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# General mental-ability-arithmetical-reasoning

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General mental-ability, arithmetical reasoning

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### General mental-ability-arithmetical-reasoning

1. 1. Click Here to Join Online Coaching Click Here www.upscportal.com General Mental Ability
2. 2. www.upscportal.com Click Here to Join Online Coaching Click Here First we should know some mathematical operations. They are add (+), subtraction (–), multiply (×) and division (÷), greater than (>), less than (<). This test is set up to test candidates skill in mathematical operations. The questions involving these operations are set using artificial symbols. You are required to substitute the real signs and solve the questions accordingly, to get the answer. Different Type of Questions There are three types of questions based on mathematical operations which are asked in various competitive examinations. They are, Problem-Solving by Substitution In such type of questions you have some substitutes for various mathematical symbols or numerals followed by a question involving calculation of an expression or choosing the correct/incorrect equation. Arithmetical Reasoning
3. 3. www.upscportal.com Click Here to Join Online Coaching Click Here Rule BODMAS Brackets Of Division Multiplication Addition Subtraction While solving a mathematical operations proceed according to the BODMAS formula. Example 1: If ‘+’ means ‘minus’ ‘×’ means ‘divided by’ ‘÷’ means ‘plus’ and ‘– ’means ‘multiplied by’ then which of the following will be the value of expression 7 × 3.5 ÷ 2 – 4 + 5 ? (a) 4 (b) 5 (c) 11 (d) None of these Solution. (b) Using the proper notations in the given expression, we have = 7 × 3.5 ÷ 2 – 4 + 5 = 7 + 3.5 + 2 ÷ 4 – 5 = 2 + 2 × 4 – 5 = 2 + 8 – 5 = 10 – 5 = 5
4. 4. www.upscportal.com Click Here to Join Online Coaching Click Here Example 2: If × means +, + means ÷, – means × and ÷ means –, then 6 × 4 – 5 + 2 ÷ 1 =? (a) 10 (b) 11 (c) 12 (d) 15 Solution. (d) Using the proper notations in the given expression, we have 6 × 4 – 5 + 2 ÷ 1 = 6 + 4 × 5 ÷ 2 – 1 = 6 + 4 × 2.5 – 1 = 6 + 10 – 1 = 16 – 1 = 15 Example 3: If P denotes ‘multiplied by’ T denotes ‘subtracted from, M denotes ‘added to’ and B denotes ‘divided by’, then 12 P 6 M 15 T 16 B 4 (a) 70 (b) 83 (c) 75 (d) 110 (e) None of these Solution. (b) 12 P 6 M 15 T 16 B 4 = 12 × 6 + 15 – 16 ÷ 4 = 12 × 6 + 15 – 4 = 72 + 15 – 4 = 87 – 4 = 83
5. 5. www.upscportal.com Click Here to Join Online Coaching Click Here Interchanging of Signs and Numbers This type of question certain signs or numbers interchanging with each other. The candidate is required to change the given signs or change the given numbers with each other and select which of the equation is correct of the given alternatives. Example 4: If signs + and –and numbers 4 and 8 interchanges with each other, which one of the following four equations would be correct? (a) 4 – 8 + 12 = 0 (b) 8 – 4 ÷ 12 = 8 (c) 4 ÷ 8 – 12 = 16 (d) 8 ÷ 4 – 12 = 24 Solution. (a) On interchanging signs + and – and numbers 4 and 8 in equation (a) 8 + 4 – 12 = 0 12 – 12 = 0 0 = 0
6. 6. www.upscportal.com Click Here to Join Online Coaching Click Here Example 5: Which one of the four interchanges in signs and number would make the given equation correct? 6 × 4 + 2 = 16 (a) + and ×, 2 and 4 (b) + and ×, 4 and 6 (c) + and ×, 2 and 6 (d) None of the above Solution. (b) On interchanging signs + and × and 4 and 6, 4 + 6 × 2 = 4 +12 = 16
7. 7. www.upscportal.com Click Here to Join Online Coaching Click Here Click Here to Join Online Coaching: http://upscportal.com/civilservices/courses Click Here to Buy Study Material in Hard Copy: http://upscportal.com/civilservices/study-kit