### Number Series

In this, generally you are given a long series of numbers. The candidate is required to find out how many times a number satisfying the conditions specified in the question, occurs.

Some Models:

3  2  5  1  7  2  8  5  9  3  5  5  4  1  6  5  3  8  5  4  3  5  1  3  2  5  6
In the above sequence in some cases, the multiplication of the two digits which immediately precede the digit '5' exceeds the multiplication of the two digits which immediately follow that digit. How many such 5's are there?
1) 7           2) 6          3) 5         4) 4            5) None of these
Ans: 4.
Hint:  3  2  5  1  7  2  8  5  9  3  5  5  4  1  6  5  3  8  5  4  3  5  1  3  2  5  6

*    In the following number series how many such 2's are there which are immediately preceded by a pair of numbers whose product is more than the product of pair of numbers immediately following?
7  7  2  1  3  9  4  2  6  5  2  4  8  3  5  2  7  6  5  2  9  2  8  6  4  3  9  2  4  6  5  7

1) 1            2) 2            3) 3             4) 4              5) None of these
Ans: 4.
Hint:  7  7  2  1  3  9  4  2  6  5  2  4  8  3  5  2  7  6  5  2  9  2  8  6  4  3  9  2  4  6  5  7

*     In the sequence given below the sum of the two digits which immediately precede the digit '3' exceeds the sum of the two digits which immediately follow the digit '3' and sum of the two digits which immediately follow the digit '5' exceeds the sum of the two digits which immediately precede the digit '5'. How many such 3's and 5's are there?
3  3  5  6  5  5  3  7  7  8  9  9  3  3  5  6  7  5  3  5  1  3  5  1  3  5  5  3  2  8  3  5
1) 5                2) 6                3) 7                 4) 8                5) None of these
Ans: 2.
Hint: 3  3  5  6  5  5  3  7  7  8  9  9  3  3  5  6  7  5  3  5  1  3  5  5  3  2  8  3  5

*     3  2  8  4  3  8  5  4  6  2  1  8  3  5  8  7  9  8  6  3  2  7  0  8  5  1  8  8  9  7  4
In the above sequence in some cases the multiplication of the two digits which immediately precede the digit 8 exceeds the addition of the two digits which immediately follow that digit. How many such 8's are there?
1) Three             2) Four            3) Five            4) Six                 5) None of these
Ans: 5.
Hint: 2  3  4  2  5  2  5  2  3  2  6  7  2  2  3  4  5  6  2  7  8  2  9  2  0  2  5  2  6  7  2  3  2

*     In the following number series how many 4's are there which are immediately preceded by a pair of number whose product is more than the product of the pair of number immediately following?
2  3  4  5  3  3  4  7  6  5  2  4  3  2  4  5  1  4  2  2  4  8  4  9  7  4  0  9  4  3  2
1) 4                 2) 5                 3) 6                 4) 2                 5) None of these
Ans: 1.
Hint: 2  3  4  5  3  3  4  7  6  5  2  4  3  2  4  5  1  4  2  2  4  8  4  9  7  4  0  9  4  3  2

*     5  3  2  1  5  5  5  2  5  7  5  9  8  5  4  3  7  5  7  5  5  5  8  2  5  6  1
In the above sequence in some cases, the sum of the two digits which immediately precede the digit '5' exceeds the sum of the two digits which immediately follow that digit. How many such 5's are there?
1) Two                  2) Three                  3) Four                  4) Five                  5) None of these
Ans: 3.
Hint: There are four such 5's.
5  3  2  1  5  5  2  5  7  5  9  8  5  4  3  7  5  7  5  5  5  8  2  5  6  1

*     If the positions of the first and fifth digits in the number 5 6 3 1 7 2 4 9 are interchanged, similarly the positions of the second and the sixth are interchanged, and
so on, which of the following will be the sixth number from the right end?
1) 4                   2) 6                   3) 3                   4) 2                   5) None of these
Ans: 1.
Hint:  7  2  4  9  5  6  3  1

*     How many such 4's are there in the following sequence that the sum of the immediately following two digits is greater than the sum of the immediately preceding two digits?
2  4  4  5  4  7  4  2  9  8  7  4  7  3  4  5  2  1  4  1  3  4  4  4  8  7  3  3  9  1  1  4  2  1
1) Seven                  2) Six                  3) Five                  4) Four                  5) None of these
Ans: 1.

*     In the following number series how many such 7's are there which are immediately precede by a pair of number whose product is more than the product of pair of numbers immediately following?
2  2  7  1  3  9  4  8  7  6  5  4  2  8  3  5  7  4  6  5  9  7  8  6  4  3  9  7  4  6  5  2
1) 1                    2) 4                    3) 2                    4) 3                    5) None of these
Ans: 4. 2  6  7  5  4  3  7  4  8  9  4  3  2  5  4  7  9  8  6  8  7  1  2  5  3  7  6  8  9  3  6

*     How many such numbers are there in the series which are immediately followed by its multiple?
1) 4                     2) 3                     3) 2                     4) 1                     5) None of these
Ans: 1.

*     If the order of last 15 numbers is reversed, which number will be eighth to the right of thirteenth number from left?
1) 7                      2) 8                      3) 4                      4) 6                      5) None of these
Ans: 4.
Hint: 8th to the right of 13th from the left  =  ( 8 + 13 )  = 21st from left. But this is the required position in the altered sequence. In original sequence, this will be the number which is 5th from the right, i.e. 6.

*     How many 7's are there in the series which are immediately preceded by an even number and immediately followed by an odd number?
1) 2                       2) 4                       3) 3                       4) 5                       5) None of these
Ans: 3.
512    325    639    841    792

*     What will be last digit of the third number from the top when they are arranged in descending order after reversing the position of the digits within each number?
1) 7                 2) 3               3) 5               4) 2                 5) None of these
Ans: 2.
Hint: Here the given numbers are:  517    325    639    841    792
After reversing, the numbers become as follows:   936    715   523    297   148
Now, the third number from the top is 523. Hence, the last digit of 523 is 3.

*     What will be the middle digit of the second lowest number after the position of only the first and the second digits with each number are interchanged?
1) 5                2) 2             3) 7                4) 3              5) None of these
Ans: 4.
Hint: After interchanging the first and the second digits, number become as follows:
157    235    369    481    972

*  When arrange in descending order the numbers become as follows:
972     481     369     235     157
Here, the second lowest number is  235.  Hence, middle digit of   235  is  3.

*     What will be the first digit of second highest number after the position of only the second and the third digits within each number are interchanged?
1) 7                  2) 2                3) 8              4) 9            5) None of these
Ans: 1.
Hint: If the positions of only the second and the third digits within each number are interchanged, the number become as follows:
571    352    693     814     729

*     Nitin was counting down from 32. Sumit was counting upwards the numbers starting from 1 and he was calling out only the odd numbers. What common number will they call out at the same time if they were calling out at the same speed?
1) 19        2) 21          3) 22       4) They will not call out the same number        5) None of these

Ans: 4.
Hint: Nitin:     32  31  30  29  28  27  26  25  24  23  22  21  20 .....
Sumit :  1  3  5  7  9  11  13  15  17  19  21  23  25 .....
Clearly, both will never call out the same number.

*     If the first and second digits in the sequence  5  9  8  1  3  2  7  4  3  8 are interchanged, also the third and fourth digits, the fifth and sixth digits and so on, which digit would be the seventh counting to your left?
1) 1        2) 4              3) 7           4) 8          5) None of these
Ans: 4.
Hint: The new sequence becomes  9  5  1  8  2  3  4  7  8  3 .
Counting to the left, the seventh number is 8.

*      If the position of the first and sixth digits of the sequence of the numbers  8  9  0  3  2  1  4  6  7  5 are interchanged, the second and the seventh and so on, which number would be seventh from the right end?
1) 2           2) 6               3) 7            4) 8               5) None of these
Ans: 3.
Hint: The new sequence becomes  1  4  6  7  5  8  9  0  3  2
From the right end, the seventh number is 7.

*     The letters  L,  M,  N,  O,  P,  Q,  R,  S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?
1) 4                  2) 5                3) 6               4) 7              5) None of these
Ans: 3.
Hint:    P   =  4   and   T  -  P   =  5      T  =  9
T  -  N  =  3  and  T  =  9       N  =  6.

*     Thirty six vehicles are parked in a parking lot in a single row. After first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half of the row.
1) 10                      2) 12                      3) 15                      4) 17                      5) None of these
Ans: 3.
Hint: Let C and S denote car and scooter respectively.

*     The following numbers are rewritten by interchanging the digits in ten's place and hundred's place and then arranged in the descending order.
What will be the second digit of the newly formed fourth number from the top?
1) 7                         2) 9                         3) 3                         4) 8                         5) 6
Ans: 5.
Hint: Interchanging, we get   749,   376,   985,   798,   839,   765.
Rearranged in descending order, this becomes  985,  839,  798,  765,  749,  376

*     If 2 is subtracted from the middle digit of the following numbers and then the positions of the digits are reversed, which of the following will be the last digit of the middle number after they are arranged in descending order?
489     362   154    271    542
1) 5              2) 4              3) 2                4) 1              5) 3
Ans: 5.
Hint: As same is subtracted from them, it will not change their relative position.

*     Below are given six three-digit numbers. The digits comprise of numerics and letters. The letters indicates its serial order in the English alphabet. What will be the middle digit of the 4th number when the numbers are arranged in the descending order after interchanging numerics in each number without altering the place of letter in the number?
19F,    2H9,    98B,    D76,    7A6,    61E
1) 8              2) 9               3) 6               4) 7               5) None of these
Ans: 5.
Hint: After interchanging numeric without altering the place of letter and then changing letters by its serial order in the English alphabet, we get, 916,   982,   892,   467,   617,  165.

*     If the first and the fifth digits of the number 9 3 1 5 2 8 6 7 are interchanged, so are the second and the sixth digits, and so on, then what should be the second digit from the right?
1) 1                 2) 6              3) 3           4) 8           5) None of these
Ans: 1.
Hint: After interchanging the number ( 9 3 1 5 2 8 6 7 ) becomes 2 8 6 7 9 3 1 5. Hence, the second digit from the right end is '1'.

*     Which of the following will be middle digit of the third number after the following numbers are arranged in ascending order after reversing the positions of the digits, within each number?
1) 6                2) 3                3) 1            4) 7              5) None of these.
Ans: 5.
Hint: Reversing the position of the digits within each number and arranging in ascending order, we get,  279,  449,  723,  816,  937,  968.

Directions (Qs. 1 - 3): Find the missing number in the series.
1. 20, 17, 34, 31, 62, 59, ___
a) 108         b) 118         c) 56         d) 115
Sol: This series is based on the logic that previous term -3, previous term × 2 and this pattern is repeated.
Hence, missing number = 59 × 2 = 118
Ans: b

2. 2, 10, 20, 28, 56, ___
a) 64           b) 66           c) 72        d) 82
Sol: This series is based on the logic that previous term +8, previous term × 2 and this pattern is repeated
i.e. 2 + 8, 10 × 2, 20 + 8, 28 × 2, 56 + 8 = 64
Ans: a

Directions (Qs. 4 - 5): Find the odd number in the series.
4. 2, 10, 30, 70, 130
a) 2          b) 10          c) 30          d) 70
Sol: (Diff.)       (Diff.)      (Diff.)      (Diff.)

5. 2, 12, 30, 80, 150
a) 2          b) 12          c) 30          d) 80
Sol: The series is 13 + 1 × 1, 23 + 2 × 2, 33 + 3 × 3, 43 + 4 × 4, 53 + 5 × 5.
So, 2, 12, 36, 80, 150
Hence, 30 is the wrong number.
Ans: c

Directions (Qs. 6 - 11): Find the missing number in the series.
6. 2, 4, 8, 3, 6, 18, 4, 5, 20, 7, 8, 56, 9, 8, __
a) 43          b) 17          c) 72          d) 45
Sol: The product of first 2 numbers is the third number, in every triplet.
Hence, the required number is
9 × 8 = 72
Ans: c

7. 3, 12, 8, 5, 14, 12, 8, 16, 17, 12, 18, 23, ____
a) 32          b) 17          c) 46          d) 28
Sol: It is a case of double alternate series
3, −, −, 5, −, −, 8, −, −, 12, −, −, 17
Ans: b

8. 5, 18, 7, 21, 9, 24, 11, 27, 13, 30, 15, ____
a) 33          b) 40          c) 43          d) 35
Sol: It is a case of alternate series:
−, 18, −, 21, −, 24, −, 27, −, 30, −, 33
Ans: a

9. 72, 27, 36, 63, 42, 24, 86, ____
a) 96          b) 34          c) 68          d) 109
Sol: The given series is based on interchange places of digits of numbers i.e., reverse of 72 is 27, reverse of 36 is 63, reverse of 42 is 24, hence, reverse of 86 is 68.
Ans: c

10. 4, 11, 29, 121, 599, ____
a) 3594       b) 3601       c) 4241       d) 4201
Sol: 4 × 2 + 3 = 11
11 × 3 − 4 = 29
29 × 4 + 5 = 121
121 × 5 − 6 = 599
599 × 6 + 7 = 3601
Ans: b

11. 1, 6, 27, 160, 1169, ____
a) 12980     b) 13000     c) 12859       d) 10602
Sol: 1 × 2 + 22 = 6
6 × 3 + 32 = 27
27 × 5 + 52 = 160
160 × 7 + 72 = 1169
1169 × 11 + 112 = 12980
Ans: a

Directions (Qs. 12 - 13): In each of the following questions a number series is given. Below this series, a number is given followed by (i), (ii), (iii), (iv) and (v). After understanding the pattern in the series, you have to form another number series in the same order, starting with the given number.
12.   2     3      10      15    26     35
50    (i)    (ii)     (iii)   (iv)   (v)
Which of the following numbers will come in the place of (iv)?
a) 122         b) 100         c) 120         d) 143
Sol: 2             3            10            15       26           35
12 + 1      22 − 1      32 + 1      42 − 1  52 + 1     62 − 1
Series is
72 + 1       82 − 1     92 + 1     102 − 1   112 + 1    122 − 1
50               63           82           99           122          143
Hence, the (iv) term is 122.
Ans: a

13. 8    8    16    48    192    960
15   (i)    (ii)    (iii)    (iv)     (v)
Which of the following numbers will come in the place of (iii)?
a) 30          b) 90          c) 60          d) 45

Ans: b

14. Find the missing number in the series. 10101, 10110, 10111, ____, 11001
a) 11010          b) 11000            c) 10001            d) 10100
Sol: These are binary numbers.

Ans: b

Odd One Out
Directions (Qs. 1 - 5): Find the odd number/ letters/ word from the given alternatives.
1. a) DWHS        b) BYDW       c) CWFS        d) EVJQ

Ans: c

2. a) DHLP    b) TXBF     c) JNRV    d) YBEH
Sol: Difference between the position numbers of the alphabets in a pair is 4 except option (d).
Ans: d

3. a) ABYZ    b) CDWX    c) EFUV    d) GHTV
Sol:

Ans: d

4. a) 5621     b) 2321       c) 2541     d) 4971
Sol: In this, sum of the first and third term is equal to the sum of second and fourth term.
5 + 2 = 6 + 1 = 7
2 + 2 = 3 + 1 = 4
2 + 4 = 5 + 1 = 6
But, 4 + 7 ≠ 9 + 1
Ans: d

5. a) Perception b) Opinion c) Belief d) Penetration Sol: Options (a), (b) and (c) are synonyms.
Ans: d

Directions (Qs. 6 - 11): Find the odd number/ letters/ word from the given alternatives.
6. a) 357         b) 496         c) 825           d) 654          e) 429
Sol: Except in 496, the digits in each term add upto 15.
Ans: b

7. a) 56       b) 72      c) 40      d) 88      e) 24
Sol: Except 72, (= 8 × 9), each term is 8 × prime number
(i.e., 56 = 8 × 7; 40 = 8 × 5; 88 = 8 × 11; 8 × 3 = 24).
Ans: b

8. a) WIPE      b) WILD           c) WIFE     d) WISE       e) WINE
Sol: Except in WILD, the other four terms have W, I and E as the first, the second and the fourth letters, respectively.
Ans: b

9. a) Violet      b) Brown           c) Orange           d) Green           e) Red
Sol: Except Brown, the other four are colours of VIBGYOR.
Ans: b

10. a) Pound           b) Metre          c) Kilogram         d) Second        e) Newton
Sol: Except Pound (which belongs to the FPS system), the other four belong to MKS system.
Ans: a

11. a) Dog      b) Tiger      c) Lion    d) Horse        e) Cat
Sol: Only horse is herbivorous.
Ans: d

Posted Date : 23-02-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.