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1, , NUMBER SERIES, , CHAPTER, , Ex.2, , CONTENTS, , , , , , , , , , , , , Definition, , Sol., , Completing the series, , 13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6., , Arithmetic Series, ,  Next number = 73 – 7 = 343 – 7 = 336, Hence, the answer is (C)., , Series of Cubes, Squares, Mixed Series, , Ex.3, , Which is the number that comes next in the, following sequence ?, 4, 6, 12, 14, 28, 30,(...), (A) 32, (B) 60, (C) 62, (D) 64, , Sol., , The given sequence is a combination of two, series :, , Two-Tier Arithemetic series, Three-Tier Arithemetic series, Twin-Series, , I. 4, 12, 28 (...) and II. 6, 14, 30., Now, the pattern followed in each of the, above two series is : +8, +16, +32 ...., So, missing number = (28 + 32) = 60, Hence, the answer is (B)., , Two line number series, Wrong Number series, , Mental ability is the ability to distinguish, between right and wrong, to judge the minutest, difference and to adapt to the ever changing, environment, the wit to master the situation, the, capacity to learn and to put past experience to the, most advantageous use in future and the ability to, distinguish between important, less important and, more important., , Ex.4, , Sol., , Completing the Given Series, , Sol., , Which number would replace question mark, in the series 7, 12, 19, ?, 39., (A) 29, (B) 28, (C) 26, (D) 24, Clearly, the given sequence follows the, pattern:, +5, +7, +9 ... i.e., 7 + 5 = 12, 12 + 7 = 19, ...,  Missing number = 19 + 9 = 28, Hence, the answer is (B)., , Find out the missing number in the following, sequence : 1, 3, 3, 6, 7, 9, ?, 12, 21., (A) 10, (B) 11, (C) 12, (D) 13, Clearly, the given sequence is a combination, of two series :, , I. 1, 3, 7, ?, 21 and II. 3, 6, 9, 12, The pattern followed in I is + 2, + 4, ...; and, the pattern followed in II is +3. Thus, missing, number = 7 + 6 = 13., Hence, the answer is (D)., , ❖ EXAMPLES ❖, , Ex.1, , Which is the number that comes next in the, sequence : 0, 6, 24, 60, 120, 210 ?, (A) 240, (B) 290 (C) 336, (D) 504, Clearly, the given series is, , Ex.5, , Which fraction comes next in the sequence, 7, 1 3 5, , ,, ,, ,?, 2 4 8 16, (A), , 9, 32, , (B), , 10, 17, , (C), , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 1, , 1, , 11, 34, , (D), , 12, 35, 1

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Sol., , Clearly, the numerators of the fractions in the, given sequence form the series 1, 3, 5, 7, in, which each term is obtained by adding 2 to, the previous term. The denominators of the, fractions form the series 2, 4, 8, 16,, i.e. 21, 22, 23, 24., So, the numerator of the next fraction will be, (7 + 12) i.e., 9 and the denominator will be 25, i.e. 32., , , Sol., , The given series in an A.P. in which a = 201, and d = 7., Let the number of terms be n., Then, 369 = 201 + (n – 1) × 7 or n = 25., Hence, the answer is (C)., , Ex.8, , In the series 7, 14, 28, ..., what will be the, 10th term ?, (A) 1792 (B) 2456 (C) 3584 (D) 4096, Clearly, 7 × 2 = 14, 14 × 2 = 28, ... and so on., So, the given series is a G.P. in which, a = 7 and r = 2.,  10th term = ar(10–1) = ar9 = 7 × 29, = 7 × 512 = 3584, Hence, the answer is (C)., , Sol., , 9, The next term is, 32, , Hence, the answer is (A)., , Elementary Idea of Progressions, (I) Arithmetic Progression (A.P.), The progression of the form a, a + d, a + 2d,, a + 3d, ... is known as an A.P. with first term, = a and common difference = d., Ex. 3, 6, 9, 12, .... is an A.P. with a = 3 and, d = 6 – 3 = 3., In an A.P., we have nth term = a + (n – 1)d., , (II) Geometric Progression (G.P.), The progression of the form a, ar, ar2, ar3, ..., is known as a G.P. with first term = a and, common ratio = r., Ex. 1, 5, 25, 125, ... is a G.P. with a = 1 and, r=, , 5 25, =, = ... = 5., 1, 5, , Ex.9, Sol., , 1, 4, 9, 16, 25, (...), (A) 35, (B) 36, (C) 48, (D) 49, 2, 2, 2, 2, 2, The numbers are 1 , 2 , 3 , 4 , 5,  Missing number = 62 = 36, , Ex.10 20, 19, 17, (...), 10, 5, (A) 12, (B) 13, (C) 14, (D) 15, Sol., The pattern is –1, –2, ...,  Missing number = 17 – 3 = 14, Ex.11 2, 3, 5, 7, 11, (...), 17, (A) 12, (B) 13, (C) 14, (D) 15, Sol., Clearly, the given series consists of prime, numbers starting from 2. The prime number, after 11 is 13. So, 13 is the missing number., , In a G.P. we have nth term = arn–1., ❖ EXAMPLES ❖, , Ex.6, , In the series 357, 363, 369, ..., what will be, the 10th term ?, (A) 405, , Sol., , (B) 411, , (C) 413, , (D) 417, , The given series is an A.P. in which a = 357, and d = 6., , , 10th term = a + (10 – 1) d = a + 9d., , Ex.12 6, 11, 21, 36, 56, (...), (A) 42, (B) 51, (C) 81, (D) 91, Sol., The pattern is +5, +10, +15, + 20, ...,  Missing number = 56 + 25 = 81, Ex.13 1, 6, 13, 22, 33, (...), (A) 44, (B) 45, (C) 46, (D) 47, Sol., The pattern is + 5, + 7, + 9, + 11, ...,  Missing number = 33 + 13 = 46, , = (357 + 9 × 6) = (357 + 54), = 411, Hence, the answer is (B)., Ex.7, , How many terms are there in the series 201,, 208, 215, .... 369 ?, (A) 23, , (B) 24, , (C) 25, , Ex.14 3, 9, 27, 81, (...), (A) 324, (B) 243 (C) 210, (D) 162, Sol., Each term of the given series is obtained by, multiplying its preceding term by 3.,  Missing number = 81 × 3 = 243, , (D) 26, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 2, , 2, , 2

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➢ 31, 27, 23, 19, 15,.....etc., , Ex.15 1, 9, 17, 33, 49, 73, (...), (A) 97, (B) 98, (C) 99, (D) 100, Sol., The pattern is +8, +8, +16, +16, +24, ...,  Missing number = 73 + 24 = 97, , are arithmetic series because in each of them, the next number can be obtained by adding or, subtracting a fixed number. For example in 3,, 5, 7, 9, 11,..... every successive number is, obtained by adding 2 to the previous number., , Ex.16 2, 5, 9, (...), 20, 27, (A) 14, (B) 16, (C) 18, (D) 24, Sol., The pattern is +3, +4, ...,  Missing number = 9 + 5 = 14, , (ii) Geometric Series., ➢, ➢, , Ex.17 5, 9, 17, 29, 45, (...), (A) 60, (B) 65, (C) 68, (D) 70, Sol., The pattern is +4, +8, +12, +16, ...,  Missing number = 45 + 20 = 65, , ➢, ➢, , Ex.18 3, 7, 15, 31, 63, (...), (A) 92, (B) 115 (C) 127, (D) 131, Sol., Each number in the series is the preceding, number multiplied by 2 and then increased by, 1., Thus, (3 × 2) + 1 = 7, (7 × 2) + 1 = 15,, (15 × 2) + 1 = 31 and so on.,  Missing number = (63 × 2) + 1 = 127, , (iii) Series of squares, cubes :, These series can be formed by squaring or, cubing every successive number., For example,, ➢ 2, 4, 16, 256,....., ➢ 3, 9, 81, 6561,...., ➢ 2, 8, 512,.... etc., are such series. (In the first and second, every, number is squared to get the next number, while in the third it is cubed)., , Ex.19 1, 6, 15, (...), 45, 66, 91, (A) 25, (B) 26, (C) 27, (D) 28, Sol., The pattern is +5, +9, ..., +21, +25,  Missing number = 15 + 13 = 28, Ex.20 1, 2, 3, 5, 8, (...), (A) 9, (B) 11, (C) 13, (D) 15, Sol., Each term in the series is the sum of the, preceding two terms., Thus, 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8 and so, on.,  Missing number = 5 + 8 = 13, , (iv) Mixed Series :, By a mixed series, we mean a series which is, created according to any non-conventional, (but logical) rule. Because there is no, limitation to people's imagination, there are, infinite ways in which a series can be created, and naturally it is not possible to club, together all of them., , Series, Series is a sequence of numbers obtained by, some particular predefined rule and applying, that predefined rule it is possible to find out, the next term of the series., A series can be created in many ways. Some, of these are discussed below :, , For example,, 4, 8, 16, 32, 64,...., 15, –30, 60, –120, 240,...., 1024, 512, 256, 128, 64,...., 3125, –625, 125, –25, 5,....., are geometric series because, in each of them,, the next number can be obtained by, multiplying (or dividing) the previous number, by a fixed number. (For example, in : 3125–, 625, 125, –25, 5... every successive number is, obtained by dividing the previous number by, –5.), , Classification, (I) Two-tier Arithmetic Series :, In an arithmetic series the difference of any, two successive numbers is fixed. A Two-tier, Arithmetic Series shall be the one in which, the differences of successive numbers, themselves form an arithmetic series., , (i) Arithmetic Series., For example,, ➢ 3, 5, 7, 9, 11,......, ➢ 10, 8, 6, 4, 2,......, ➢ 13, 22, 31, 40, 49,....., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 3, , 3, , 3

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For example,, , (a) Arithmetico-geometric Series :, , (a) 1, 2, 5, 10, 17, 26, 37,....., , This series each successive term should be, found by first adding a fixed number to the, previous term and then multiplying it by, another fixed number., For example, 1, 6, 21, 66, 201,........., is an arithmetico-geometric series. (Each, successive term is obtained by first adding 1, to the previous term and then multiplying it, by 3)., , (b) 3, 5, 9, 15, 23, 33, .....etc., are examples of such series. In 1, 2, 5, 10, 17,, 26, 37, ......; for example, the differences of, successive numbers are 1, 3, 5, 7, 9, 11,, ....which is an arithmetic series., Note :, Two-tier arithmetic series can be denoted as a, quadratic function. For example, the above, series, (a) is 02 + 1, 12 + 1, 22 + 1, 32 + 1,.... which can, be denoted as f(x) = x2 + 1, where x = 0, 1,, 2,.... similarly example (b) can be denoted as, f(x) = x2 + x + 3, x = 0, 1, 2, 3,....., , Note :, The differences of successive numbers should, be in Geometric Progression., In this case, the successive differences are 5,, 15, 45, 135,.... which are in G.P., , (II) Three-tier Arithmetic Series :, (b) Geometrico-Arithmetic Series, This, as the name suggests, is a series in, which the differences of successive numbers, form a two-tier arithmetic series; whose, successive term's differences, in turn, form an, arithmetic series., For example, (a) 336, 210, 120, 60, 24, 6, 0,..., is an example of three-tier arithmetic series., [The differences of successive terms are 126,, 90, 60, 36, 18, 6,....., The differences of successive terms of this, new series are 36, 30, 24, 18, 12,....., which is an arithmetic series.], , A geometrico-arithmetic series should be the, one in which each successive term is found, by first multiplying (or dividing) the previous, term by a fixed number and then adding (or, deducting) another fixed number., For example, 3, 4, 7, 16, 43, 124,...., is a geometrico-arithmetic series. (Each, successive term is obtained by first, multiplying the previous number by 3 and, then subtracting 5 from it.), , Note :, The differences of successive numbers should, be in geometric progression. In this case, the, successive differences are 1, 3, 9, 27, 81,, ....which are in G.P., , Note :, Three-tier arithmetic series can be denoted as, a cubic function. For example, the above, series is (from right end) 13 –1, 23 –2, 33 –3,, 43 –4, .... which can also be denoted as f(x) =, x3 –x; x = 1, 2,...., , (IV) Twin Series :, We shall call these twin series, because they, are two series packed in one., 1, 3, 5, 1, 9, –3, 13, –11, 17,......., is an example of twin series. (The first, third,, fifth etc., terms are 1, 5, 9, 13, 17 which is an, arithmetic series. The second, fourth, sixth, etc. are 3, 1, –3, –11 which is a geometricoarithmetic series in which successive terms, are obtained by multiplying the previous term, by 2 and then subtracting 5.), , (III) Important Results, ➢ In an arithmetic series we add (or deduct) a, , fixed number to find the next number, and, ➢ In a geometric series we multiply (or divide) a, , fixed number to find the next number., We can combine these two ideas into one to, from, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 4, , 4, , 4

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(vi) 16, 17, 21, 30, 46, 71, (vii), 3, 3, 6, 18, 72, 360, (viii) 3, 4, 8, 17, 33, 58, (ix) 6, 16, 36, 76, 156, 316, (x) –2, 4, 22, 58, 118, 208, , (V) Other Series :, Besides, numerous other series are possible, and it is impossible to even think of all of, them., , SUMMARY OF THREE STEPS, , Solution, , [Very Important], , (i) Sharp increase and terms roughly doubling, every time. On checking with 2 as multiple, the series is:, next term = previous term × 2 –2. Next term =, 382., , Step I : Do a preliminary screening of the series., If it is a simple series you will be able to solve it, easily., Step II : If you fail in preliminary screening then, determine the trend of the series. Determine, whether it is increasing, decreasing or alternating., , (ii) Irregular. Very irregular. Likely to be,, therefore, mixed. On checking it is a mix of, two series:, 8, 9, 11, 14, (+1, +2, +3 etc.) and 8, 9, 10, 11., Next term = 14 + 4 + 18., , Step III (A) : Perform this step only if a series is, increasing or decreasing. Use the following rules :, (a) If the rise of a series is slow or gradual, the, series is likely to have an addition-based increase;, successive numbers are obtained by adding some, numbers., , (iii) Gradual slow decrease. Likely to be, arithmetical decrease. Check the differences, of successive terms. They are 66, 55, 44, 33,, 22. Hence, next decrease will be : 11., Next term = 105 – 11 = 94., , (b) If the rise of a series is very sharp initially but, slows down later on, the series is likely to be, formed by adding squared or cubed numbers., , (iv) Gradual slow decrease. Likely to be, arithmetical decrease. Check the differences., They are 11, 9, 7, 5, 3. Hence, next decrease, will be 1. Next term = 19 – 1 = 18., , (c) If the rise of a series is throughout equally, sharp, the series is likely to be multiplicationbased; successive terms are obtained by, multiplying by some terms (and, maybe, some, addition or subtraction could be there, too)., , (v) Sharp decrease and terms roughly being, halved every time. Checking with 2 as divisor, the series is :, , (d) If the rise of a series is irregular, there may be, two possibilities. Either there may be a mix of two, series or two different kinds of operations may be, going on alternately. (The first is more likely, when the increase is very irregular : the second is, more likely when there is a pattern, even in the, irregularity of the series)., , Next term (previous term – 8)  2., Next term = 5., (vi) preliminary screening tells us that each term, is obtained by adding 12, 22, 32, 42, 52......, respectively., Next term = 71 + 62 = 107, , Step (III) (B) : (to be performed when the series, is alternating), [Same as (iv) of step (iii), Check two possibilities], , (vii) Sharp increase. The series is : × 1, × 2, ×3,, ×4, ×5, ....Next term = 360 × 6 = 2160, (viii) Sharp increase that slows down later no., (Ratios of successive terms rise sharply from, 4  3 = 1.3 to 8  4 = 2 to 17  8 = 2. 125 and, then start falling to 33  17  1.9 and then to, 58  33  1.8). Hence likely to be addition of, squared or cubed numbers. On checking the, series is:, , Some Solved Examples, Ex., , Find the next number of the series, (i) 8, 14, 26, 50, 98, 194, (ii) 8, 8, 9, 9, 11, 10, 14, 11, (iii) 325, 259, 204, 160, 127, 105, (iv) 54, 43, 34, 27, 22, 19, (v) 824, 408, 200, 96, 44, 18, , + 12 +22, +32, +42, +52, .... Next term =, 58 + 62 = 94., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 5, , 5, , 5

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(ix) Sharp increase with terms roughly doubling, each time. Likely to have geometrical nature, with 2 as multiple. On checking the series is:, ×2 +4. Next term = 316 × 2 + 4 = 636, , Sol., , (x) Series increases sharply but then its speed of, rise slows down. Likely to be addition of, squared or cubed numbers. On checking, the, series is: 13 – 3, 23 – 4, 33 – 5, 43 – 6.... Next, term = 73 – 9 = 334., , Whenever you find that most of the fractions, have the same denominators, change all the, denominators to the same value. For example,, in this question, the series becomes :, 12 7 1, 8, 3, ,, , ,− ,−, 15 15 15 15 15, , Now, it is clear that numerators must decrease, successively by 5. Therefore,, , Wrong Number in Series, In examinations, a series is more likely to be, given the format of a complete series in, which an incorrect number is included & it is, required to find out the wrong number. On, studying a given series and applying the, concepts employed so far you should be able, to understand and thus "decode" the, formation of the series. Usually six terms are, given and it means that at least five correct, terms are given., , replaced by, 2., Sol., , 2, ., 15, , 4 23 18 12 8, 3, ,, ,, ,, ,, ,, 5 35 35 35 35 35, , By the above rule if we change all the, fractions with the same denominators, the, series is, , 28 23 18 12 8 3, ,, ,, ,, ,, , ., 35 35 35 35 35 35, , We see that numerators decrease by 5, thus, , Some Unique Series, , 12, 13, should be replaced by, ., 35, 35, , These series may be asked in examinations, so, you must be aware of them., , I. Series of Date or Time, 1., Which of the following doesn't fit into the, series?, 5–1–96, 27–1–96, 18–2–96, 12–3–96,, Sol., Each successive date differs by 22 days., Recall that 96 is a leap year, you will find that, 12–3–96 should be replaced by 11–3–96., 2., Which of the following doesn't fit into the, series?, 5.40, 8.00, 10.20, 12.30, 3.00, 5.20, Sol., Each successive time differs by 2 hrs. 20, minutes., So 12.30 should be replaced, by 12.40., Note : Keep in mind that the problem of series may, be based on dates or times. Sometimes it, doesn't strike our mind and the question is, solved wrongly., , Now, we conclude that the above fractions, decrease successively by, 3, Sol., , 1, 5, or ., 7, 35, , 118 100 82 66, 46 28, ,, ,, ,, ,, ,, 225 199 173 147 121 95, , We see that all the denominators differ, so we, can't use the above rule. In this case usually,, the numerators and denominators change in a, definite pattern. Here, numerators decrease, successively by 18 whereas denominators, decrease successively by 26. Thus, 66, 64, should be replaced by, ., 147, 147, , 4., Sol., , II. Fractional series, , 1., , 1, should be, 15, , Which of the following doesn't fit into the, series?, 4 7 1, 1, 8, ,, ,, , − ,−, 5 15 15, 5 15, , 12 15 18 21 24 27, ,, ,, ,, ,, ,, 89 86 82 80 77 74, , Numerators increase successively by 3, whereas denominators decrease successively, by 3. Thus, , 18, 18, should be replaced by, ., 83, 82, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 6, , 6, , 6

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III. Some numbers followed by their LCM or, HCF, 1., Sol., , 2., Sol., , 1, 2, 3, 6, 4, 5, 6, 60, 5, 6, 7,..... (Fill up the, blank), The series can be separated in three parts. 1,, 2, 3, 6/4, 5, 6, 60/5, 6, 7..... In each part fourth, number is LCM of first three, 8, 6, 24, 7, 3, 21, 5, 4, 20,.....,9, 18, (1) 1 (2) 3 (3) 4, (4) 5 (5) 6, 8, 6, 24/7, 3, 21/5, 4, 20/_, 9, 18, Third number in each part is LCM of first two, numbers. Thus, the answer should be 6., , 3., Sol., , 8, 4, 4, 7, 8, 1, 3, 9, 3, 2, 1,...., (1) 1 (2) 2 (3) 3, (4) 5, , VI. Odd number out, Sometimes a group of numbers is written out, of which one is different from others., 1., , 22, 44, 88, 132, 165, 191, 242. Find the, number which doesn't fit in the above series, (or group)., , Sol., , 191; Others are divisible by 11 or 191 is the, single prime number., , 2., , Which one of the following series doesn't fit, into the series ?, 29, 31, 37, 43, 47, 51, 53, , Sol., , Two-line Number Series, , (5) N.O.T, , 8, 4, 4/7, 8, 1/3, 9, 3/2, 1..., In each part, third number is HCF of first to, numbers. Thus our answer should be 1., , Now a days this type of number series is also, being asked in examinations., In this type of no. series one complete series, is given while the other is incomplete. Both, the series have the same definite rule., Applying the very definite rule of the, complete series, you have to determine the, required no. of the incomplete series. For, example:, , IV. Some numbers followed by their product, 1., , Sol., , 2, 3, 6, 18, 108, 1844, Which of the above numbers does not fit into, the series?, 1844 is wrong, because, 2 × 3 = 6, 3 × 6 = 18, 18 × 6 = 108,, but 108 × 18 = 1944., , Ex.21 4 14 36 114 460, 2 a b c d e, , V. By use of digit-sum, 1., , Sol., , 2., Sol., , 51; All other are prime numbers., , Find the value of e., Sol., , 14, 19, 29, 40, 44, 51, 59, 73, Which of the above numbers doesn't fit into, the series ?, Next number = Previous number + Digit-sum, of previous number Like,, 19 = 14 + (4 + 1), 29 = 19 + (1 + 9), 40 = 29 + (2 + 9), Thus, we see that 51 should be replaced by, 52., , The first series is ×1 + 10, ×2 +8, ×3 +6, ×4 +, 4,....., , , a = 2 × 1 + 10 = 12, b = 12 × 2 + 8 = 32,, c = 32 × 3 + 6 = 102, d = 102 × 4 + 4 = 412,, and finally e = 412 × 5 + 2 = 2062, , Ex.22 5 6 11 28 71 160, 2 3 a, , b, , c, , d, , e, , What is the value of e?, Sol., , Fill up the blanks, 14, 5, 18, 9, 22, 4, 26, 8, 30, 3, ....., ....., 1st, 3rd, 5th, 7th, ... numbers follow the, pattern of +4 (14 + 4 = 18, 18 + 4 = 22,...)., Where as 2nd, 4th, 6th are the digit-sums of, their respective previous number (5 = 1 + 4, 9, = 1 + 8),...) Thus, our answer is 34 and 7., , The differences of two successive terms of the, first series are 1, 5, 17, 43, 89, the sequence, of which is 03 + 12, 13 + 22, 23 + 32, 33 + 42,, 43 + 52.,  a = 3 + 5 = 8, b = 8 + 17 = 25, c = 25 + 43, = 68, d = 68 + 89 = 157, and finally, e = 157 + (53 + 62, = 125 + 36 =) 161 = 318, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 7, , 7, , 7

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Ex.23 1296 864 576 384 256, 1080 a, b, c, d, What should replace c ?, Sol., , e, , The first series is  3 × 2, , , a = 1080  3 × 2 = 720, b = 720  3 × 2=480,, and finally c = 480  3 × 2 = 320, , Ex.29 5 8 41 33 57 42 61, 3 4 a b c d e, Find the value of d., Sol., This is an alternate number series having two, series :, S1 = 5 41 57 61., The differences between two successive terms, are 36 (= 62), 16 (= 42), 4( = 22) and, S2 = 8 33 42, , Ex.24 7 13 78 83 415, 3 a b c d e, Find the value of b., Sol., The first series is +6, ×6, +5, ×5, , The differences between two successive terms, are 25 (= 52), 9 (= 32),  b = 4 + 25 = 29 and d = 29 + 9 = 38., ,  a = 3 + 6 = 9 and b = 9 × 6 = 54, Ex.25 3240 540 108 27 9, 3720 a, b c d, What is the value of d?, Sol., , e, , The first series is  6,  5,  4,  3,  a = 3720  6 = 620, b = 620  5 = 124, c =, 124  4 = 31, and finally d = 31  3 = 10.33, , Ex.26 27 44 71 108 155, 34 a b c d e, What is the should replace e?, Sol., The differences of two successive terms of, the series are 17, 27, 37, 47.,  a = 34 + 17 = 51, b = 51 + 27 = 78,, c = 78 + 37 = 115, d = 115 + 47 = 162, and, finally e = 162 + 57 = 219, Ex.27. 108 52 24 10 3, 64 a b c d e, What is the value of c ?, Sol., , The series is –4  2, , , a = (64 – 4)  2 = 30, b =(30 – 4)  2 = 13,, , c = (13 – 4)  2 = 4.5, Ex.28 –4 –2 –1 8 31, –1 a b c d e, Find the value of b., Sol., The series is repeated as ×2 + 6 and, × 3 + 7 alternately., , , a = –1 × 2 + 6 = 4 and b = 4 × 3 + 7 = 19, , Ex.30 Find the wrong number in the series :, 7, 28, 63, 124, 215, 342, 511, (A) 7, (B) 28, (C) 124, (D) 215, Sol., Clearly, the correct sequence is, 23 – 1, 33 – 1, 43 – 1, 53 – 1, 63 – 1, 73 – 1,, 83–1,  28 is wrong and should be replaced by, (33 – 1) i.e. 26., Hence, the answer is (B)., Ex.31 Find the wrong number in the series :, 3, 8, 15, 24, 34, 48, 63, (A) 15, (B) 24, (C) 34, (D) 48, Sol., The difference between consecutive terms of, the given series are respectively 5, 7, 9, 11, and 13., Clearly, 34 is a wrong number and must be, replaced by (24 + 11) i.e. 35., Hence, the answer is (C)., Ex.32 24, 27, 31, 33, 36, (A) 24, (B) 27, (C) 31, (D) 33, Sol., Each term in the series is increased by 3 to, obtain the next term., So, 31 is wrong and must be replaced by, (27 + 3) i.e. 30., Ex.33 196, 169, 144, 121, 80, (A) 80, (B) 121 (C) 169, (D) 196, 2, 2, Sol., The sequence is (14) , (13) , (12)2, (11)2,, (10)2., So, 80 is wrong and must be replaced by (10)2, i.e. 100., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 8, , 8, , 8

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Ex.34 3, 5, 7, 9, 11, 13, (A) 3, Sol., , (B) 5, , Ex.37 8, 14, 26, 48, 98, 194, 386, (C) 7, , (D) 9, , (A) 14, , The series consists of consecutive prime, numbers. So, 9 is wrong., , Sol., , Sol., , (B) 165, , (C) 186, , (C) 98, , (D) 194, , Each term in the series is less than twice the, preceding term by 2., So, 48 is wrong and should be replaced by, (26 × 2 – 2) i.e. 50., , Ex.35 121, 143, 165, 186, 209, (A) 143, , (B) 48, , (D) 209, , Each term of the series is increased by 22 to, obtain the next term., , Ex.38 8, 13, 21, 32, 47, 63, 83, , So, 186 is wrong and must be replaced by, (165 + 22) i.e. 187., , Sol., , (A) 13, , (B) 21, , (C) 32, , (D) 47, , The sequence is + 5, + 8, +11, ..., , , 47 is wrong and must be replaced by, (32 + 14) i.e. 46., , Ex.36 1, 2, 4, 8, 16, 32, 64, 96, (A) 4, Sol., , (B) 32, , (C) 64, , (D) 96, , Ex.39 3, 10, 27, 4, 16, 64, 5, 25, 125, , Each term of the series is obtained by, multiplying the preceding term by 2, , (A) 3, Sol., , So, 96 is wrong and must be replaced by, (64 × 2) i.e. 128., , (B) 4, , (C) 10, , The correct sequence is, 3, 32, 33, 4, 42, 43, 5, 52, 53., So, 10 is wrong and must be replaced by 32, i.e. 9., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 9, , (D) 27, , 9, , 9

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EXERCISE, Q.1, Q.2, Q.3, Q.4, Q.5, Q.6, Q.7, Q.8, Q.9, Q.10, Q.11, Q.12, Q.13, Q.14, Q.15, Q.16, Q.17, Q.18, Q.19, Q.20, Q.21, , 3, 15, 35, ...., 99, 143., (A) 63, (B) 69, 5, 11, 17, ...., 29, 41., (A) 19, (B) 21, , Q.22, (C) 77, , Q.23, (C) 23, , 7, 17, 31, 49 ...., 97, 127, (A) 59, (B) 61, (C) 71, 1, 3, 6, 10, 15 ...., 28, 36., (A) 20, (B) 21, (C) 23, 2, 5, 9, ....., 20, 27, (A) 14, (B) 15, , (D) 81, (D) 25, Q.24, (D) 87, Q.25, (D) 24, Q.26, , (C) 16, , (D) 17, , 0, 2, 8, 14, 24, 34, ...., 62., (A) 40, (B) 42, (C) 48, , (D) 52, , 4, 9, 20, 37, 60,...., (A) 88, (B) 89, , Q.27, Q.28, , (C) 90, , (D) 91, , 1, 3, 3, 6, 7, 9 ...., 12, 21, (A) 10, (B) 11, (C) 12, , (D) 13, , Q.29, Q.30, , 8, 10, 14, 18, ...., 34, 50, 66, (A) 28, (B) 27, (C) 26, , (D) 25, , 19, 2, 38, 3, 114, 4, ...., (A) 228, (B) 256, (C) 352, , (D) 456, , 4, 9, 17, 35, ...., 139., (A) 89, (B) 79, , Q.32, (C) 69, , 7, 15, 32, ...., 138, 281., (A) 57, (B) 67, (C) 77, 8, 12, 10, 16, 12, ...., (A) 20, (B) 18, 10, 2, 20, 3, 30, 4, ...., (A) 40, (B) 50, , (C) 16, , Q.33, (D) 87, (D) 14, Q.35, , (C) 60, , 3, 10, 18, 27, 37, 48, ....., (A) 60, (B) 70, (C) 80, 1, 3, 9, 27, 81, 243, ........, (A) 729, (B) 730, (C) 731, , 5, 2, 6, 2, 7, 2, ....., (A) 8, (B) 9, , (D) 59, , Q.34, , 24, 6, 48, 12, 96, 24 ....., (A) 191, (B) 192, (C) 193, , 10, 7, 6, 8, 5, 4, ...., (A) 4, (B) 5, , Q.31, , (D) 70, Q.36, (D) 194, , 4, 8, 16, 32, 64, 128 ....., (A) 256, (B) 257, (C) 258, 0.5, 1.5, 4.5, 13.5, (.....), (A) 45.5, (B) 39.5 (C) 30.5, , (D) 729, , 0, 2, 8, 14, (.....), 34, (A) 24, (B) 22, , (C) 20, , (D) 18, , 19, 2, 38, 3, 114, 4, (.....), (A) 228, (B) 256, (C) 352, , (D) 456, , 1, 2, 3, 6, 9, 18, (.....), 54, (A) 18, (B) 27, (C) 36, , (D) 81, , 4, 5, 9, 18, 34, (.....), (A) 43, (B) 49, , (C) 50, , (D) 59, , 3, 6, 18, 72, (.....), (A) 144, (B) 216, , (C) 288, , (D) 360, , 66, 36, 18, (.....), (A) 3, (B) 6, , (C) 8, , (D) 9, , 21, 25, 33, 49, 81, (.....), (A) 145, (B) 129, (C) 113, , (D) 97, , 12, 32, 72, 152, (.....), (A) 312, (B) 325, , (D) 613, , (C) 515, , 3, 6, 5, 20, 7, 42, 9, (.....), (A) 54, (B) 60, (C) 66, , (D) 72, , 1, 3, 4, 8, 15, 27, (.....), (A) 37, (B) 44, (C) 50, , (D) 55, , 2, 15, 41, 80, (.....), (A) 111, (B) 120, , (D) 132, , (C) 121, , 8, 10, 14, 18, (.....), 34, 50, 66, (A) 24, (B) 25, (C) 26, , (D) 27, , 1, 2, 6, 24, (.....), (A) 60, (B) 95, , (C) 120, , (D) 150, , 2, 3, 8, 63, (.....), (A) 1038 (B) 1998, , (C) 3008, , (D) 3968, , 95, 115.5, 138, (.....), 189, (A) 154.5 (B) 162.5 (C) 164.5 (D) 166.5, , Q.38, , 4, 10, (.....), 82, 244, 730, (A) 24, (B) 28, (C) 77, , (D) 218, , 4, 32, 128, (.....), (A) 128, (B) 144, , (C) 192, , (D) 256, , 2, 5, 9, 19, 37, (.....), (A) 76, (B) 75, , (C) 74, , (D) 72, , (D) 90, (D) 732, (D) 7, Q.40, , (C) 10, , (C) 529, , Q.37, , Q.39, (C) 6, , 121, 225, 361, (.....), (A) 441, (B) 484, , (D) 11, Q.41, (D) 259, Q.42, (D) 40.5, , 24, 60, 120, 210, (.....), (A) 300, (B) 336, (C) 420, , (D) 525, , 165, 195, 255, 285, 345, (.....), (A) 375, (B) 420, (C) 435, , (D) 390, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 10, , 10, , 10

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Q.43, Q.44, Q.45, Q.46, Q.47, Q.48, Q.49, Q.50, , 5, 17, 37, 65, (.....), 145, (A) 95, (B) 97, (C) 99, , (D) 101, , 9, 11, 20, 31, (.....), 82, (A) 41, (B) 51, (C) 60, , (D) 71, , 5, 16, 49, 104, (.....), (A) 115, (B) 148, , (C) 170, , (D) 181, , 34, 18, 10, 6, 4, (.....), (A) 0, (B) 1, , (C) 2, , (D) 3, , Q.67, , (D) 352, , Q.68, , 462, 420, 380, (.....), 306, (A) 322, (B) 332, (C) 342, 3, 8, 22, 63, 185, (.....), (A) 550, (B) 310, (C) 295, 1, 2, 5, 12, 27, 58, 121, (.....), (A) 246, (B) 247, (C) 248, 0.5, 0.55, 0.65, 0.8, (.....), (A) 0.9, (B) 0.82 (C) 1, , Q.64, Q.65, Q.66, , Q.69, , (D) 285, (D) 249, , Q.70, , (D) 0.95, , Directions :, In each of the following questions, one term in the, number series is wrong. Find out the wrong term., Q.51, Q.52, Q.53, Q.54, Q.55, Q.56, Q.57, Q.58, Q.59, Q.60, Q.61, Q.62, Q.63, , 380, 188, 92, 48, 20, 8, 2, (A) 188, (B) 92, (C) 48, , (D) 20, , 1, 3, 7, 15, 27, 63, 127, (A) 7, (B) 15, (C) 27, , (D) 63, , 5, 10, 17, 24, 37, (A) 10, (B) 17, , (D) 37, , Q.72, , Q.74, (C) 24, , (D) 256, , 15, 16, 22, 29, 45, 70, (A) 16, (B) 22, , (C) 45, , (D) 70, , 6, 14, 30, 64, 126, (A) 6, (B) 14, , (C) 64, , 10, 26, 74, 218, 654, 1946, 5834, (A) 26, (B) 74, (C) 218, 3, 7, 15, 39, 63, 127, 255, 511, (A) 15, (B) 39, (C) 63, , 1, 5, 5, 9, 7, 11, 11, 15, 12, 17, (A) 11, (B) 12, (C) 17, , (D) 15, , 11, 2, 21, 3, 32, 4, 41, 5, 51, 6, (A) 21, (B) 11, (C) 32, , (D) 51, , 11, 5, 20, 12, 40, 26, 74, 54, (A) 5, (B) 20, (C) 40, , (D) 26, , 56, 72, 90, 110, 132, 150, (A) 72, (B) 90, (C) 110, , (D) 150, , 8, 13, 21, 32, 47, 63, 83, (A) 13, (B) 32, (C) 47, , (D) 63, , 89, 78, 86, 80, 85, 82, 83, (A) 83, (B) 82, (C) 86, , (D) 78, , 25, 36, 49, 81, 121, 169, 225, (A) 36, (B) 49, (C) 169, , (D) 225, , 2, 5, 10, 17, 26, 37, 50, 64, (A) 17, (B) 26, (C) 37, , (D) 64, , 4, 7, 11, 18, 29, 47, ....., 123, 199, (A) 76, (B) 70, (C) 84, , (D) 102, , 2, 6, 12, 20, ........, 42, 56, 72, 90, (A) 20, (B) 21, (C) 30, , (D) 12, , Q.75, , 17, 7, 24, 19, 9, 28, ...., 8, 31, 27, 10, 37, (A) 20, (B) 21, (C) 18, (D) 23, , Q.76, , 6, 126,........, 9, 108, 12, 7, 133, 19, 12, 72, 6, (A) 21, (B) 23, (C) 30, (D) 35, , (D) 126, , Q.77, , 2, ...........8, 16, 32, 64, 128, 256, (A) 2, (B) 3, (C) 4, , (D) 5, , (D) 654, , Q.78, , 45, 54, 47,......, 49, 56, 51, 57, 53, (A) 48, (B) 55, (C) 50, , (D) 53, , 3, 128, 6, 64, 9, ....., 12, 16, 15, 8, (A) 32, (B) 12, (C) 108, , (D) 72, , 5, 7, 11, 19, 35, 67, ...., 259, (A) 64, (B) 131, (C) 135, , (D) 32, , 8, 4, 12, 6, 18,......27, (A) 9, (B) 12, , (D) 24, , (D) 127, , Q.79, , 445, 221, 109, 46, 25, 11, 4, (A) 25, (B) 46, (C) 109, , (D) 221, , 1236, 2346, 3456, 4566, 5686, (A) 1236 (B) 3456 (C) 4566, , (D) 5686, , 5, 10, 40, 80, 320, 550, 2560, (A) 80, (B) 320, (C) 550, , (D) 2560, , 3, 2, 8, 9, 13, 22, 18, 32, 23, 42, (A) 8, (B) 9, (C) 13, , (D) 22, , Q.80, Q.81, Q.82, Q.83, , (C) 1331, , (D) 132, , Find the missing number in the following series, Q.73, , 1, 3, 10, 21, 64, 129, 256, 778, (A) 10, (B) 21, (C) 129, , 8, 27, 125, 343, 1331, (A) 8, (B) 343, , Q.71, , 10, 14, 28, 32, 64, 68, 132, (A) 28, (B) 32, (C) 64, , (D) None, , (C) 18, , 16, 22, 34, 58, 106, ....., 394, (A) 178, (B) 175, (C) 288, , (D) 202, , 2, 3, 5, 9, 17, 33,......, (A) 85, (B) 37, , (D) 65, , (C) 63, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 11, , 11, , 11

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Q.84, Q.85, Q.86, Q.87, Q.88, Q.89, Q.90, Q.91, Q.92, Q.93, Q.94, , 2, 9, 23, 3, 8, 25, 4, ......, 27, (A) 7, (B) 29, (C) 23, , (D) 14, , 121, 112, ........, 97, 91, 86, (A) 102, (B) 108, (C) 99, , (D) 104, , 6, 9, 15, 27,.....,99, (A) 51, (B) 34, , (C) 37, , (D) 84, , 4, 7, 12,......, 28, 39, (A) 19, (B) 24, , (C) 14, , (D) 16, , 83, 82, 81, ....., 69, 60, 33, (A) 73, (B) 80, (C) 75, , (D) 77, , 77, 78, 77, 81, 73, ...., 55, (A) 69, (B) 71, (C) 82, 6, 7, 9, 13, 21,......, (A) 25, (B) 29, , (C) 37, , 1, 2, 3, 5, 7,....., (A) 8, (B) 9, , (D) 89, (D) 32, , (D) 96, , (C) 10, , (D) 13, , 3, 6, 6, 12, 9,...........12, (A) 15, (B) 18, (C) 11, , (D) 13, , Q.96, , Q.97, , Q.98, , Q.99, , 3, 5, 12, 39, 154, 772, 4634, (A) 5, (B) 3, (C) 39, (E) none of these, , Q.103 2, 3, 9, 27, 112, 565, 3396, (A) 565, (B) 9, (C) 112, (E) 3396, , (D) 27, , Q.104 1788, 892, 444, 220, 112, 52, 24, (A) 52, (B) 112, (C) 220, (E) 892, , (D) 444, , Q.105 225, 289, 398, 374, 397, 415, 424, (A) 415, (B) 289, (C) 338, (E) 397, , (D) 374, , Q.106 5, 7.5, 11.25, 17.5, 29.75, 50, 91.25, (A) 7.5, (B) 17.5 (C) 29.75 (D) 91.25, (E) None of these, Q.107 35, 118, 280, 600, 1238, 2504, 5036, (A) 118, (B) 280, (C) 600, (D) 1238, (E) 2504, , Directions (95 – 103) :, In each of the following questions, one number is, wrong in the series. Find out the wrong number :, Q.95, , (D) 8, , Direction :, In the following number series, one of the numbers, does not fit into the series. Find the wrong number., , 11, 10, ......, 100, 1001, 1000, 10001, (A) 101, (B) 110, (C) 111, (D) None, 4, 8, 12, 24, 36, 72,......, (A) 108, (B) 98, (C) 92, , Q.102 701, 348, 173, 85, 41, 19, 8, (A) 173, (B) 41, (C) 19, (E) 348, , (D) 154, , Q.108 10, 12, 28, 90, 368, 1840, 11112, (A) 1840 (B) 368, (C) 90, (E) 12, , (D) 28, , Directions :, In each of the following one number is wrong in the, series. Find out the wrong number in each case, (C) 14, , (D) 41, , (D) 188, , Q.109 1, 2, 5, 14, 41, 124, (A) 2, (B) 5, (E) 124, , 444, 300, 200, 136, 87, 84, 80, (A) 200, (B) 136, (C) 87, (E) none of these, , (D) 86, , (D) 80, , Q.110 100, 97, 90, 86, 76, 71, 62, 55, (A) 55, (B) 62, (C) 76, (E) 97, , 2, 3, 12, 37, 86, 166, 288, (A) 2, (B) 3, (C) 166, (E) 37, , (D) 86, , Q.111 1, 2, 6, 24, 120, 620, 5040, (A) 5040 (B) 620, (C) 120, (E) 6, , (D) 24, , Q.112 4, 10, 22, 40, 64, 84, 130, (A) 22, (B) 40, (C) 64, (E) 130, , (D) 84, , (D) 5, , Q.113 1, 4, 8, 16, 31, 64, 127, 256, (A) 31, (B) 16, (C) 8, (E) 1, , (D) 6, , (D) 104, , Q.114 49, 56, 64, 71, 81, 90, 100, 110, (A) 56, (B) 64, (C) 71, (E) 90, , (D) 81, , 376, 188, 88, 40, 16, 4, –2, (A) 4, (B) 16, (C) 40, (E) none of these, , 4, 9, 19, 43, 90, 185, 375, (A) 9, (B) 19, (C)90, (E) none of these, , Q.100 572, 284, 140, 72, 32, 14, 5, (A) 14, (B) 32, (C) 72, (E) 140, Q.101 4, 10, 23, 50, 104, 216, 439, (A) 4, (B) 10, (C) 23, (E) 216, , (D) 185, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 12, , 12, , 12

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Directions (115- 119) :, In each questions given below, Four out of the five, given sets of numbers follow the same pattern, while, the fifth one is different. You have to find out the set, that does not match with others., Q.115 (A) 3 (58) 7, (C) 2 (20) 4, (E) 8(145) 9, , (B) 1 (10) 3, (D) 5 (51) 6, , Q.116 (A) 4(36)2, (C) 6 (121)5, (E) 7(225) 8, , (B) 10(102)1, (D) 3(49) 4, , Q.117 (A) 8(39)5, (C) 7(48) 1, (E) 5(17)2, , (B) 12(44)10, (D) 9(45)6, , Q.118 (A) 5(68)9, (C) 3(27)6, (E) 6(64)10, , (B) 11(8)13, (D) 7(125)12, , Q.123 288,, 140,, 66,, 29,, 488,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (e) ?, (A) 106, (B) 18.5 (C) 49, (D) 6.25, (E) none of these, Q.124 140,, 68,, 36,, 16,, 10, 3, 284,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (b) ?, (A) 38, (B) 72, (C) 84, (D) 91, (E) none of these, Q.125 25,, , 194,, , 73,, , 154,, , 105, 14,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (d) ?, (A) 90, (B) 84, (C) 102, (D) 94, (E) none of these, , Directions (119- 128) :, In each of the following questions, a number series is, given. After the series , below it in the next line, a, number is given followed by (A), (B), (C), (D) and, (E). You have to complete the series starting with the, number given following sequence of the given series., Then, answer the questions given below it., Q.119 535,, 366,, 245,, 164,, 817 , (a),, (b),, (c),, (d),, Which of the following numbers will come in, place of (e) ?, (A) 648, (B) 507 (C) 387, (D) 372, (E) none of these, Q.120 3,, 5,, 18,, 72,, 7,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (d) ?, (A) 416, (B) 9, (C) 2100 (D) 96, (E) none of these, Q.121 2,, 9,, 57,, 337,, 3,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (b) ?, (A) 113, (B) 17, (C) 3912 (D) 8065, (E) none of these, Q.122 15,, 159,, 259,, 323,, 7,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (c) ?, (A) 251, (B) 315 (C) 176, (D) 151, (E) none of these, , Q.126 6,, 9,, 18,, 45,, 135, 20,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (c) ?, (A) 324, (B) 81, (C) 175, (D) 150, (E) 216, Q.127 2, 9, 57, 337, 1681, 3, (a),, (b),, (c),, (d),, (e), (e), Which of the following numbers will come in, place of (e) ?, (A) 32416 (B) 4231 (C) 13441 (D) 6392, (E) none of these, Q.128 3,, 4,, 10,, 33,, 136, 7,, (a),, (b),, (c),, (d),, (e), Which of the following numbers will come in, place of (e) ?, (A) 1035, (B) 1165 (C) 1039 (D) 891, (E) none of these, , Directions (129- 137) :, Each of the following questions consists of a pair of, numbers that have a certain relationship to each other,, followed by four other pairs of numbers given as, alternatives. Select the pair in which the numbers are, similarly related as in the given pair., Q.129 27 : 9, (A) 64 : 9, (C) 135 : 15, , (B) 125 : 5, (D) 729 : 81, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 13, , 13, , 13

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Q.130 11 : 1210, (A) 6 : 216, (C) 8 : 448, , Directions (138- 142) :, Find the missing term of the pair, , (B) 7 : 1029, (D) 9 : 729, , Q.131 Find a group similar to (3, 7, 11)., (A) 2, 9, 21, (B) 2, 17, 23, (C) 4, 6 , 14, (D) 7, 9, 16, Q.132 Given set : (49, 25, 9), (A) (36, 16, 4), (C) (39, 26, 13), , (B) (36, 25, 16), (D) (64, 27, 8), , Q.133 Given set : (21, 51, 15), (A) (21, 30, 51), (B) (21, 35, 41), (C) (21, 51, 42), (D) (21, 91, 35), Q.134 Given set : (9, 15, 21), (A) (10, 14, 16), (C) (5, 10, 25), Q.135 11 : 17 : : 19 : ?, (A) 23, (B) 27, , (B) (7, 21, 28), (D) (4, 8, 12), , (C) 33, , (D) 21, , Q.138 7528 : 5362 : : 4673 : ?, (A) 2367 (B) 2451 (C) 2531, (E) None of these, , (D) 2617, , Q.139 9 : 9 : : 8 : ?, (A) 14, (B) 64, (E) 20, , (C) 25, , (D) 27, , Q.140 6 : 24 : : 5 : ?, (A) 23, (B) 22, (E) 20, , (C) 25, , (D) 27, , Q.141 25 : 125 : : 36 : ?, (A) 180, (B) 206, (E) 72, , (C) 216, , (D) 318, , Q.142 3 : 7 : : 08 : ?, (A) 10, (B) 13, (E) 16, , (C) 17, , (D) 14, , Q.136 Which number is the given set of numbers ?, Given set : (3, 17, 31), (A) 5, (B) 15, (C) 45, (D) 49, Q.137 As 425 is related to 2, in the same way 613 is, related to (A) 1, (B) 2, (C) 3, (D) 4, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 14, , 14, , 14

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ANSWER KEY, EXERCISE-1, Q.No, Ans., Q.No, Ans., Q.No, Ans., Q.No, Ans., Q.No, Ans., Q.No, Ans., Q.No, Ans., Q.No, Ans., , 1, A, 21, D, 41, B, 61, C, 81, A, 101, D, 121, A, 141, C, , 2, C, 22, C, 42, C, 62, B, 82, D, 102, E, 122, B, 142, C, , 3, C, 23, A, 43, D, 63, D, 83, D, 103, B, 123, D, , 4, B, 24, D, 44, B, 64, D, 84, A, 104, B, 124, B, , 5, A, 25, B, 45, D, 65, B, 85, D, 105, E, 125, D, , 6, C, 26, D, 46, D, 66, C, 86, A, 106, C, 126, D, , 7, B, 27, D, 47, C, 67, C, 87, A, 107, D, 127, C, , 8, D, 28, C, 48, A, 68, D, 88, D, 108, A, 128, B, , 9, C, 29, A, 49, C, 69, C, 89, C, 109, E, 129, D, , 10, D, 30, A, 50, C, 70, C, 90, C, 110, A, 130, C, , 11, C, 31, D, 51, C, 71, A, 91, A, 111, B, 131, B, , 12, B, 32, C, 52, C, 72, D, 92, A, 112, D, 132, A, , 13, A, 33, D, 53, C, 73, A, 93, C, 113, C, 133, D, , 14, A, 34, C, 54, D, 74, C, 94, B, 114, C, 134, D, , 15, B, 35, C, 55, B, 75, D, 95, C, 115, D, 135, C, , 16, A, 36, D, 56, C, 76, A, 96, D, 116, B, 136, A, , 17, A, 37, B, 57, D, 77, C, 97, C, 117, E, 137, A, , 18, C, 38, B, 58, B, 78, B, 98, C, 118, A, 138, B, , 19, A, 39, D, 59, B, 79, A, 99, B, 119, D, 139, C, , 20, A, 40, B, 60, D, 80, B, 100, C, 120, A, 140, E, , HINTS & SOLUTIONS, 1., , 22 – 1, 42 – 1, 62 – 1, , 2., , +6, +6, +6 ..., , 3., , +10, +14, ..., , 8., , Ist series = 1, 3, 7 .... 21, IInd series = 3, 6, 9, 12, The pattern is Ist series is +2, +4, ..., missing number = 7 + 6 = 13, , 10., , Ist series 19, 38, 114, ......, IInd series 2, 3, 4 ....., The pattern followed in Ist is ×2, ×3 ....,  missing number = 114 × 4 = 456, , 24., , The sequence is a combination of two series:, I. 19, 38, 114, (...) and II. 2, 3, 4, The pattern followed in I is ×2, ×3, ...,  Missing number = 144 × 4 = 456., , 25., , The numbers are alternately multiplied by 2, 3, 3, and . Thus, 1 × 2 = 2, 2 ×, = 3, 3 × 2 = 6,, 2, 2, 3, 6×, = 9 and so on., 2, 3,  Missing number = 18 ×, = 27., 2, , 26., , The pattern is +1, +4, + 9, + 16,... i.e.,, + 12, + 22, + 32, 42, ....,  Missing number = 34 + 52 = 34 + 25 = 59., , 11., , 4 × 2 + 1, 9 × 2 – 1, ..., , 14., , 10 × 2 = 20, 10 × 3 = 30 ...., , 27., , 21., , Each term of the series is obtained by, multiplying the preceding term by 3.,  Missing number = 13. 5 × 3 = 40.5., , The pattern is ×2, ×3, ×4, ...,  Missing number = 72 × 5 = 360., , 28., , 22., , The numbers are 112, 152, 192,... i.e. 112, (11 + 4 × 1)2, (11 + 4 × 2)2, ...,  Missing number = (11 + 4 × 3)2, = (23)2 = 529., , Each number in the series is the product of, the digits of the preceding number., Thus, 6 × 6 = 36, 3 × 6 = 18 and so on.,  Missing number = 1 × 8 = 8., , 29., , The pattern is +4, +8, +16, +32, ... i.e., + 22, +, 23, + 24, + 25,...,  Missing number = 81 + 26 = 81 + 64=145., , 30., , The pattern is +20, +40, +80,...,  Missing number = 152 + 160 = 312., , 23., , The numbers are, 12 – 1, 22 – 2, 32 – 1, 42 – 2....,  Missing number = 52 – 1 = 24., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 15, , 15, , 15

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31., , The sequence is a combination of two series:, , 3, 5, 7, 9 and . 6, 20, 42, (.....), The pattern followed in  is + 14, + 22,...,  Missing number = 42 + 30 = 72., , 32., , The sum of any three consecutive terms of the, series gives the next term. Thus,, 1 + 3 + 4 = 8; 3 + 4 + 8 = 15; 4 + 8 + 15=27, and so on.,  Missing number = 8 + 15 + 27 = 50., , 45., , The pattern is + 11, + 33, + 55, ... i.e., + (11 × 1), + (11 × 3), + (11 × 5),...,  Missing number = 104 + (11 × 7) = 181., , 46., , Each term is divided by 2 and then increased, by 1 to obtain the next term.,  Missing term = (4  2) + 1 = 3., , 47., , The pattern is –42, –40, ...,  Missing number = 380 – 38 = 342., , 33., , The pattern is + 13, + 26, + 39, ...,  Missing number = 80 + 52 = 132., , 48., , The pattern is × 3 – 1, × 3 – 2, × 3 – 3, × 3 – 4,...,  Missing number = (185 × 3) – 5 = 550., , 34., , The pattern is + 2, + 4, + 4, ... 16, + 16.,  Missing number = 18 + 8 = 26., , 49., , 35., , The pattern is ×2, ×3, ×4, ....,  Missing number = 24 × 5 = 120., , The pattern is × 2 + 0, × 2 + 1, × 2 + 2,, × 2 + 3, × 2 + 4, × 2 + 5,...,  Missing number = 121 × 2 + 6 = 248., , 50., , The pattern is + 0.05, 0.10, + 0.15,...,  Missing number = 0.8 + 0.20 = 1., , 51., , Each term in the series is four more than two, times the next term. So, 48 is wrong and must, be replaced by (20 × 2 + 4) i.e.44., , 52., , The sequence is +2, +4, +8,... i.e. +2, + 22,, 23,... So 27 is wrong and must be replaced by, (15 + 24) i.e. (15 + 16) or 31., , 53., , The pattern is ×8, ×4, ...,  Missing number = 128 × 2 = 256., , The sequence is +5, +7,..., So, 24 is wrong and should be replaced by, (17 + 9) i.e. 26., , 54., , The pattern is, × 2 + 1, × 2 – 1, × 2 + 1, × 2 – 1, ...,  Missing number = 37 × 2 + 1 = 75., , The sequence is × 2 + 1, × 3 + 1, × 2 + 1, × 3 + 1,..., So, 256 is wrong and must be replaced by, (129 × 2 + 1) i.e. 259., , 55., , The pattern is + 36, + 60, + 90,... i.e., +[6×(6+0)],+[6×(6 + 4)], + [6×(6+9)],....,  Missing number = 210 + [6 × (6 + 15)], = 210 + 126 = 336., , The pattern is +1, +4, +9, +16, +25, ... i.e., +12, + 22 + 32, + 42, + 52,..., So, 22 is wrong and must be replaced by, (16 + 4) i.e. 20., , 56., , Each number is 15 multiplied by a prime, number i.e. 15 × 11, 15 × 13 , 15 × 17, 15 ×, 19, 15 × 23.,  Missing number = 15 × 29 = 435., , Each term is multiplied by 2 and then, increased by 2 to obtain the next term. So 64, is wrong and must be replaced by (30 × 2 + 2), i.e. 62., , 57., , The numbers are 22 + 1, 42 + 1, 62 + 1,, 82 + 1, ....122 + 1.,  Missing number = 102 + 1 = 101., , Each term is 4 less than thrice the preceding, number. So, 654 is wrong and must be, replaced by (218 × 3 – 4) = 650., , 58., , Each number in the series is multiplied by 2, and the result increased by 1 to obtain the, next number., So, 39 is wrong and should be replaced by, (15 × 2 + 1) i.e. 31., , 36., , Each term in the series is one less than the, square of the preceding term., Thus, 22 –1 = 3, 32 – 1 = 8, 82 – 1 = 63.,  Missing number = (63)2 –1= 3969 –1= 3968., , 37., , The pattern is + 20.5, + 22.5, ...,  Missing number = 138 + 24.5 = 162.5., , 38., , Each number in the series is the preceding, number multiplied by 3 and then decreased, by 2., , 39., 40., , 41., , 42., , 43., , 44., , Each term in the series is the sum of the, preceding two terms.,  Missing number = 20 + 31 = 51., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 16, , 16, , 16

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59., , 60., , 3 is subtracted from each number and the, result is divided by 2 to obtain the next, number of the series., So, 46 is wrong and must be replaced by i.e., 53., The first digits of the numbers form the series, 1, 2, 3, 4, 5; the second digits form the series, 2, 3, 4, 5, 6; the third digits form the series 3,, 4, 5, 6; while the last digit in each of the, numbers is 6. So, 5686 is wrong and must be, replace by 5676., , 61., , The sequence is × 2, × 4, × 2, × 4,..., So, 550 is wrong and must be replaced by, (320 × 2) i.e. 640., , 62., , The given sequence is a combination of two, series :, I. 3, 8, 13, 18, 23 and II. 2, 9, 22, 32, 42, The pattern in  is +5, and the pattern in II is, +10. So, in , 9 is wrong and must be, replaced by (2 + 10) i.e., 12., , 63., , The numbers are cubes of prime numbers i.e., 23, 33, 53, 73, 113. Clearly, none is wrong., , 64., , Alternately, the numbers are increased by, four and doubled to get the next number. So,, 132 is wrong and must be replaced by (68 ×, 2) i.e. 136., , 65., , The given sequence is a combination of two, series :, I. 1, 5, 7, 11, 12 and II. 5, 9, 11, 15, 17, The pattern in both I and II is +4, +2, +4, +2., So, 12 is wrong and must be replaced by, (11 + 2) i.e., 13., , 66., , The given sequence is a combination of two, series :, I. 11,21, 32, 41, 51 and II 2, 3, 4, 5, 6., Clearly, the pattern in I is + 10., So, 32 is wrong and should be replaced by, (21 + 10) i.e. 31., , 67., , The given sequence is a combination of two, series :, I. 11, 20, 40, 74 and II 5, 12, 26, 54., The pattern  becomes +9, + 18, + 36,... if 40, is replaced by 38., So, 40 is wrong., , 68., , The numbers are 7 × 8, 8 × 9, 9 × 10,, 10 × 11, 11 × 12, 12 × 13., So, 150 is wrong and must be replaced by, (12 × 13) i.e. 156., , 69., , The sequence is +5, +8, +11, ..., So, 47 is wrong and must be replaced by, (32 + 14) i.e., 46., , 70., , The sequence is –11, +9, –7, +5, –3, +1., So, 86 is wrong and must be replaced by, (78 + 9) i.e., 87., , 71., , The correct sequence is 52, 72, 92, 112, 132,, 152., So, 36 is wrong., , 72., , The numbers are 12 + 1, 22 + 1, 32 + 1 and so, on., So, 64 is wrong. The correct term is (82 + 1), i.e. 65., , 91., , Ist :, 11, ..... 1001, 10001, IInd : 10, 100, 1000, In Ist, an extra zero is added between the two, 1's, So, missing number is 101., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number Series, , 17, , 17, , 17