Simplification
1. Find the value of (25 × (10 + 5) – 15) ÷ 62

A. 20 B. 10 C. 60 D. 0 E. None of these

Answer: Option B
Explanation: Follow BODMAS rule to solve this question, as per the order is given below, Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, the BODMAS rule must be followed, Step-2- Any mathematical 'Of' or 'Exponent' must be solved next, Step-3-Next, the parts of the equation that contains 'Division' and 'Multiplication' are calculated, Step-4-Last but not least, the parts of the equation that contains 'Addition' and 'Subtraction' should be calculated. The given expression is, (25 × (10 + 5) – 15) ÷ 6[latex]^ {2}[/latex] = (25 × 15 – 15) ÷ 6[latex]^ {2}[/latex] = (375 - 15) ÷ 6[latex]^ {2}[/latex] = 360 ÷ 6[latex]^ {2}[/latex] = 360 ÷ 36 = 10
Simple Interest
1. A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?

A. Rs. 7000 B. Rs. 8500 C. Rs. 8000 D. Rs. 7500 E. None of these

Answer: Option A
Explanation: Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000.
Surds and Indices
1. Simplify : ([latex]y^ {4b-a }[/latex]. [latex]y^ {4c-b}[/latex] . [latex]y^ {4a-c}[/latex]) / [latex](y^ {a}. y^ {b}. y^ {c})^{3}[/latex]

A. 0 B. 1 C. y D. y[latex]^ {2}[/latex] E. None of these

Answer: Option B
Explanation: ([latex]y^ {4b-a }[/latex]. [latex]y^ {4c-b}[/latex] . [latex]y^ {4a-c}[/latex]) / [latex](y^ {a}. y^ {b}. y^ {c})^{3}[/latex] =([latex]y^ {4b-a }[/latex]. [latex]y^ {4c-b}[/latex] . [latex]y^ {4a-c}[/latex]) / [latex](y^ {a + b + c} )^{3}[/latex] =([latex]y^ {4b-a+4c-b+4a-c}[/latex] / [latex]y ^{3(a + b + c)}[/latex] =[latex]y ^{3(a + b + c)}[/latex] / [latex]y ^{3(a + b + c)}[/latex] = 1.
Mensuration
1. The actual height of a man is 6 feet but due to the position of Sun he casts a shadow of 4 feet. He is standing next to an electricity tower and notices that it casts a shadow of 36 feet. Find the height of the electricity tower.

A. 48 ft B. 54 ft C. 63 ft D. 72 ft

Answer: Option B
Explanation: Both the man and tower are near each other and are illuminated by the same sun from the same direction.
So the angle of elevation for the sun is the same for both. So the ratio of object to shadow will be same for all objects. (Proportionality Rule) [latex]\frac {Object height}{Shadow length}[/latex]=[latex]\frac {6}{4}[/latex]=[latex]\frac {H}{36}[/latex] ∴ H = 54 ft = Height of tower.
2. The perimeter of a semi circle is 144 cm then the radius is?

A. 25 cm B. 28 cm C. 30 cm D. 35 cm

Answer: Option B
Explanation: 36/7 r = 144 => r = 28
Ratio and Proportion
1. 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?

A. 28 days B. 30 days C. 32 days D. 35 days

Answer: Option C
Explanation: 1600 ---- 28 days 1600 ---- 24 1200----? 1600*24 = 1200*x x = 32 days
Compound Interest
1. Rohit says that, an amount became 4 times in 6 years. His friend wanted to know, how many years will it take for the amount to become 64 times, provided the rate of interest remains same?

A. 12 years B. 16 years C. 18 years D. 24 years

Answer: Option C
Explanation: Initial Amount = P. P becomes 4 times in 6 years ∴ P → 4P in 6 years ∴ 4P → 4 x (4P) = 16P in next 6 years. Continuing this, 16P → 4 x (16P) = 64P in next 6 years. So total time to get to 64 times i.e. 64P = 6+6+6 = 18 years.
Time and Work
1. A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.

A. 420 days B. 120 days C. 105 days D. 60 days

Answer: Option D
Explanation: A = 140 days B = 105 days 1/140 + 1/105 = 7/420 = 1/60 =>60 days
Allegation or Mixture
1. Three vessels contain a milk mixture 30 liter each. When put in a big vessel, they result in a mixture of milk and water in the ratio 2:1. If the ratio is to be reversed to make it 1: 2, how much more water should be added to the mix?

A. 20L B. 40L C. 90L D. 100L

Answer: Option C
Explanation: 3 vessels of 30 litres each = 3 X 30 = 90 ml milk mixture Amount of milk in mixture = [latex]\frac {2}{2+1}[/latex] x 90 = 60L Amount of water = 90-60 = 30L To make milk to water ratio 1:2, we simply need to make water double of milk. By direct observation, we can say that we should have 60L x 2 = 120L water to make the required ratio We already have 30L, we need (120-30) = 90L more water.
Probability
1. India is playing 3 sets of badminton matches against Japan at Singapore. The probability of India winning the three sets is 1/7, 1/5, 3/4. What is the probability of winning at least 1 set of the game?

A. [latex]\frac {7}{24}[/latex] B. [latex]\frac {23}{24}[/latex] C. [latex]\frac {23}{35}[/latex] D. [latex]\frac {29}{35}[/latex]

Answer: Option D
Number System
1. The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?

A. 34 B. 28 C. 12 D. 17

Answer: Option B
Explanation: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place. P + Q = 10 ----- (1) (10Q + P) - (10P + Q) = 54 9(Q - P) = 54 (Q - P) = 6 ----- (2) Solve (1) and (2) P = 2 and Q = 8 The required number is = 28
Permutation and Combination
1. A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?

A. 20 B. 40 C. 512 D. 1024

Answer: Option D
Explanation: Each question can be answered in 2 ways. 10 Questions can be answered = 2[latex]^ {10}[/latex]= 1024 ways.
Data Interpretation
Directions (1–5): Study the following graph carefully and answer the question given below.
Preference of People in using Different Modes of Transport over the Years

1. From 1999 to 2004, the total difference between the number of people who preferred to travel by rail and airlines in millions is:

A. 700 B. 650 C. 750 D. 600 E. 800

Answer: Option B
2. The average number of people preferring to travel by rail in 2000, 2002, 2004, was how many million fewer than the average number of people preferring to travel by bus in 1999, 2000, 2003?

A. 70 B. 85 C. 75 D. 90 E. None of these

Answer: Option E
3. In 2001, the people preferring to travel by bus is approximately what per cent of the people preferring to travel by buses, rail and airlines together in the year 1999 ?

A. 35.7 B. 36.7 C. 37 D. 36.5 E. 35.5

Answer: Option A
4. What is the respective ratio of the number of people preferring to travel by bus in year 2001 to the number of people preferring to travel by rail in the year 2002?

A. 15 : 11 B. 9 : 7 C. 7 : 9 D. 11 : 15 E. None of the above

Answer: Option A
5. In the year 2003, if all the airlines reduced their rates by 50% and 50% of the people who preferred to travel by rail, now preferred airlines, approximately how much percentage increase will be there in people prefer to travel by air?

A. 88.5 B. 82.7 C. 85.7 D. 85 E. 89.5

Answer: Option C
Profit & Loss
A person sold an article at 11.11% loss. If he would have bought it Rs.90 less and sold it Rs. 90 less, then loss would be 3.17% more. Then find the initial cost price of an article?

A. 445 B.450 C.405 D.504 E.None of these

Answer: Option C 11.11% = 1/9 11.11 + 3.17 = 14.28% 14.28% = -1/7 CP : SP 9 : 8 7 : 6 Difference is same 9 – 7 = 8 – 6 = 2 Here 2 = 90 9 = (90/2) * 9 = Rs. 405