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Logical Quantitative Aptitude

Scientific Reasoning

Useful for: UPSC Civil Services, OSSC RHT — Regular High School Teacher, CSIR NET, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Arts, OSEPA Upper Primary — Science, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts

and 2 more exams

OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM

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Overview

Basic numeracy covers Class X level arithmetic: numbers, percentages, ratios, averages, time–speed–work and simple counting.

Key points

Percentage change = change ÷ original × 100.
Ratio problems: convert to parts.
Average = total ÷ number.
Time–speed–distance: distance = speed × time.
Work: one-day work = 1/days; together, add rates.
Counting: use systematic listing for small cases.

Explanation

Divisibility and remainders appear often.
Use options to back-solve.
Approximate to save time when options are far apart.
Clock and calendar problems use fixed rules.
Keep units consistent.

Step by step

Identify the concept, rule or fact asked.
Recall the definition, formula, example or year.
Apply it and eliminate mismatched options.

Examples

Price rises from ₹80 to ₹100 → increase 25%.
A does a job in 10 days, B in 15 → together 6 days.
Average of 5 numbers is 20; one number 30 is removed → new average of 4 numbers = (100 − 30)/4 = 17.5.

Traps and advanced points

Trap: Using the new value as the base.
Trap: Adding days instead of rates.
Trap: Forgetting to update the count in averages.

Quick revision

Base = original.
Add rates.
Totals for averages.

Practice MCQs

From the perspective of definition and scope, which one of the following statements about Basic Numeracy is correct?
1. Basic Numeracy has no exceptions or limitations in exam analysis.
2. Ratios compare like quantities and should be simplified before calculation.
3. Successive percentage changes can always be added arithmetically.
4. Basic Numeracy is unrelated to institutions, processes or real-world applications.
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Answer: (b) Ratios compare like quantities and should be simplified before calculation.. Ratios compare like quantities and should be simplified before calculation.
Consider the following statements on Basic Numeracy and Decision Making, focusing on definition and scope: 1. Successive percentage changes can always be added arithmetically. 2. An administratively convenient option is automatically the most ethical and lawful option. Which of the statements given above is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
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Answer: (d) Neither 1 nor 2. Neither statement is correct; both are common misconceptions.
With reference to Basic Numeracy (definition and scope), consider the following statements: 1. Successive percentage changes can always be added arithmetically. 2. Percentage change uses the original value as the base. Which of the statements given above is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
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Answer: (b) 2 only. Only statement 2 is correct.
A value rises from 80 to 100. Percentage increase —
1. 25%
2. 80%
3. 100%
4. 20%
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Answer: (a) 25%. 20/80 × 100 = 25%.
Average of 12, 15, 18 is —
1. 45
2. 14
3. 15
4. 16
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Answer: (c) 15. 45/3 = 15.
Distance covered at 40 km/h in 2.5 hours —
1. 120 km
2. 65 km
3. 80 km
4. 100 km
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Answer: (d) 100 km. 40 × 2.5 = 100.
A does a job in 6 days, B in 12. Together —
1. 9 days
2. 18 days
3. 3 days
4. 4 days
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Answer: (d) 4 days. 1/6 + 1/12 = 1/4.
₹900 divided in ratio 2 : 1. The larger share —
1. ₹600
2. ₹700
3. ₹300
4. ₹450
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Answer: (a) ₹600. 900 × 2/3.
The remainder when 100 is divided by 7 is —
1. 4
2. 1
3. 2
4. 3
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Answer: (c) 2. 7 × 14 = 98; remainder 2.
How many 2-digit numbers are divisible by 5?
1. 19
2. 16
3. 18
4. 20
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Answer: (c) 18. 10, 15, …, 95 → 18.