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# Quant01. Ratio & Proportion, Indices, Logarithms

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Revision Notes for CPT
Chapter: Ratio & Proportion, Indices, Logarithms
Subject: Quantitative Aptitude

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### Quant01. Ratio & Proportion, Indices, Logarithms

1. 1. CPTSuccess<br />Revision Notes – Quantitative Aptitude<br />Chapter 1. Ratio & Proportion, Indices, Logarithms<br />
2. 2. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Ratio - A ratio is a comparison of the sizes of two or more quantities of the same kind by division.
3. 3. Notes:</li></ul>Both terms of a ratio can be multiplied or divided by the same (non-zero) number. A ratio is usually expressed in lowest terms (or simplest form)<br />The order of the terms in a ratio is important<br />Ratio exists only between quantities of the same kind<br />Quantities to be compared (by division) must be in the same units<br />To compare two ratios, convert them into equivalent like fractions<br />If a quantity increases or decreases in the ratio a:b then new quantity = (b of the original quantity)/a. The fraction by which the original quantity is multiplied to get a new quantity is called multiplying factor (or ratio)<br />©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
4. 4. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Inverse Ratio - One ratio is the inverse of another if their product is 1. Thus a : b is the inverse of b:a and vice versa.
5. 5. Notes:</li></ul>A ratio a : b is said to be of greater inequality if a > b and of less inequality if a < b<br />The ratio compound of two ratios a : b and c : d is ac : bd<br />a2 : b2 is the duplicate ratio of a : b (ratio compounded by itself), a3 : b3 is the triplicate ratio of a : b<br />The sub-duplicate ratio of a : b is a : b and the sub triplicate ratio of a : b is 3a : 3b<br />If the ratio of two similar quantities can be expressed as a ratio of two integers the quantities are said to be commensurable, otherwise they are said to be incommensurable<br />Continued ratio is the relation between the magnitudes of three or more quantities of the same kind. (a: b : c)<br />©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
6. 6. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Proportion - An equality of two ratios is called a proportion.
7. 7. Notes:</li></ul>Four quantities a, b, c, d are said to be in proportion if a : b = c : d => a / b = c / d => ad = bc<br />a, b, c, d are called the first, second, third and fourth terms of the proportion. The frist and fourth terms are called extremes (a, d) and second and third are called means (b, c)<br />Cross product rule: product of extremes = product of means = ad = bc<br />If three terms a, b, c are in continuous proportion, then the middle term b is the mean proportional between a and c.<br />Numbers in continued proportion: a / b = b / c = c / d = d / e….. where a, b, c, d, e … are in continued proportion<br />©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
8. 8. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Difference between Ratio and Proportion</li></ul>In a ratio a : b, both quantities must be of the same kind <br />In a proportion a : b = c : d all the four quantities need not be of the same kind. a, b should be of the same kind and c, d should be of the same kind<br />©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
9. 9. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Properties of Proportion</li></ul>For a : b = c : d, <br /><ul><li> ad = bc
10. 10. b : a = d : c (Invertendo)
11. 11. a : c = b : d (Alternendo)
12. 12. a + b : a = c + d : c (Componendo)
13. 13. a - b : b = c – d : d (Dividendo)
14. 14. a + b : a - b = c + d : c – d (Componendo and Dividendo)</li></ul>For a : b = c : d = e : f = ….., each of these ratios is equal to:<br /><ul><li> (a + c + e + …..) = (b + d + f + ….) (Addendo)
15. 15. (a - c - e - …..) = (b - d - f - ….) (Subtrahendo)</li></ul>©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
16. 16. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li> Indices</li></ul>Law 1: am x an = am+n, where m and n are positive integers<br />Law 2: am / an = am-n, where m and n are positive integers and m > n<br />Law 3: (am)n = am.n, where m and n are positive integers<br />Law 4: (ab)n = an. bn, where n can take any value<br />Law 5: a0 = 1<br />Law 6: na = a1/n<br />Law 7: if ax = ay, then x = y<br />Law 8: if xa = ya, then x = y<br />Law 9: if an = bn and a = b, then n = 0<br />©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
17. 17. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Logarithm - The logarithm of a number to a given base is the index or the power to which the base must be raised to produce the number, i.e. to make it equal to the given number.
18. 18. If ax = n, then x is said to be the logarithm of the number n to the base ‘a’, symbolically written as logan = x
19. 19. The two equations ax = n and logan = x are only transformations of each other </li></ul>©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
20. 20. Chapter 1. Ratio & Proportion, Indices, Logarithms<br /><ul><li>Laws of Logarithms
21. 21. logam.n= logam + logan
22. 22. loga(m/n) = logam - logan
23. 23. logamn= n logam
24. 24. loga1 = 0 (The logarithm of 1 to any base is 0. Since a0 = 1)
25. 25. logaa= 1 (The logarithm of any quantity to the same base is unity. Since a1 = a)
26. 26. logabx logba = 1
27. 27. logbax logcb = logca
28. 28. logbm= (Change of base)</li></ul>©<br />Revision Notes – Quantitative Aptitude<br />CPTSuccess<br />www.cptsuccess.com<br />
29. 29. CPTSuccess<br />