Generate the skills needed to solve the following math problems.

Q: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options: A)209, B)210, C)211, D)213, E)215

Skills:
1. Combination Calculation
2. Inclusion-Exclusion
3. Logical Reasoning
4. Basic Arithmetic

Q: If a positive odd integer N has p positive factors, how many positive factors will 3N have ?
Options: A)p, B)2p, C)P+1, D)2p+1, E)Cannot be determined

Skills:
1. Prime Factorization
2. Factor Counting Formula
3. Multiplication Effect on Factors
4. Logical Reasoning
5. Basic Arithmetic

Q: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
Options: A)6 %, B)6.1 %, C)6.2 %, D)6.3 %, E)6.4 %

Skills:
1. Interest Calculation
2. Algebraic Equation Setup
3. Basic Arithmetic
4. Logical Reasoning

Q: q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10?
Options: A)10, B)6, C)4, D)0, E)It Cannot Be Determined

Skills:
1. Pattern Recognition
2. Modular Arithmetic
3. Exponentiation
4. Basic Arithmetic
5. Logical Reasoning

Q: If x-y=10, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
Options: A)I only, B)II only, C)III only, D)I and II, E)II and III

Skills:
1. Algebraic Manipulation
2. Logical Reasoning
3. Understanding Inequalities
4. Basic Arithmetic

Q: On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between
Options: A)10 and 20, B)20 and 30, C)30 and 40, D)40 and 50, E)50 and 60

Skills:
1. Percentage Calculation
2. Compound Growth/Decay
3. Algebraic Equation Setup
4. Logical Reasoning
5. Basic Arithmetic

Q: How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?
Options: A)10 litres, B)12 litres, C)15 litres of water, D)18 litres, E)21 litres

Skills:
1. Ratio and Proportion Calculation
2. Mixture and Alligation
3. Algebraic Equation Setup
4. Logical Reasoning
5. Basic Arithmetic

Q: Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
Options: A)81, B)59, C)166, D)285, E)334

Skills:
1. Pigeonhole Principle
2. Logical Reasoning
3. Counting Principles
4. Basic Arithmetic

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