5%
Solution:
cp = 1500 + 500
= 2000
sp = 1800
%loss = (2000 – 1800)/2000
=(200/2000) * 100
=10%
Answer: (A) 10%
25. Find the LCM of a3b4, ab5 and a2b7
(A) a7 b3
(B) a3b7
(C) a2b5
(D) ab5
Solution:
Find the LCM of a and b
LCM of a3, a, a2
a | a3, a1, a2
a | a2, 1, a1
a | a1, 1, 1
| 1, 1, 1
LCM of a3, a, a2 = a3
LCM of b4, b5, b7
b | b4, b5, b7
b | b3, b4, b6
b | b2, b3, b5
b | b`, b2, b4
b | 1, b1, b3
b | 1, 1, b2
b | 1, 1, b1
| 1, 1, 1
LCM of b4, b5, b7 = b7
Answer: (B) a3b7
18. If 22 men can build a wall of 110 meters in 10 days. The length of a similar wall built by 30 men in 6 days is
(A) 100 mts
(B) 90 mts
(C) 80 mts
(D) 70 mts
Solution:
m1 = 22
w1 = 110
t1 = 10
m2 = 30
w2 = ?
t2 = 6
w2 = m2 w1 t2 / m1 t1
w2 = (6 * 30 * 110)/(22 * 10)
w2 = 90 mts
Answer: (B) 90 mts
19. If the ratio of length and breadth of a rectangle is 4 : 7. Find the length while its breadth is 77 cm.
(A) 22 cm
(B) 33 cm
(C) 44 cm
(D) 55 cm
Solution:
7x = 77
X= 77
4x = L
4*11= L
L= 44cm
Answer: (C) 44 cm
20. A room is 5 m 40 cm long and 4 m 50 cm broad. Its Area is
(A) 23.4 m2
(B) 24.3 m2
(C) 25 m2
(D) 98.01 m2
Solution:
= l * b
= 25 m2
Answer: (B) 24.3 m2
21. Simplify
5 ¼ + 4 ¾ + 7 5/8 + 6 7/8 ÷ 11 ¾
(A) 98/47
(B) 108/49
(C) 98/45
(D) 96/47
Solution:
22 + (20/8) = 22 + 2(1/2)
= 24(1/2) * 4/47
=98/47
Answer: (A) 98/47
22. Find the rate of interest at which, a sum of money becomes 9/4 times in 2 years.
(A) 69 ½ %
(B) 67 ½ %
(C) 62 ½ %
(D) 61 ½ %
Solution:
n = 9/4
T = 2
= (n-1)/T *100
= (5/4)/2 *100
=5/(4*2)*100
=62 ½ %
Answer: (C) 62 ½ %
23. The breadth, height and volume of a cuboid are 10 cm, 11 cm and 3080 cm3 respectively. Find the length of the cuboid.
(A) 21 cm
(B) 28 cm
(C) 24 cm
(D) 30 cm
Solution:
Volume of a Cuboids is Length X Breath X Height
Therefore, 10 x 11 x length = 3080
110 x length = 3080
Length = 3080/110 = 28
Answer: (B) 28 cm
24. A man bought an old bicycle for Rs. 1, 500. He spends Rs. 500 on its repair and sells it for Rs. 1,800. Find the percentage of his loss.
(A) 10%
(B) 15%
(C) 20%
(D) 5%
Solution:
cp = 1500 + 500
= 2000
sp = 1800
%loss = (2000 – 1800)/2000
=(200/2000) * 100
=10%
Answer: (A) 10%
25. Find the LCM of a3b4, ab5 and a2b7
(A) a7 b3
(B) a3b7
(C) a2b5
(D) ab5
Solution:
Find the LCM of a and b
LCM of a3, a, a2
a | a3, a1, a2
a | a2, 1, a1
a | a1, 1, 1
| 1, 1, 1
LCM of a3, a, a2 = a3
LCM of b4, b5, b7
b | b4, b5, b7
b | b3, b4, b6
b | b2, b3, b5
b | b`, b2, b4
b | 1, b1, b3
b | 1, 1, b2
b | 1, 1, b1
| 1, 1, 1
LCM of b4, b5, b7 = b7
Answer: (B) a3b7
(A) 3/7
(B) 5/7
(C) 11/7
(D) 19/7
Solution:
[-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)]
= (-9/7) + (-26/7) + (46/7)
= -35/7+ 46/7
=11/7
Answer: (C) 11/7
2. The population of a city in the year 2014 is 1,80,000 and increases at a rate 20% per year.
(A) 2,40,000
(B) 2,59,200
(C) 2,55,000
(D) 2,54,300
Solution:
Principle (P) = 1,80,000
Rate of interest (R) = 20%
Number of years (n) = 2
= P [(1+R)/100]2
=180000 [(1+20)/100]2
=180000 [(120/100 )*(120/100)]
=18(120*120)
=259200
Answer: (B) 2,59,200
3. 3 — 25 here, which of the following number is suitable in —, so that the number will be a perfect square?
(A) 1
(B) 0
(C) 4
(D) 6
Solution:
Note: Question of the this types needs to be solved from the options. When a question directly indicates the options in the question itself, then it is solved by taking each and every options and substituting that option in the question until we can arrive at the solution.
A number among the options at the — will make 3—25 as a perfect square.
Hence, we have 3125, 3025, 3425, 3625 from the options. Among this, we have to find the perfect square.
Now,
√3125 = 55.90 –> Not a perfect Square
√3025 = 55 –> Perfect Square.
√3425 = 58.52 –> Not a perfect Square
√3625 = 60.20 –> Not a perfect Square
Answer: (B) 0
Also note that,
Step 1: option a) is taken and solved, no solution is arrived.
Step 2: option b) is taken and solved, Solution is arrived.
DO NOT STOP WITH THIS, Take all the other options c) & d) and solve it and confirm that, they were not the answers.
4. The average mark of 10 children is 80 then their total mark is
(A) 200
(B) 300
(C) 800
(D) 400
Solution:
Number of children= 10
Average mark of 10 children = 80
Total mark = number of children * Average
Answer: (C) 800
5. A man and woman are engaged in a work. A man can do a piece of work in 4 days and the woman can do in 12 days. Find how many days will they take to finish it together?
(A) 6 days
(B) 5 days
(C) 4 days
(D) 3 days
Solution:
A (Man) do work in = 4 days
B (Woman) do work in = 12
So lets take,
X= 4
Y= 12
Therefore,
xy/x+y
=(12*4)/16
=(3*4)/4
=3
Answer: (D) 3 days
6. Which of the following set of measurements will form a right angle triangle?
(A) 6, 9, 12
(B) 5, 8, 10
(C) 5, 5, 5√2
(D) 3, 4, 4√2
Solution:
Note: This question is also from Option to Question Approach.
For a Right Angled Triangle, consider the three sides, AB, BC & AC
Condition for a Right Angled Triangle is, AB2 + BC2 = AC2
Take option a) 62 + 92 = 117 is not equal to 122
b) 52 + 82 = 89 is not equal to 102
c) 52 + 52 = 50 is Equal to (5√2) 2
(5√2) 2 = 25×2 = 50
d) 3 + 4 = 25 is not equal to (4√2)
Answer: (C) 5, 5, 5√2
7. The value of
(A) 20
(B) 25
(C) 16
(D) 9
Solution:
First Solve the smaller roots within the larger roots so that we can obtain the solution.
√81 = 9
√7+9 = √16 = 4
√60+4 = √64 = 8
√ 248+8 = √256 = 16
√609+16 = √625 = 25
Answer: (B) 25
8. The price of a house is decreased from rupees fifteen lakhs to rupees twelve lakhs. The percentage of decrease is
(A) 10 %
(B) 20 %
(C) 30 %
(D) 40 %
Solution:
Initial price = 15,00,000
Final price = 12,00,000
100% = 150000
? %= 120000
=(100*12)/15
= (100*3)/4
=80%
So 80% is 120000 in 150000
Therefore sub 80 from 100 to get decreased percent
=100-80
=20%
Answer: (B) 20 %
9. If 3 (t – 3) = 5 (2t + 1) then t = ?
(A) -2
(B) 2
(C) -3
(D) 3
Solution:
3(t-3) = 5(2t + 1)
3t – 9 = 10t +5
3t-10t = 5+9
-7t = 14
t=14/7
t=-2
Answer: (A) -2
10. The value of (1.75 * 1.75 + 2 * 1.75 * 0.75 + 0.75 * 0.75) / (1.75 * 1.75 – 0.75 * 0.75)
(A) 3.5
(B) 6.25
(C) 1
(D) 2.5
Solution:
[(a2+2ab+b2)/ (a2+b2)] = a+b
Here,
a = 1.75
b = 0.75
a + b = 1.75+0.75
=2.5
Answer: (D) 2.5
11. The value of 163 + 73 – 233 is
(A) -7728
(B) 7028
(C) 7728
(D) -7718
Solution:
163 = 4096
73 = 343
233 = 12167
=-12167 + 4096 + 343
=-7728
Answer: (A) -7728
12. Find the next term of 4 in the series is 1, 1, 2, 8, 3, 27, 4, …..
(A) 31
(B) 29
(C) 16
(D) 64
Solution:
1, 1, 2, 8, 3, 27, 4, ——
1, 13, 2, 23, 3, 33, 4, 43
1, 1, 2, 8, 3, 27, 4, 64
Answer: (D) 64
13. Three angles of a triangle are x-30°, x – 45°, x + 15°, find the value of x.
(A) 60°
(B) 40°
(C) 80°
(D) 100°
Solution:
Three angles of a triangle are given.
Sum of All the angles of a triangle will be equal to 180°
Therefore, (x-30°) + (x – 45°) + (x + 15°) = 180°
x-30°+x-45°+x+15° = 180°
3x- 60° = 180°
3x = 180° + 60°
3x = 240°
x = 80°
To check the answer, substitute x=80° in the above equation,
(80° – 30°) + (80° – 45°) + (80° + 15°) = 180°
Answer: (C) 80°
14. The difference between simple interest and compound interest for a sum of Rs. 12,000 lent at 10 % per annum in 2 years, is
(A) RS. 80
(B) Rs. 90
(C) Rs. 120
(D) Rs. 100
Solution:
Principle (P) = 12000
Rate of interest (R) = 10%
Number of years (n) = 2
= (PR2)/1002
= [12000* (10*10)/(100*100)]
=120
Answer: (C) Rs. 120
15. The base of a triangle is four times its height and its area is 50m2. The length of the base is
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m
Solution:
b = 4h
½ bh= 50 m2
½ * 4 * h * h = 50
½ * 4 h2 = 50
2 * h2 = 50
h2 = 25
h = 5
b * h = 5 * 4
=20
Answer: (C) 20 m
16. A can do a piece of work in 20 days and B can do it in 25 days. Both of them finished the work and earned Rs. 3600. Then A’s Share is
(A) Rs. 1, 600
(B) Rs. 2,000
(C) Rs. 3,000
(D) Rs. 3,100
Solution:
A can do a work in 20 days
B can do it in 25 days
LCM of 20 and 25 is
5 | 20, 25
5 | 4, 5
2 | 4, 1
2 | 2, 1
| 1, 1
Therefore LCM of 20 and 25 is 5 x 5 x 2 x 2 = 100
Here 100 is the Total Work done.
For A
100 (Total Work)/20(days) = 5
i.e, A is doing 5 part work
For B
100 (Total Work)/25 (days) = 4
i.e, B is doing 4 part work
Per day, Out of 9 parts work, A is doing 5 parts and B is doing 4 parts
Therefore 5/9 is the total work done by A
5/9 x 3600(total share) = 5 x 400 = 2000
Answer: (B) Rs. 2,000
17. If (7/12)-4 * (7/12)3x = (7/12)5
(A) -1
(B) 1
(C) 2
(D) 3
Solution:
-4 + 3x = 5
3x = 9
X= 3
1. [-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)] is ________________
(A) 3/7
(B) 5/7
(C) 11/7
(D) 19/7
Solution:
[-1(2 / 7)] + [-3(5 / 7)] + [6(4 / 7)]
= (-9/7) + (-26/7) + (46/7)
= -35/7+ 46/7
=11/7
Answer: (C) 11/7
2. The population of a city in the year 2014 is 1,80,000 and increases at a rate 20% per year.
(A) 2,40,000
(B) 2,59,200
(C) 2,55,000
(D) 2,54,300
Solution:
Principle (P) = 1,80,000
Rate of interest (R) = 20%
Number of years (n) = 2
= P [(1+R)/100]2
=180000 [(1+20)/100]2
=180000 [(120/100 )*(120/100)]
=18(120*120)
=259200
Answer: (B) 2,59,200
3. 3 — 25 here, which of the following number is suitable in —, so that the number will be a perfect square?
(A) 1
(B) 0
(C) 4
(D) 6
Solution:
Note: Question of the this types needs to be solved from the options. When a question directly indicates the options in the question itself, then it is solved by taking each and every options and substituting that option in the question until we can arrive at the solution.
A number among the options at the — will make 3—25 as a perfect square.
Hence, we have 3125, 3025, 3425, 3625 from the options. Among this, we have to find the perfect square.
Now,
√3125 = 55.90 –> Not a perfect Square
√3025 = 55 –> Perfect Square.
√3425 = 58.52 –> Not a perfect Square
√3625 = 60.20 –> Not a perfect Square
Answer: (B) 0
Also note that,
Step 1: option a) is taken and solved, no solution is arrived.
Step 2: option b) is taken and solved, Solution is arrived.
DO NOT STOP WITH THIS, Take all the other options c) & d) and solve it and confirm that, they were not the answers.
4. The average mark of 10 children is 80 then their total mark is
(A) 200
(B) 300
(C) 800
(D) 400
Solution:
Number of children= 10
Average mark of 10 children = 80
Total mark = number of children * Average
Answer: (C) 800
5. A man and woman are engaged in a work. A man can do a piece of work in 4 days and the woman can do in 12 days. Find how many days will they take to finish it together?
(A) 6 days
(B) 5 days
(C) 4 days
(D) 3 days
Solution:
A (Man) do work in = 4 days
B (Woman) do work in = 12
So lets take,
X= 4
Y= 12
Therefore,
xy/x+y
=(12*4)/16
=(3*4)/4
=3
Answer: (D) 3 days
6. Which of the following set of measurements will form a right angle triangle?
(A) 6, 9, 12
(B) 5, 8, 10
(C) 5, 5, 5√2
(D) 3, 4, 4√2
Solution:
Note: This question is also from Option to Question Approach.
For a Right Angled Triangle, consider the three sides, AB, BC & AC
Condition for a Right Angled Triangle is, AB2 + BC2 = AC2
Take option a) 62 + 92 = 117 is not equal to 122
b) 52 + 82 = 89 is not equal to 102
c) 52 + 52 = 50 is Equal to (5√2) 2
(5√2) 2 = 25×2 = 50
d) 3 + 4 = 25 is not equal to (4√2)
Answer: (C) 5, 5, 5√2
7. The value of
(A) 20
(B) 25
(C) 16
(D) 9
Solution:
First Solve the smaller roots within the larger roots so that we can obtain the solution.
√81 = 9
√7+9 = √16 = 4
√60+4 = √64 = 8
√ 248+8 = √256 = 16
√609+16 = √625 = 25
Answer: (B) 25
8. The price of a house is decreased from rupees fifteen lakhs to rupees twelve lakhs. The percentage of decrease is
(A) 10 %
(B) 20 %
(C) 30 %
(D) 40 %
Solution:
Initial price = 15,00,000
Final price = 12,00,000
100% = 150000
? %= 120000
=(100*12)/15
= (100*3)/4
=80%
So 80% is 120000 in 150000
Therefore sub 80 from 100 to get decreased percent
=100-80
=20%
Answer: (B) 20 %
9. If 3 (t – 3) = 5 (2t + 1) then t = ?
(A) -2
(B) 2
(C) -3
(D) 3
Solution:
3(t-3) = 5(2t + 1)
3t – 9 = 10t +5
3t-10t = 5+9
-7t = 14
t=14/7
t=-2
Answer: (A) -2
10. The value of (1.75 * 1.75 + 2 * 1.75 * 0.75 + 0.75 * 0.75) / (1.75 * 1.75 – 0.75 * 0.75)
(A) 3.5
(B) 6.25
(C) 1
(D) 2.5
Solution:
[(a2+2ab+b2)/ (a2+b2)] = a+b
Here,
a = 1.75
b = 0.75
a + b = 1.75+0.75
=2.5
Answer: (D) 2.5
11. The value of 163 + 73 – 233 is
(A) -7728
(B) 7028
(C) 7728
(D) -7718
Solution:
163 = 4096
73 = 343
233 = 12167
=-12167 + 4096 + 343
=-7728
Answer: (A) -7728
12. Find the next term of 4 in the series is 1, 1, 2, 8, 3, 27, 4, …..
(A) 31
(B) 29
(C) 16
(D) 64
Solution:
1, 1, 2, 8, 3, 27, 4, ——
1, 13, 2, 23, 3, 33, 4, 43
1, 1, 2, 8, 3, 27, 4, 64
Answer: (D) 64
13. Three angles of a triangle are x-30°, x – 45°, x + 15°, find the value of x.
(A) 60°
(B) 40°
(C) 80°
(D) 100°
Solution:
Three angles of a triangle are given.
Sum of All the angles of a triangle will be equal to 180°
Therefore, (x-30°) + (x – 45°) + (x + 15°) = 180°
x-30°+x-45°+x+15° = 180°
3x- 60° = 180°
3x = 180° + 60°
3x = 240°
x = 80°
To check the answer, substitute x=80° in the above equation,
(80° – 30°) + (80° – 45°) + (80° + 15°) = 180°
Answer: (C) 80°
14. The difference between simple interest and compound interest for a sum of Rs. 12,000 lent at 10 % per annum in 2 years, is
(A) RS. 80
(B) Rs. 90
(C) Rs. 120
(D) Rs. 100
Solution:
Principle (P) = 12000
Rate of interest (R) = 10%
Number of years (n) = 2
= (PR2)/1002
= [12000* (10*10)/(100*100)]
=120
Answer: (C) Rs. 120
15. The base of a triangle is four times its height and its area is 50m2. The length of the base is
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m
Solution:
b = 4h
½ bh= 50 m2
½ * 4 * h * h = 50
½ * 4 h2 = 50
2 * h2 = 50
h2 = 25
h = 5
b * h = 5 * 4
=20
Answer: (C) 20 m
16. A can do a piece of work in 20 days and B can do it in 25 days. Both of them finished the work and earned Rs. 3600. Then A’s Share is
(A) Rs. 1, 600
(B) Rs. 2,000
(C) Rs. 3,000
(D) Rs. 3,100
Solution:
A can do a work in 20 days
B can do it in 25 days
LCM of 20 and 25 is
5 | 20, 25
5 | 4, 5
2 | 4, 1
2 | 2, 1
| 1, 1
Therefore LCM of 20 and 25 is 5 x 5 x 2 x 2 = 100
Here 100 is the Total Work done.
For A
100 (Total Work)/20(days) = 5
i.e, A is doing 5 part work
For B
100 (Total Work)/25 (days) = 4
i.e, B is doing 4 part work
Per day, Out of 9 parts work, A is doing 5 parts and B is doing 4 parts
Therefore 5/9 is the total work done by A
5/9 x 3600(total share) = 5 x 400 = 2000
Answer: (B) Rs. 2,000
17. If (7/12)-4 * (7/12)3x = (7/12)5
(A) -1
(B) 1
(C) 2
(D) 3
Solution:
-4 + 3x = 5
3x = 9
X= 3
Answer: (D) 3
18. If 22 men can build a wall of 110 meters in 10 days. The length of a similar wall built by 30 men in 6 days is
(A) 100 mts
(B) 90 mts
(C) 80 mts
(D) 70 mts
Solution:
m1 = 22
w1 = 110
t1 = 10
m2 = 30
w2 = ?
t2 = 6
w2 = m2 w1 t2 / m1 t1
w2 = (6 * 30 * 110)/(22 * 10)
w2 = 90 mts
Answer: (B) 90 mts
19. If the ratio of length and breadth of a rectangle is 4 : 7. Find the length while its breadth is 77 cm.
(A) 22 cm
(B) 33 cm
(C) 44 cm
(D) 55 cm
Solution:
7x = 77
X= 77
4x = L
4*11= L
L= 44cm
Answer: (C) 44 cm
20. A room is 5 m 40 cm long and 4 m 50 cm broad. Its Area is
(A) 23.4 m2
(B) 24.3 m2
(C) 25 m2
(D) 98.01 m2
Solution:
= l * b
= 25 m2
Answer: (B) 24.3 m2
21. Simplify
5 ¼ + 4 ¾ + 7 5/8 + 6 7/8 ÷ 11 ¾
(A) 98/47
(B) 108/49
(C) 98/45
(D) 96/47
Solution:
22 + (20/8) = 22 + 2(1/2)
= 24(1/2) * 4/47
=98/47
Answer: (A) 98/47
22. Find the rate of interest at which, a sum of money becomes 9/4 times in 2 years.
(A) 69 ½ %
(B) 67 ½ %
(C) 62 ½ %
(D) 61 ½ %
Solution:
n = 9/4
T = 2
= (n-1)/T *100
= (5/4)/2 *100
=5/(4*2)*100
=62 ½ %
Answer: (C) 62 ½ %
23. The breadth, height and volume of a cuboid are 10 cm, 11 cm and 3080 cm3 respectively. Find the length of the cuboid.
(A) 21 cm
(B) 28 cm
(C) 24 cm
(D) 30 cm
Solution:
Volume of a Cuboids is Length X Breath X Height
Therefore, 10 x 11 x length = 3080
110 x length = 3080
Length = 3080/110 = 28
Answer: (B) 28 cm
24. A man bought an old bicycle for Rs. 1, 500. He spends Rs. 500 on its repair and sells it for Rs. 1,800. Find the percentage of his loss.
(A) 10%
(B) 15%
(C) 20%
(D) 5%
Solution:
cp = 1500 + 500
= 2000
sp = 1800
%loss = (2000 – 1800)/2000
=(200/2000) * 100
=10%
Answer: (A) 10%
25. Find the LCM of a3b4, ab5 and a2b7
(A) a7 b3
(B) a3b7
(C) a2b5
(D) ab5
Solution:
Find the LCM of a and b
LCM of a3, a, a2
a | a3, a1, a2
a | a2, 1, a1
a | a1, 1, 1
| 1, 1, 1
LCM of a3, a, a2 = a3
LCM of b4, b5, b7
b | b4, b5, b7
b | b3, b4, b6
b | b2, b3, b5
b | b`, b2, b4
b | 1, b1, b3
b | 1, 1, b2
b | 1, 1, b1
| 1, 1, 1
LCM of b4, b5, b7 = b7
Answer: (B) a3b7
18. If 22 men can build a wall of 110 meters in 10 days. The length of a similar wall built by 30 men in 6 days is
(A) 100 mts
(B) 90 mts
(C) 80 mts
(D) 70 mts
Solution:
m1 = 22
w1 = 110
t1 = 10
m2 = 30
w2 = ?
t2 = 6
w2 = m2 w1 t2 / m1 t1
w2 = (6 * 30 * 110)/(22 * 10)
w2 = 90 mts
Answer: (B) 90 mts
19. If the ratio of length and breadth of a rectangle is 4 : 7. Find the length while its breadth is 77 cm.
(A) 22 cm
(B) 33 cm
(C) 44 cm
(D) 55 cm
Solution:
7x = 77
X= 77
4x = L
4*11= L
L= 44cm
Answer: (C) 44 cm
20. A room is 5 m 40 cm long and 4 m 50 cm broad. Its Area is
(A) 23.4 m2
(B) 24.3 m2
(C) 25 m2
(D) 98.01 m2
Solution:
= l * b
= 25 m2
Answer: (B) 24.3 m2
21. Simplify
5 ¼ + 4 ¾ + 7 5/8 + 6 7/8 ÷ 11 ¾
(A) 98/47
(B) 108/49
(C) 98/45
(D) 96/47
Solution:
22 + (20/8) = 22 + 2(1/2)
= 24(1/2) * 4/47
=98/47
Answer: (A) 98/47
22. Find the rate of interest at which, a sum of money becomes 9/4 times in 2 years.
(A) 69 ½ %
(B) 67 ½ %
(C) 62 ½ %
(D) 61 ½ %
Solution:
n = 9/4
T = 2
= (n-1)/T *100
= (5/4)/2 *100
=5/(4*2)*100
=62 ½ %
Answer: (C) 62 ½ %
23. The breadth, height and volume of a cuboid are 10 cm, 11 cm and 3080 cm3 respectively. Find the length of the cuboid.
(A) 21 cm
(B) 28 cm
(C) 24 cm
(D) 30 cm
Solution:
Volume of a Cuboids is Length X Breath X Height
Therefore, 10 x 11 x length = 3080
110 x length = 3080
Length = 3080/110 = 28
Answer: (B) 28 cm
24. A man bought an old bicycle for Rs. 1, 500. He spends Rs. 500 on its repair and sells it for Rs. 1,800. Find the percentage of his loss.
(A) 10%
(B) 15%
(C) 20%
(D) 5%
Solution:
cp = 1500 + 500
= 2000
sp = 1800
%loss = (2000 – 1800)/2000
=(200/2000) * 100
=10%
Answer: (A) 10%
25. Find the LCM of a3b4, ab5 and a2b7
(A) a7 b3
(B) a3b7
(C) a2b5
(D) ab5
Solution:
Find the LCM of a and b
LCM of a3, a, a2
a | a3, a1, a2
a | a2, 1, a1
a | a1, 1, 1
| 1, 1, 1
LCM of a3, a, a2 = a3
LCM of b4, b5, b7
b | b4, b5, b7
b | b3, b4, b6
b | b2, b3, b5
b | b`, b2, b4
b | 1, b1, b3
b | 1, 1, b2
b | 1, 1, b1
| 1, 1, 1
LCM of b4, b5, b7 = b7
Answer: (B) a3b7
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